0.12/0.15 % Problem : Vampire---4.8_19171 : TPTP v0.0.0. Released v0.0.0. 0.12/0.16 % Command : do_cvc5 %s %d 0.17/0.36 % Computer : n003.cluster.edu 0.17/0.36 % Model : x86_64 x86_64 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.36 % Memory : 8042.1875MB 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.36 % CPULimit : 1440 0.17/0.36 % WCLimit : 180 0.17/0.36 % DateTime : Mon Jul 3 13:01:01 EDT 2023 0.17/0.36 % CPUTime : 0.22/0.56 %----Proving TH0 0.41/0.57 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type, 0.41/0.57 list_nat: $tType ). 0.41/0.57 0.41/0.57 thf(ty_n_t__List__Olist_Itf__a_J,type, 0.41/0.57 list_a: $tType ). 0.41/0.57 0.41/0.57 thf(ty_n_t__Nat__Onat,type, 0.41/0.57 nat: $tType ). 0.41/0.57 0.41/0.57 thf(ty_n_tf__a,type, 0.41/0.57 a: $tType ). 0.41/0.57 0.41/0.57 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type, 0.41/0.57 minus_minus_nat: nat > nat > nat ). 0.41/0.57 0.41/0.57 thf(sy_c_List2_Olist__asc_001t__Nat__Onat,type, 0.41/0.57 list_asc_nat: list_nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_List2_Olist__desc_001t__Nat__Onat,type, 0.41/0.57 list_desc_nat: list_nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_List2_Olist__strict__asc_001t__Nat__Onat,type, 0.41/0.57 list_strict_asc_nat: list_nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_List2_Olist__strict__desc_001t__Nat__Onat,type, 0.41/0.57 list_strict_desc_nat: list_nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001t__Nat__Onat,type, 0.41/0.57 listIn923761578nd_nat: list_nat > ( nat > nat ) > nat > nat ). 0.41/0.57 0.41/0.57 thf(sy_c_ListInf__Mirabelle__akbajwqfbr_Oi__append_001tf__a,type, 0.41/0.57 listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Olinorder__class_Osorted_001t__Nat__Onat,type, 0.41/0.57 linorder_sorted_nat: list_nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Olist__ex_001t__Nat__Onat,type, 0.41/0.57 list_ex_nat: ( nat > $o ) > list_nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Olist__ex_001tf__a,type, 0.41/0.57 list_ex_a: ( a > $o ) > list_a > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Onth_001t__Nat__Onat,type, 0.41/0.57 nth_nat: list_nat > nat > nat ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Onth_001tf__a,type, 0.41/0.57 nth_a: list_a > nat > a ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Orev_001t__Nat__Onat,type, 0.41/0.57 rev_nat: list_nat > list_nat ). 0.41/0.57 0.41/0.57 thf(sy_c_List_Orev_001tf__a,type, 0.41/0.57 rev_a: list_a > list_a ). 0.41/0.57 0.41/0.57 thf(sy_c_Nat_OSuc,type, 0.41/0.57 suc: nat > nat ). 0.41/0.57 0.41/0.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type, 0.41/0.57 size_size_list_nat: list_nat > nat ). 0.41/0.57 0.41/0.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type, 0.41/0.57 size_size_list_a: list_a > nat ). 0.41/0.57 0.41/0.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type, 0.41/0.57 ord_less_nat: nat > nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type, 0.41/0.57 ord_less_eq_nat: nat > nat > $o ). 0.41/0.57 0.41/0.57 thf(sy_v_f,type, 0.41/0.57 f: nat > a ). 0.41/0.57 0.41/0.57 thf(sy_v_g,type, 0.41/0.57 g: nat > a ). 0.41/0.57 0.41/0.57 thf(sy_v_xs,type, 0.41/0.57 xs: list_a ). 0.41/0.57 0.41/0.57 thf(sy_v_ys,type, 0.41/0.57 ys: list_a ). 0.41/0.57 0.41/0.57 thf(fact_80_less__not__refl2,axiom, 0.41/0.57 ! [N: nat,M2: nat] : 0.41/0.57 ( ( M2 != N ) 0.41/0.57 <= ( ord_less_nat @ N @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_214_less__eq__Suc__le,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_231_list__ex__rev,axiom, 0.41/0.57 ! [P: nat > $o,Xs: list_nat] : 0.41/0.57 ( ( list_ex_nat @ P @ ( rev_nat @ Xs ) ) 0.41/0.57 = ( list_ex_nat @ P @ Xs ) ) ). 0.41/0.57 0.41/0.57 thf(fact_215_less__Suc__eq__le,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ M2 @ ( suc @ N ) ) 0.41/0.57 = ( ord_less_eq_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_196_Suc__less__SucD,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ M2 @ N ) 0.41/0.57 <= ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_167_nat_Oinject,axiom, 0.41/0.57 ! [X22: nat,Y22: nat] : 0.41/0.57 ( ( ( suc @ X22 ) 0.41/0.57 = ( suc @ Y22 ) ) 0.41/0.57 = ( X22 = Y22 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_186_nat__induct__at__least,axiom, 0.41/0.57 ! [M2: nat,N: nat,P: nat > $o] : 0.41/0.57 ( ( ( P @ M2 ) 0.41/0.57 => ( ! [N3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N3 ) 0.41/0.57 => ( ( P @ N3 ) 0.41/0.57 => ( P @ ( suc @ N3 ) ) ) ) 0.41/0.57 => ( P @ N ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_44_not__less__iff__gr__or__eq,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) ) 0.41/0.57 = ( ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 | ( X2 = Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_110_le__less__linear,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 ) 0.41/0.57 | ( ord_less_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_31_le__cases3,axiom, 0.41/0.57 ! [X2: nat,Y2: nat,Z2: nat] : 0.41/0.57 ( ( ( ( ord_less_eq_nat @ Y2 @ X2 ) 0.41/0.57 => ~ ( ord_less_eq_nat @ X2 @ Z2 ) ) 0.41/0.57 => ( ( ( ord_less_eq_nat @ X2 @ Z2 ) 0.41/0.57 => ~ ( ord_less_eq_nat @ Z2 @ Y2 ) ) 0.41/0.57 => ( ( ~ ( ( ord_less_eq_nat @ Z2 @ X2 ) 0.41/0.57 => ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) 0.41/0.57 <= ( ~ ( ord_less_eq_nat @ Z2 @ X2 ) 0.41/0.57 <= ( ord_less_eq_nat @ Y2 @ Z2 ) ) ) 0.41/0.57 <= ( ~ ( ord_less_eq_nat @ Y2 @ X2 ) 0.41/0.57 <= ( ord_less_eq_nat @ Z2 @ Y2 ) ) ) ) ) 0.41/0.57 <= ( ~ ( ord_less_eq_nat @ Y2 @ Z2 ) 0.41/0.57 <= ( ord_less_eq_nat @ X2 @ Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_117_not__less,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ~ ( ord_less_nat @ X2 @ Y2 ) ) 0.41/0.57 = ( ord_less_eq_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_138_list__strict__desc__imp__list__desc,axiom, 0.41/0.57 ! [Xs: list_nat] : 0.41/0.57 ( ( list_strict_desc_nat @ Xs ) 0.41/0.57 => ( list_desc_nat @ Xs ) ) ). 0.41/0.57 0.41/0.57 thf(fact_54_antisym__conv3,axiom, 0.41/0.57 ! [Y2: nat,X2: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) ) 0.41/0.57 = ( X2 = Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_11_list__desc__trans__le,axiom, 0.41/0.57 ( list_desc_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [J: nat] : 0.41/0.57 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) 0.41/0.57 => ! [I2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ I2 @ J ) 0.41/0.57 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_5_nth__equalityI,axiom, 0.41/0.57 ! [Xs: list_a,Ys: list_a] : 0.41/0.57 ( ( ( Xs = Ys ) 0.41/0.57 <= ! [I: nat] : 0.41/0.57 ( ( ( nth_a @ Xs @ I ) 0.41/0.57 = ( nth_a @ Ys @ I ) ) 0.41/0.57 <= ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) ) ) ) 0.41/0.57 <= ( ( size_size_list_a @ Xs ) 0.41/0.57 = ( size_size_list_a @ Ys ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_155_pinf_I6_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ~ ( ord_less_eq_nat @ X5 @ T ) 0.41/0.57 <= ( ord_less_nat @ Z3 @ X5 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_39_ord__eq__le__subst,axiom, 0.41/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ( ord_less_eq_nat @ A @ ( F @ C ) ) 0.41/0.57 <= ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ B @ C ) ) 0.41/0.57 <= ( A 0.41/0.57 = ( F @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_73_ord__less__eq__subst,axiom, 0.41/0.57 ! [A: nat,B: nat,F: nat > nat,C: nat] : 0.41/0.57 ( ( ( ( ord_less_nat @ ( F @ A ) @ C ) 0.41/0.57 <= ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) 0.41/0.57 <= ( ord_less_nat @ X4 @ Y4 ) ) ) 0.41/0.57 <= ( ( F @ B ) 0.41/0.57 = C ) ) 0.41/0.57 <= ( ord_less_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_198_Suc__less__eq2,axiom, 0.41/0.57 ! [N: nat,M2: nat] : 0.41/0.57 ( ( ord_less_nat @ ( suc @ N ) @ M2 ) 0.41/0.57 = ( ? [M6: nat] : 0.41/0.57 ( ( ord_less_nat @ N @ M6 ) 0.41/0.57 & ( M2 0.41/0.57 = ( suc @ M6 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_133_complete__interval,axiom, 0.41/0.57 ! [A: nat,B: nat,P: nat > $o] : 0.41/0.57 ( ( ord_less_nat @ A @ B ) 0.41/0.57 => ( ( ~ ( P @ B ) 0.41/0.57 => ? [C2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A @ C2 ) 0.41/0.57 & ( ord_less_eq_nat @ C2 @ B ) 0.41/0.57 & ! [D: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ D @ C2 ) 0.41/0.57 <= ! [X4: nat] : 0.41/0.57 ( ( P @ X4 ) 0.41/0.57 <= ( ( ord_less_nat @ X4 @ D ) 0.41/0.57 & ( ord_less_eq_nat @ A @ X4 ) ) ) ) 0.41/0.57 & ! [X5: nat] : 0.41/0.57 ( ( P @ X5 ) 0.41/0.57 <= ( ( ord_less_eq_nat @ A @ X5 ) 0.41/0.57 & ( ord_less_nat @ X5 @ C2 ) ) ) ) ) 0.41/0.57 <= ( P @ A ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_197_less__antisym,axiom, 0.41/0.57 ! [N: nat,M2: nat] : 0.41/0.57 ( ( ( ord_less_nat @ N @ ( suc @ M2 ) ) 0.41/0.57 => ( M2 = N ) ) 0.41/0.57 <= ~ ( ord_less_nat @ N @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_85_le__antisym,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ( M2 = N ) 0.41/0.57 <= ( ord_less_eq_nat @ N @ M2 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_142_pinf_I8_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ T @ X5 ) 0.41/0.57 <= ( ord_less_nat @ Z3 @ X5 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_250_Nat_Odiff__diff__eq,axiom, 0.41/0.57 ! [K: nat,M2: nat,N: nat] : 0.41/0.57 ( ( ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) ) 0.41/0.57 = ( minus_minus_nat @ M2 @ N ) ) 0.41/0.57 <= ( ord_less_eq_nat @ K @ N ) ) 0.41/0.57 <= ( ord_less_eq_nat @ K @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_153_minf_I5_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_nat @ X5 @ Z3 ) 0.41/0.57 => ( ord_less_nat @ X5 @ T ) ) ). 0.41/0.57 0.41/0.57 thf(fact_101_dual__order_Ostrict__trans2,axiom, 0.41/0.57 ! [B: nat,A: nat,C: nat] : 0.41/0.57 ( ( ord_less_nat @ B @ A ) 0.41/0.57 => ( ( ord_less_eq_nat @ C @ B ) 0.41/0.57 => ( ord_less_nat @ C @ A ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_202_Ex__less__Suc,axiom, 0.41/0.57 ! [N: nat,P: nat > $o] : 0.41/0.57 ( ( ? [I2: nat] : 0.41/0.57 ( ( P @ I2 ) 0.41/0.57 & ( ord_less_nat @ I2 @ ( suc @ N ) ) ) ) 0.41/0.57 = ( ( P @ N ) 0.41/0.57 | ? [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ N ) 0.41/0.57 & ( P @ I2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_223_nat__induct_H,axiom, 0.41/0.57 ! [P: nat > $o,N0: nat,N: nat] : 0.41/0.57 ( ( P @ N0 ) 0.41/0.57 => ( ! [N3: nat] : 0.41/0.57 ( ( ( P @ ( suc @ N3 ) ) 0.41/0.57 <= ( P @ N3 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ N0 @ N3 ) ) 0.41/0.57 => ( ( P @ N ) 0.41/0.57 <= ( ord_less_eq_nat @ N0 @ N ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_99_dual__order_Oorder__iff__strict,axiom, 0.41/0.57 ( ord_less_eq_nat 0.41/0.57 = ( ^ [B2: nat,A2: nat] : 0.41/0.57 ( ( ord_less_nat @ B2 @ A2 ) 0.41/0.57 | ( A2 = B2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_248_diff__le__self,axiom, 0.41/0.57 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ). 0.41/0.57 0.41/0.57 thf(fact_41_order__subst1,axiom, 0.41/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ B @ C ) 0.41/0.57 => ( ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) 0.41/0.57 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ ( F @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_163_sorted__rev__nth__mono,axiom, 0.41/0.57 ! [Xs: list_nat,I3: nat,J2: nat] : 0.41/0.57 ( ( ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) ) 0.41/0.57 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ J2 ) @ ( nth_nat @ Xs @ I3 ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ I3 @ J2 ) ) 0.41/0.57 <= ( linorder_sorted_nat @ ( rev_nat @ Xs ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_190_rev__swap,axiom, 0.41/0.57 ! [Xs: list_nat,Ys: list_nat] : 0.41/0.57 ( ( ( rev_nat @ Xs ) 0.41/0.57 = Ys ) 0.41/0.57 = ( Xs 0.41/0.57 = ( rev_nat @ Ys ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_132_nat__descend__induct,axiom, 0.41/0.57 ! [N: nat,P: nat > $o,M2: nat] : 0.41/0.57 ( ( ! [K2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ K2 @ N ) 0.41/0.57 => ( ( P @ K2 ) 0.41/0.57 <= ! [I4: nat] : 0.41/0.57 ( ( ord_less_nat @ K2 @ I4 ) 0.41/0.57 => ( P @ I4 ) ) ) ) 0.41/0.57 => ( P @ M2 ) ) 0.41/0.57 <= ! [K2: nat] : 0.41/0.57 ( ( ord_less_nat @ N @ K2 ) 0.41/0.57 => ( P @ K2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_115_antisym__conv1,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ X2 @ Y2 ) 0.41/0.57 = ( X2 = Y2 ) ) 0.41/0.57 <= ~ ( ord_less_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_181_Suc__le__D,axiom, 0.41/0.57 ! [N: nat,M4: nat] : 0.41/0.57 ( ? [M5: nat] : 0.41/0.57 ( M4 0.41/0.57 = ( suc @ M5 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ ( suc @ N ) @ M4 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_47_exists__least__iff,axiom, 0.41/0.57 ( ( ^ [P2: nat > $o] : 0.41/0.57 ? [X: nat] : ( P2 @ X ) ) 0.41/0.57 = ( ^ [P3: nat > $o] : 0.41/0.57 ? [N2: nat] : 0.41/0.57 ( ! [M: nat] : 0.41/0.57 ( ( ord_less_nat @ M @ N2 ) 0.41/0.57 => ~ ( P3 @ M ) ) 0.41/0.57 & ( P3 @ N2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_77_nat__less__induct,axiom, 0.41/0.57 ! [P: nat > $o,N: nat] : 0.41/0.57 ( ( P @ N ) 0.41/0.57 <= ! [N3: nat] : 0.41/0.57 ( ! [M3: nat] : 0.41/0.57 ( ( ord_less_nat @ M3 @ N3 ) 0.41/0.57 => ( P @ M3 ) ) 0.41/0.57 => ( P @ N3 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_240_nat__diff__right__cancel__eq1,axiom, 0.41/0.57 ! [M2: nat,K: nat,N: nat] : 0.41/0.57 ( ( ( minus_minus_nat @ M2 @ K ) 0.41/0.57 = ( minus_minus_nat @ N @ K ) ) 0.41/0.57 => ( ( M2 = N ) 0.41/0.57 <= ( ord_less_nat @ K @ M2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_15_less__imp__le__nat,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 <= ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_177_length__rev,axiom, 0.41/0.57 ! [Xs: list_nat] : 0.41/0.57 ( ( size_size_list_nat @ ( rev_nat @ Xs ) ) 0.41/0.57 = ( size_size_list_nat @ Xs ) ) ). 0.41/0.57 0.41/0.57 thf(fact_216_le__less__Suc__eq,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ( ord_less_nat @ N @ ( suc @ M2 ) ) 0.41/0.57 = ( N = M2 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_18_le__neq__implies__less,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( ( M2 != N ) 0.41/0.57 => ( ord_less_nat @ M2 @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_68_neq__iff,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( X2 != Y2 ) 0.41/0.57 = ( ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 | ( ord_less_nat @ X2 @ Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_102_dual__order_Ostrict__trans1,axiom, 0.41/0.57 ! [B: nat,A: nat,C: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ B @ A ) 0.41/0.57 => ( ( ord_less_nat @ C @ A ) 0.41/0.57 <= ( ord_less_nat @ C @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_222_sorted__rev__iff__nth__Suc,axiom, 0.41/0.57 ! [Xs: list_nat] : 0.41/0.57 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) ) 0.41/0.57 = ( ! [I2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( nth_nat @ Xs @ ( suc @ I2 ) ) @ ( nth_nat @ Xs @ I2 ) ) 0.41/0.57 <= ( ord_less_nat @ ( suc @ I2 ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_194_less__Suc__induct,axiom, 0.41/0.57 ! [I3: nat,J2: nat,P: nat > nat > $o] : 0.41/0.57 ( ( ! [I: nat] : ( P @ I @ ( suc @ I ) ) 0.41/0.57 => ( ! [I: nat,J3: nat,K2: nat] : 0.41/0.57 ( ( ord_less_nat @ I @ J3 ) 0.41/0.57 => ( ( ord_less_nat @ J3 @ K2 ) 0.41/0.57 => ( ( P @ I @ J3 ) 0.41/0.57 => ( ( P @ J3 @ K2 ) 0.41/0.57 => ( P @ I @ K2 ) ) ) ) ) 0.41/0.57 => ( P @ I3 @ J2 ) ) ) 0.41/0.57 <= ( ord_less_nat @ I3 @ J2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_19_less__mono__imp__le__mono,axiom, 0.41/0.57 ! [F: nat > nat,I3: nat,J2: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ I3 @ J2 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J2 ) ) ) 0.41/0.57 <= ! [I: nat,J3: nat] : 0.41/0.57 ( ( ord_less_nat @ ( F @ I ) @ ( F @ J3 ) ) 0.41/0.57 <= ( ord_less_nat @ I @ J3 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_50_dual__order_Oirrefl,axiom, 0.41/0.57 ! [A: nat] : 0.41/0.57 ~ ( ord_less_nat @ A @ A ) ). 0.41/0.57 0.41/0.57 thf(fact_219_dec__induct,axiom, 0.41/0.57 ! [I3: nat,J2: nat,P: nat > $o] : 0.41/0.57 ( ( ord_less_eq_nat @ I3 @ J2 ) 0.41/0.57 => ( ( P @ I3 ) 0.41/0.57 => ( ( P @ J2 ) 0.41/0.57 <= ! [N3: nat] : 0.41/0.57 ( ( ( ord_less_nat @ N3 @ J2 ) 0.41/0.57 => ( ( P @ N3 ) 0.41/0.57 => ( P @ ( suc @ N3 ) ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ I3 @ N3 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_111_less__le__trans,axiom, 0.41/0.57 ! [X2: nat,Y2: nat,Z2: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ Y2 @ Z2 ) 0.41/0.57 => ( ord_less_nat @ X2 @ Z2 ) ) 0.41/0.57 <= ( ord_less_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_241_nat__diff__right__cancel__eq2,axiom, 0.41/0.57 ! [M2: nat,K: nat,N: nat] : 0.41/0.57 ( ( ( minus_minus_nat @ M2 @ K ) 0.41/0.57 = ( minus_minus_nat @ N @ K ) ) 0.41/0.57 => ( ( M2 = N ) 0.41/0.57 <= ( ord_less_nat @ K @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_46_linorder__less__wlog,axiom, 0.41/0.57 ! [P: nat > nat > $o,A: nat,B: nat] : 0.41/0.57 ( ( ( ! [A3: nat,B3: nat] : 0.41/0.57 ( ( P @ B3 @ A3 ) 0.41/0.57 => ( P @ A3 @ B3 ) ) 0.41/0.57 => ( P @ A @ B ) ) 0.41/0.57 <= ! [A3: nat] : ( P @ A3 @ A3 ) ) 0.41/0.57 <= ! [A3: nat,B3: nat] : 0.41/0.57 ( ( ord_less_nat @ A3 @ B3 ) 0.41/0.57 => ( P @ A3 @ B3 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_25_order__trans,axiom, 0.41/0.57 ! [X2: nat,Y2: nat,Z2: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ X2 @ Z2 ) 0.41/0.57 <= ( ord_less_eq_nat @ Y2 @ Z2 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_169_rev__is__rev__conv,axiom, 0.41/0.57 ! [Xs: list_a,Ys: list_a] : 0.41/0.57 ( ( ( rev_a @ Xs ) 0.41/0.57 = ( rev_a @ Ys ) ) 0.41/0.57 = ( Xs = Ys ) ) ). 0.41/0.57 0.41/0.57 thf(fact_67_order_Oasym,axiom, 0.41/0.57 ! [A: nat,B: nat] : 0.41/0.57 ( ( ord_less_nat @ A @ B ) 0.41/0.57 => ~ ( ord_less_nat @ B @ A ) ) ). 0.41/0.57 0.41/0.57 thf(fact_71_order__less__subst2,axiom, 0.41/0.57 ! [A: nat,B: nat,F: nat > nat,C: nat] : 0.41/0.57 ( ( ord_less_nat @ A @ B ) 0.41/0.57 => ( ( ord_less_nat @ ( F @ B ) @ C ) 0.41/0.57 => ( ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) 0.41/0.57 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_233_i__append__nth2,axiom, 0.41/0.57 ! [Xs: list_nat,N: nat,F: nat > nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) 0.41/0.57 => ( ( listIn923761578nd_nat @ Xs @ F @ N ) 0.41/0.57 = ( F @ ( minus_minus_nat @ N @ ( size_size_list_nat @ Xs ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_9_list__eq__iff__nth__eq,axiom, 0.41/0.57 ( ( ^ [Y: list_a,Z: list_a] : ( Y = Z ) ) 0.41/0.57 = ( ^ [Xs2: list_a,Ys2: list_a] : 0.41/0.57 ( ( ( size_size_list_a @ Xs2 ) 0.41/0.57 = ( size_size_list_a @ Ys2 ) ) 0.41/0.57 & ! [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs2 ) ) 0.41/0.57 => ( ( nth_a @ Xs2 @ I2 ) 0.41/0.57 = ( nth_a @ Ys2 @ I2 ) ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_112_le__less__trans,axiom, 0.41/0.57 ! [X2: nat,Y2: nat,Z2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 ) 0.41/0.57 => ( ( ord_less_nat @ Y2 @ Z2 ) 0.41/0.57 => ( ord_less_nat @ X2 @ Z2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_34_eq__refl,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( X2 = Y2 ) 0.41/0.57 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_75_linorder__neqE__nat,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( X2 != Y2 ) 0.41/0.57 => ( ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 <= ~ ( ord_less_nat @ X2 @ Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_14_nat__less__le,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [M: nat,N2: nat] : 0.41/0.57 ( ( M != N2 ) 0.41/0.57 & ( ord_less_eq_nat @ M @ N2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_28_ord__eq__le__trans,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ A @ C ) 0.41/0.57 <= ( ord_less_eq_nat @ B @ C ) ) 0.41/0.57 <= ( A = B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_65_less__asym,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 <= ( ord_less_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_94_Ex__list__of__length,axiom, 0.41/0.57 ! [N: nat] : 0.41/0.57 ? [Xs3: list_nat] : 0.41/0.57 ( ( size_size_list_nat @ Xs3 ) 0.41/0.57 = N ) ). 0.41/0.57 0.41/0.57 thf(fact_0_i__append__eq__i__append__conv,axiom, 0.41/0.57 ! [Xs: list_nat,Ys: list_nat,F: nat > nat,G: nat > nat] : 0.41/0.57 ( ( ( ( listIn923761578nd_nat @ Xs @ F ) 0.41/0.57 = ( listIn923761578nd_nat @ Ys @ G ) ) 0.41/0.57 = ( ( F = G ) 0.41/0.57 & ( Xs = Ys ) ) ) 0.41/0.57 <= ( ( size_size_list_nat @ Xs ) 0.41/0.57 = ( size_size_list_nat @ Ys ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_32_order_Otrans,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ A @ C ) 0.41/0.57 <= ( ord_less_eq_nat @ B @ C ) ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_4_nth__equalityI,axiom, 0.41/0.57 ! [Xs: list_nat,Ys: list_nat] : 0.41/0.57 ( ( ! [I: nat] : 0.41/0.57 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) ) 0.41/0.57 => ( ( nth_nat @ Xs @ I ) 0.41/0.57 = ( nth_nat @ Ys @ I ) ) ) 0.41/0.57 => ( Xs = Ys ) ) 0.41/0.57 <= ( ( size_size_list_nat @ Xs ) 0.41/0.57 = ( size_size_list_nat @ Ys ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_81_less__not__refl,axiom, 0.41/0.57 ! [N: nat] : 0.41/0.57 ~ ( ord_less_nat @ N @ N ) ). 0.41/0.57 0.41/0.57 thf(fact_180_le__SucI,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_106_order_Ostrict__trans1,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_nat @ B @ C ) 0.41/0.57 => ( ord_less_nat @ A @ C ) ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_120_order__less__le__subst1,axiom, 0.41/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ B @ C ) 0.41/0.57 => ( ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) 0.41/0.57 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) 0.41/0.57 <= ( ord_less_nat @ A @ ( F @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_206_Suc__lessE,axiom, 0.41/0.57 ! [I3: nat,K: nat] : 0.41/0.57 ( ~ ! [J3: nat] : 0.41/0.57 ( ( ord_less_nat @ I3 @ J3 ) 0.41/0.57 => ( K 0.41/0.57 != ( suc @ J3 ) ) ) 0.41/0.57 <= ( ord_less_nat @ ( suc @ I3 ) @ K ) ) ). 0.41/0.57 0.41/0.57 thf(fact_174_lessI,axiom, 0.41/0.57 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_12_length__induct,axiom, 0.41/0.57 ! [P: list_nat > $o,Xs: list_nat] : 0.41/0.57 ( ( P @ Xs ) 0.41/0.57 <= ! [Xs3: list_nat] : 0.41/0.57 ( ! [Ys3: list_nat] : 0.41/0.57 ( ( P @ Ys3 ) 0.41/0.57 <= ( ord_less_nat @ ( size_size_list_nat @ Ys3 ) @ ( size_size_list_nat @ Xs3 ) ) ) 0.41/0.57 => ( P @ Xs3 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_95_list__desc__trans,axiom, 0.41/0.57 ( list_desc_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [J: nat] : 0.41/0.57 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) 0.41/0.57 => ! [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ J ) 0.41/0.57 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_16_le__eq__less__or__eq,axiom, 0.41/0.57 ( ord_less_eq_nat 0.41/0.57 = ( ^ [M: nat,N2: nat] : 0.41/0.57 ( ( ord_less_nat @ M @ N2 ) 0.41/0.57 | ( M = N2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_210_lift__Suc__mono__less,axiom, 0.41/0.57 ! [F: nat > nat,N: nat,N4: nat] : 0.41/0.57 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) ) 0.41/0.57 => ( ( ord_less_nat @ N @ N4 ) 0.41/0.57 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_192_not__less__less__Suc__eq,axiom, 0.41/0.57 ! [N: nat,M2: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ N @ M2 ) 0.41/0.57 => ( ( ord_less_nat @ N @ ( suc @ M2 ) ) 0.41/0.57 = ( N = M2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_122_order__le__less__subst1,axiom, 0.41/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ( ord_less_nat @ A @ ( F @ C ) ) 0.41/0.57 <= ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) ) 0.41/0.57 <= ( ord_less_nat @ B @ C ) ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ ( F @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_42_dual__order_Ostrict__implies__not__eq,axiom, 0.41/0.57 ! [B: nat,A: nat] : 0.41/0.57 ( ( ord_less_nat @ B @ A ) 0.41/0.57 => ( A != B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_212_lift__Suc__mono__le,axiom, 0.41/0.57 ! [F: nat > nat,N: nat,N4: nat] : 0.41/0.57 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) ) 0.41/0.57 => ( ( ord_less_eq_nat @ N @ N4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_170_rev__rev__ident,axiom, 0.41/0.57 ! [Xs: list_nat] : 0.41/0.57 ( ( rev_nat @ ( rev_nat @ Xs ) ) 0.41/0.57 = Xs ) ). 0.41/0.57 0.41/0.57 thf(fact_6_Skolem__list__nth,axiom, 0.41/0.57 ! [K: nat,P: nat > nat > $o] : 0.41/0.57 ( ( ! [I2: nat] : 0.41/0.57 ( ? [X: nat] : ( P @ I2 @ X ) 0.41/0.57 <= ( ord_less_nat @ I2 @ K ) ) ) 0.41/0.57 = ( ? [Xs2: list_nat] : 0.41/0.57 ( ! [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ K ) 0.41/0.57 => ( P @ I2 @ ( nth_nat @ Xs2 @ I2 ) ) ) 0.41/0.57 & ( ( size_size_list_nat @ Xs2 ) 0.41/0.57 = K ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_21_dual__order_Oeq__iff,axiom, 0.41/0.57 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) ) 0.41/0.57 = ( ^ [A2: nat,B2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A2 @ B2 ) 0.41/0.57 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_2_i__append__nth1,axiom, 0.41/0.57 ! [N: nat,Xs: list_nat,F: nat > nat] : 0.41/0.57 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) ) 0.41/0.57 => ( ( listIn923761578nd_nat @ Xs @ F @ N ) 0.41/0.57 = ( nth_nat @ Xs @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_141_minf_I6_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_nat @ X5 @ Z3 ) 0.41/0.57 => ( ord_less_eq_nat @ X5 @ T ) ) ). 0.41/0.57 0.41/0.57 thf(fact_17_less__or__eq__imp__le,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 <= ( ( M2 = N ) 0.41/0.57 | ( ord_less_nat @ M2 @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_220_Suc__le__eq,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) 0.41/0.57 = ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_56_less__not__sym,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ~ ( ord_less_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_221_Suc__leI,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) 0.41/0.57 <= ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_161_verit__comp__simplify1_I1_J,axiom, 0.41/0.57 ! [A: nat] : 0.41/0.57 ~ ( ord_less_nat @ A @ A ) ). 0.41/0.57 0.41/0.57 thf(fact_129_list__strict__desc__trans,axiom, 0.41/0.57 ( list_strict_desc_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [J: nat] : 0.41/0.57 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) 0.41/0.57 => ! [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ ( nth_nat @ Xs2 @ J ) @ ( nth_nat @ Xs2 @ I2 ) ) 0.41/0.57 <= ( ord_less_nat @ I2 @ J ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_247_le__diff__iff_H,axiom, 0.41/0.57 ! [A: nat,C: nat,B: nat] : 0.41/0.57 ( ( ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) ) 0.41/0.57 = ( ord_less_eq_nat @ B @ A ) ) 0.41/0.57 <= ( ord_less_eq_nat @ B @ C ) ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ C ) ) ). 0.41/0.57 0.41/0.57 thf(fact_20_dual__order_Oantisym,axiom, 0.41/0.57 ! [B: nat,A: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ B @ A ) 0.41/0.57 => ( ( A = B ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_59_ord__less__eq__trans,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( ( B = C ) 0.41/0.57 => ( ord_less_nat @ A @ C ) ) 0.41/0.57 <= ( ord_less_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_146_pinf_I4_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_nat @ Z3 @ X5 ) 0.41/0.57 => ( X5 != T ) ) ). 0.41/0.57 0.41/0.57 thf(fact_166_old_Onat_Oinject,axiom, 0.41/0.57 ! [Nat: nat,Nat2: nat] : 0.41/0.57 ( ( ( suc @ Nat ) 0.41/0.57 = ( suc @ Nat2 ) ) 0.41/0.57 = ( Nat = Nat2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_103_order_Ostrict__iff__order,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [A2: nat,B2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A2 @ B2 ) 0.41/0.57 & ( A2 != B2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_236_less__diff__imp__less,axiom, 0.41/0.57 ! [I3: nat,J2: nat,M2: nat] : 0.41/0.57 ( ( ord_less_nat @ I3 @ J2 ) 0.41/0.57 <= ( ord_less_nat @ I3 @ ( minus_minus_nat @ J2 @ M2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_107_not__le__imp__less,axiom, 0.41/0.57 ! [Y2: nat,X2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 <= ~ ( ord_less_eq_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_208_Nat_OlessE,axiom, 0.41/0.57 ! [I3: nat,K: nat] : 0.41/0.57 ( ( ~ ! [J3: nat] : 0.41/0.57 ( ( K 0.41/0.57 != ( suc @ J3 ) ) 0.41/0.57 <= ( ord_less_nat @ I3 @ J3 ) ) 0.41/0.57 <= ( K 0.41/0.57 != ( suc @ I3 ) ) ) 0.41/0.57 <= ( ord_less_nat @ I3 @ K ) ) ). 0.41/0.57 0.41/0.57 thf(fact_84_nat__le__linear,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 | ( ord_less_eq_nat @ N @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_83_Nat_Oex__has__greatest__nat,axiom, 0.41/0.57 ! [P: nat > $o,K: nat,B: nat] : 0.41/0.57 ( ( ? [X4: nat] : 0.41/0.57 ( ( P @ X4 ) 0.41/0.57 & ! [Y5: nat] : 0.41/0.57 ( ( P @ Y5 ) 0.41/0.57 => ( ord_less_eq_nat @ Y5 @ X4 ) ) ) 0.41/0.57 <= ! [Y4: nat] : 0.41/0.57 ( ( P @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ Y4 @ B ) ) ) 0.41/0.57 <= ( P @ K ) ) ). 0.41/0.57 0.41/0.57 thf(fact_127_list__strict__asc__trans__le,axiom, 0.41/0.57 ! [Xs: list_nat] : 0.41/0.57 ( ( list_strict_asc_nat @ Xs ) 0.41/0.57 => ! [J4: nat] : 0.41/0.57 ( ! [I4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J4 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ I4 @ J4 ) ) 0.41/0.57 <= ( ord_less_nat @ J4 @ ( size_size_list_nat @ Xs ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_53_less__imp__not__eq2,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( Y2 != X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_104_order_Oorder__iff__strict,axiom, 0.41/0.57 ( ord_less_eq_nat 0.41/0.57 = ( ^ [A2: nat,B2: nat] : 0.41/0.57 ( ( A2 = B2 ) 0.41/0.57 | ( ord_less_nat @ A2 @ B2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_193_strict__inc__induct,axiom, 0.41/0.57 ! [I3: nat,J2: nat,P: nat > $o] : 0.41/0.57 ( ( ( ( P @ I3 ) 0.41/0.57 <= ! [I: nat] : 0.41/0.57 ( ( ord_less_nat @ I @ J2 ) 0.41/0.57 => ( ( P @ I ) 0.41/0.57 <= ( P @ ( suc @ I ) ) ) ) ) 0.41/0.57 <= ! [I: nat] : 0.41/0.57 ( ( P @ I ) 0.41/0.57 <= ( J2 0.41/0.57 = ( suc @ I ) ) ) ) 0.41/0.57 <= ( ord_less_nat @ I3 @ J2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_37_eq__iff,axiom, 0.41/0.57 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) ) 0.41/0.57 = ( ^ [X3: nat,Y3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ Y3 @ X3 ) 0.41/0.57 & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_55_less__induct,axiom, 0.41/0.57 ! [P: nat > $o,A: nat] : 0.41/0.57 ( ( P @ A ) 0.41/0.57 <= ! [X4: nat] : 0.41/0.57 ( ( P @ X4 ) 0.41/0.57 <= ! [Y5: nat] : 0.41/0.57 ( ( ord_less_nat @ Y5 @ X4 ) 0.41/0.57 => ( P @ Y5 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_10_order__refl,axiom, 0.41/0.57 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ). 0.41/0.57 0.41/0.57 thf(fact_235_zero__induct__lemma,axiom, 0.41/0.57 ! [P: nat > $o,K: nat,I3: nat] : 0.41/0.57 ( ( P @ K ) 0.41/0.57 => ( ( P @ ( minus_minus_nat @ K @ I3 ) ) 0.41/0.57 <= ! [N3: nat] : 0.41/0.57 ( ( P @ ( suc @ N3 ) ) 0.41/0.57 => ( P @ N3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_23_linorder__wlog,axiom, 0.41/0.57 ! [P: nat > nat > $o,A: nat,B: nat] : 0.41/0.57 ( ! [A3: nat,B3: nat] : 0.41/0.57 ( ( P @ A3 @ B3 ) 0.41/0.57 <= ( ord_less_eq_nat @ A3 @ B3 ) ) 0.41/0.57 => ( ( P @ A @ B ) 0.41/0.57 <= ! [A3: nat,B3: nat] : 0.41/0.57 ( ( P @ A3 @ B3 ) 0.41/0.57 <= ( P @ B3 @ A3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_251_le__diff__iff,axiom, 0.41/0.57 ! [K: nat,M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ K @ M2 ) 0.41/0.57 => ( ( ord_less_eq_nat @ K @ N ) 0.41/0.57 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K ) @ ( minus_minus_nat @ N @ K ) ) 0.41/0.57 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_232_list__ex__rev,axiom, 0.41/0.57 ! [P: a > $o,Xs: list_a] : 0.41/0.57 ( ( list_ex_a @ P @ ( rev_a @ Xs ) ) 0.41/0.57 = ( list_ex_a @ P @ Xs ) ) ). 0.41/0.57 0.41/0.57 thf(fact_144_pinf_I2_J,axiom, 0.41/0.57 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] : 0.41/0.57 ( ? [Z4: nat] : 0.41/0.57 ! [X4: nat] : 0.41/0.57 ( ( ( P @ X4 ) 0.41/0.57 = ( P4 @ X4 ) ) 0.41/0.57 <= ( ord_less_nat @ Z4 @ X4 ) ) 0.41/0.57 => ( ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_nat @ Z3 @ X5 ) 0.41/0.57 => ( ( ( P @ X5 ) 0.41/0.57 | ( Q @ X5 ) ) 0.41/0.57 = ( ( Q2 @ X5 ) 0.41/0.57 | ( P4 @ X5 ) ) ) ) 0.41/0.57 <= ? [Z4: nat] : 0.41/0.57 ! [X4: nat] : 0.41/0.57 ( ( ord_less_nat @ Z4 @ X4 ) 0.41/0.57 => ( ( Q @ X4 ) 0.41/0.57 = ( Q2 @ X4 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_7_Skolem__list__nth,axiom, 0.41/0.57 ! [K: nat,P: nat > a > $o] : 0.41/0.57 ( ( ! [I2: nat] : 0.41/0.57 ( ? [X: a] : ( P @ I2 @ X ) 0.41/0.57 <= ( ord_less_nat @ I2 @ K ) ) ) 0.41/0.57 = ( ? [Xs2: list_a] : 0.41/0.57 ( ! [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ K ) 0.41/0.57 => ( P @ I2 @ ( nth_a @ Xs2 @ I2 ) ) ) 0.41/0.57 & ( ( size_size_list_a @ Xs2 ) 0.41/0.57 = K ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_162_sorted__iff__nth__mono__less,axiom, 0.41/0.57 ( linorder_sorted_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [I2: nat,J: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ J ) 0.41/0.57 => ( ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) 0.41/0.57 <= ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_126_leD,axiom, 0.41/0.57 ! [Y2: nat,X2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ Y2 @ X2 ) 0.41/0.57 => ~ ( ord_less_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_72_order__less__subst1,axiom, 0.41/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] : 0.41/0.57 ( ( ord_less_nat @ A @ ( F @ B ) ) 0.41/0.57 => ( ( ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) 0.41/0.57 <= ( ord_less_nat @ X4 @ Y4 ) ) 0.41/0.57 => ( ord_less_nat @ A @ ( F @ C ) ) ) 0.41/0.57 <= ( ord_less_nat @ B @ C ) ) ) ). 0.41/0.57 0.41/0.57 thf(conj_1,hypothesis, 0.41/0.57 ord_less_eq_nat @ ( size_size_list_a @ xs ) @ ( size_size_list_a @ ys ) ). 0.41/0.57 0.41/0.57 thf(fact_1_i__append__eq__i__append__conv,axiom, 0.41/0.57 ! [Xs: list_a,Ys: list_a,F: nat > a,G: nat > a] : 0.41/0.57 ( ( ( size_size_list_a @ Xs ) 0.41/0.57 = ( size_size_list_a @ Ys ) ) 0.41/0.57 => ( ( ( listIn1312259492pend_a @ Xs @ F ) 0.41/0.57 = ( listIn1312259492pend_a @ Ys @ G ) ) 0.41/0.57 = ( ( Xs = Ys ) 0.41/0.57 & ( F = G ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_242_nat__diff__right__cancel__less,axiom, 0.41/0.57 ! [N: nat,K: nat,M2: nat] : 0.41/0.57 ( ( ord_less_nat @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M2 @ K ) ) 0.41/0.57 => ( ord_less_nat @ N @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_35_linear,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ Y2 @ X2 ) 0.41/0.57 | ( ord_less_eq_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_173_Suc__mono,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) 0.41/0.57 <= ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_237_nat__diff__left__cancel__eq1,axiom, 0.41/0.57 ! [K: nat,M2: nat,N: nat] : 0.41/0.57 ( ( ( minus_minus_nat @ K @ M2 ) 0.41/0.57 = ( minus_minus_nat @ K @ N ) ) 0.41/0.57 => ( ( ord_less_nat @ M2 @ K ) 0.41/0.57 => ( M2 = N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_182_le__Suc__eq,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) 0.41/0.57 = ( ( M2 0.41/0.57 = ( suc @ N ) ) 0.41/0.57 | ( ord_less_eq_nat @ M2 @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_74_ord__eq__less__subst,axiom, 0.41/0.57 ! [A: nat,F: nat > nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_nat @ B @ C ) 0.41/0.57 => ( ( ord_less_nat @ A @ ( F @ C ) ) 0.41/0.57 <= ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) 0.41/0.57 <= ( ord_less_nat @ X4 @ Y4 ) ) ) ) 0.41/0.57 <= ( A 0.41/0.57 = ( F @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_114_antisym__conv2,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X2 @ Y2 ) 0.41/0.57 => ( ( ~ ( ord_less_nat @ X2 @ Y2 ) ) 0.41/0.57 = ( X2 = Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_108_less__le__not__le,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [X3: nat,Y3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X3 @ Y3 ) 0.41/0.57 & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_225_rev__nth,axiom, 0.41/0.57 ! [N: nat,Xs: list_nat] : 0.41/0.57 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) ) 0.41/0.57 => ( ( nth_nat @ ( rev_nat @ Xs ) @ N ) 0.41/0.57 = ( nth_nat @ Xs @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ ( suc @ N ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_38_ord__le__eq__subst,axiom, 0.41/0.57 ! [A: nat,B: nat,F: nat > nat,C: nat] : 0.41/0.57 ( ( ( ( F @ B ) 0.41/0.57 = C ) 0.41/0.57 => ( ( ord_less_eq_nat @ ( F @ A ) @ C ) 0.41/0.57 <= ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_58_dual__order_Oasym,axiom, 0.41/0.57 ! [B: nat,A: nat] : 0.41/0.57 ( ( ord_less_nat @ B @ A ) 0.41/0.57 => ~ ( ord_less_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_226_list__ex__length,axiom, 0.41/0.57 ( list_ex_a 0.41/0.57 = ( ^ [P3: a > $o,Xs2: list_a] : 0.41/0.57 ? [N2: nat] : 0.41/0.57 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs2 ) ) 0.41/0.57 & ( P3 @ ( nth_a @ Xs2 @ N2 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_135_greater__le__neq__conv,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [A2: nat,N2: nat] : 0.41/0.57 ! [X3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X3 @ A2 ) 0.41/0.57 => ( N2 != X3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_229_diff__Suc__Suc,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) ) 0.41/0.57 = ( minus_minus_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_33_le__cases,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ Y2 @ X2 ) 0.41/0.57 <= ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_48_less__imp__not__less,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 <= ( ord_less_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_176_length__rev,axiom, 0.41/0.57 ! [Xs: list_a] : 0.41/0.57 ( ( size_size_list_a @ ( rev_a @ Xs ) ) 0.41/0.57 = ( size_size_list_a @ Xs ) ) ). 0.41/0.57 0.41/0.57 thf(fact_157_sorted__iff__nth__mono,axiom, 0.41/0.57 ( linorder_sorted_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [I2: nat,J: nat] : 0.41/0.57 ( ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) 0.41/0.57 => ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ I2 @ J ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_128_list__asc__trans__le,axiom, 0.41/0.57 ( list_asc_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [J: nat] : 0.41/0.57 ( ! [I2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) 0.41/0.57 <= ( ord_less_eq_nat @ I2 @ J ) ) 0.41/0.57 <= ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_63_less__trans,axiom, 0.41/0.57 ! [X2: nat,Y2: nat,Z2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( ( ord_less_nat @ X2 @ Z2 ) 0.41/0.57 <= ( ord_less_nat @ Y2 @ Z2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_145_pinf_I3_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( X5 != T ) 0.41/0.57 <= ( ord_less_nat @ Z3 @ X5 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_205_Suc__lessI,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ( ord_less_nat @ ( suc @ M2 ) @ N ) 0.41/0.57 <= ( ( suc @ M2 ) 0.41/0.57 != N ) ) 0.41/0.57 <= ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_134_le__greater__neq__conv,axiom, 0.41/0.57 ( ord_less_eq_nat 0.41/0.57 = ( ^ [N2: nat,A2: nat] : 0.41/0.57 ! [X3: nat] : 0.41/0.57 ( ( N2 != X3 ) 0.41/0.57 <= ( ord_less_nat @ A2 @ X3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_66_less__imp__neq,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( X2 != Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_100_order_Ostrict__implies__order,axiom, 0.41/0.57 ! [A: nat,B: nat] : 0.41/0.57 ( ( ord_less_nat @ A @ B ) 0.41/0.57 => ( ord_less_eq_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_156_verit__comp__simplify1_I3_J,axiom, 0.41/0.57 ! [B4: nat,A4: nat] : 0.41/0.57 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) ) 0.41/0.57 = ( ord_less_nat @ A4 @ B4 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_30_antisym__conv,axiom, 0.41/0.57 ! [Y2: nat,X2: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ X2 @ Y2 ) 0.41/0.57 = ( X2 = Y2 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_121_order__le__less__subst2,axiom, 0.41/0.57 ! [A: nat,B: nat,F: nat > nat,C: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A @ B ) 0.41/0.57 => ( ( ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) 0.41/0.57 => ( ord_less_nat @ ( F @ A ) @ C ) ) 0.41/0.57 <= ( ord_less_nat @ ( F @ B ) @ C ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_203_less__SucI,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ M2 @ N ) 0.41/0.57 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_187_transitive__stepwise__le,axiom, 0.41/0.57 ! [M2: nat,N: nat,R: nat > nat > $o] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( ! [X4: nat] : ( R @ X4 @ X4 ) 0.41/0.57 => ( ( ( R @ M2 @ N ) 0.41/0.57 <= ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) ) ) 0.41/0.57 <= ! [X4: nat,Y4: nat,Z3: nat] : 0.41/0.57 ( ( R @ X4 @ Y4 ) 0.41/0.57 => ( ( R @ Y4 @ Z3 ) 0.41/0.57 => ( R @ X4 @ Z3 ) ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_209_lift__Suc__mono__less__iff,axiom, 0.41/0.57 ! [F: nat > nat,N: nat,M2: nat] : 0.41/0.57 ( ( ( ord_less_nat @ ( F @ N ) @ ( F @ M2 ) ) 0.41/0.57 = ( ord_less_nat @ N @ M2 ) ) 0.41/0.57 <= ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_150_minf_I2_J,axiom, 0.41/0.57 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] : 0.41/0.57 ( ? [Z4: nat] : 0.41/0.57 ! [X4: nat] : 0.41/0.57 ( ( ( P @ X4 ) 0.41/0.57 = ( P4 @ X4 ) ) 0.41/0.57 <= ( ord_less_nat @ X4 @ Z4 ) ) 0.41/0.57 => ( ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ( ( Q @ X5 ) 0.41/0.57 | ( P @ X5 ) ) 0.41/0.57 = ( ( P4 @ X5 ) 0.41/0.57 | ( Q2 @ X5 ) ) ) 0.41/0.57 <= ( ord_less_nat @ X5 @ Z3 ) ) 0.41/0.57 <= ? [Z4: nat] : 0.41/0.57 ! [X4: nat] : 0.41/0.57 ( ( ord_less_nat @ X4 @ Z4 ) 0.41/0.57 => ( ( Q @ X4 ) 0.41/0.57 = ( Q2 @ X4 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_79_less__not__refl3,axiom, 0.41/0.57 ! [S: nat,T: nat] : 0.41/0.57 ( ( ord_less_nat @ S @ T ) 0.41/0.57 => ( S != T ) ) ). 0.41/0.57 0.41/0.57 thf(fact_88_le__refl,axiom, 0.41/0.57 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ). 0.41/0.57 0.41/0.57 thf(fact_213_le__imp__less__Suc,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_92_neq__if__length__neq,axiom, 0.41/0.57 ! [Xs: list_nat,Ys: list_nat] : 0.41/0.57 ( ( Xs != Ys ) 0.41/0.57 <= ( ( size_size_list_nat @ Xs ) 0.41/0.57 != ( size_size_list_nat @ Ys ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_125_leI,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( ord_less_eq_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_165_sorted__iff__nth__Suc,axiom, 0.41/0.57 ( linorder_sorted_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [I2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ ( suc @ I2 ) ) ) 0.41/0.57 <= ( ord_less_nat @ ( suc @ I2 ) @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_86_eq__imp__le,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( M2 = N ) 0.41/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_51_linorder__cases,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 <= ( X2 != Y2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_52_less__imp__triv,axiom, 0.41/0.57 ! [X2: nat,Y2: nat,P: $o] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( P 0.41/0.57 <= ( ord_less_nat @ Y2 @ X2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_40_order__subst2,axiom, 0.41/0.57 ! [A: nat,B: nat,F: nat > nat,C: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A @ B ) 0.41/0.57 => ( ( ord_less_eq_nat @ ( F @ B ) @ C ) 0.41/0.57 => ( ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) 0.41/0.57 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_22_dual__order_Otrans,axiom, 0.41/0.57 ! [B: nat,A: nat,C: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ B @ A ) 0.41/0.57 => ( ( ord_less_eq_nat @ C @ A ) 0.41/0.57 <= ( ord_less_eq_nat @ C @ B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_230_diff__diff__cancel,axiom, 0.41/0.57 ! [I3: nat,N: nat] : 0.41/0.57 ( ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I3 ) ) 0.41/0.57 = I3 ) 0.41/0.57 <= ( ord_less_eq_nat @ I3 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_154_minf_I7_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_nat @ X5 @ Z3 ) 0.41/0.57 => ~ ( ord_less_nat @ T @ X5 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_70_gt__ex,axiom, 0.41/0.57 ! [X2: nat] : 0.41/0.57 ? [X_1: nat] : ( ord_less_nat @ X2 @ X_1 ) ). 0.41/0.57 0.41/0.57 thf(fact_13_length__induct,axiom, 0.41/0.57 ! [P: list_a > $o,Xs: list_a] : 0.41/0.57 ( ( P @ Xs ) 0.41/0.57 <= ! [Xs3: list_a] : 0.41/0.57 ( ! [Ys3: list_a] : 0.41/0.57 ( ( ord_less_nat @ ( size_size_list_a @ Ys3 ) @ ( size_size_list_a @ Xs3 ) ) 0.41/0.57 => ( P @ Ys3 ) ) 0.41/0.57 => ( P @ Xs3 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_151_minf_I3_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( X5 != T ) 0.41/0.57 <= ( ord_less_nat @ X5 @ Z3 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_224_rev__nth,axiom, 0.41/0.57 ! [N: nat,Xs: list_a] : 0.41/0.57 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) ) 0.41/0.57 => ( ( nth_a @ ( rev_a @ Xs ) @ N ) 0.41/0.57 = ( nth_a @ Xs @ ( minus_minus_nat @ ( size_size_list_a @ Xs ) @ ( suc @ N ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_246_diff__le__mono2,axiom, 0.41/0.57 ! [M2: nat,N: nat,L: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_43_order_Ostrict__implies__not__eq,axiom, 0.41/0.57 ! [A: nat,B: nat] : 0.41/0.57 ( ( ord_less_nat @ A @ B ) 0.41/0.57 => ( A != B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_243_diff__less__mono2,axiom, 0.41/0.57 ! [M2: nat,N: nat,L: nat] : 0.41/0.57 ( ( ( ord_less_nat @ M2 @ L ) 0.41/0.57 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) 0.41/0.57 <= ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_98_dual__order_Ostrict__iff__order,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [B2: nat,A2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ B2 @ A2 ) 0.41/0.57 & ( A2 != B2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_245_diff__commute,axiom, 0.41/0.57 ! [I3: nat,J2: nat,K: nat] : 0.41/0.57 ( ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J2 ) @ K ) 0.41/0.57 = ( minus_minus_nat @ ( minus_minus_nat @ I3 @ K ) @ J2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_139_ge__less__neq__conv,axiom, 0.41/0.57 ( ord_less_eq_nat 0.41/0.57 = ( ^ [A2: nat,N2: nat] : 0.41/0.57 ! [X3: nat] : 0.41/0.57 ( ( ord_less_nat @ X3 @ A2 ) 0.41/0.57 => ( N2 != X3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_78_less__irrefl__nat,axiom, 0.41/0.57 ! [N: nat] : 0.41/0.57 ~ ( ord_less_nat @ N @ N ) ). 0.41/0.57 0.41/0.57 thf(fact_189_Suc__inject,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ( suc @ X2 ) 0.41/0.57 = ( suc @ Y2 ) ) 0.41/0.57 => ( X2 = Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_26_order__class_Oorder_Oantisym,axiom, 0.41/0.57 ! [A: nat,B: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A @ B ) 0.41/0.57 => ( ( ord_less_eq_nat @ B @ A ) 0.41/0.57 => ( A = B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_109_le__imp__less__or__eq,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ( X2 = Y2 ) 0.41/0.57 | ( ord_less_nat @ X2 @ Y2 ) ) 0.41/0.57 <= ( ord_less_eq_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_91_neq__if__length__neq,axiom, 0.41/0.57 ! [Xs: list_a,Ys: list_a] : 0.41/0.57 ( ( ( size_size_list_a @ Xs ) 0.41/0.57 != ( size_size_list_a @ Ys ) ) 0.41/0.57 => ( Xs != Ys ) ) ). 0.41/0.57 0.41/0.57 thf(fact_76_infinite__descent,axiom, 0.41/0.57 ! [P: nat > $o,N: nat] : 0.41/0.57 ( ! [N3: nat] : 0.41/0.57 ( ? [M3: nat] : 0.41/0.57 ( ( ord_less_nat @ M3 @ N3 ) 0.41/0.57 & ~ ( P @ M3 ) ) 0.41/0.57 <= ~ ( P @ N3 ) ) 0.41/0.57 => ( P @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_87_le__trans,axiom, 0.41/0.57 ! [I3: nat,J2: nat,K: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ I3 @ J2 ) 0.41/0.57 => ( ( ord_less_eq_nat @ J2 @ K ) 0.41/0.57 => ( ord_less_eq_nat @ I3 @ K ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_159_list__ord__le__sorted__eq,axiom, 0.41/0.57 list_asc_nat = linorder_sorted_nat ). 0.41/0.57 0.41/0.57 thf(fact_238_nat__diff__left__cancel__eq2,axiom, 0.41/0.57 ! [K: nat,M2: nat,N: nat] : 0.41/0.57 ( ( ( minus_minus_nat @ K @ M2 ) 0.41/0.57 = ( minus_minus_nat @ K @ N ) ) 0.41/0.57 => ( ( ord_less_nat @ N @ K ) 0.41/0.57 => ( M2 = N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_61_less__irrefl,axiom, 0.41/0.57 ! [X2: nat] : 0.41/0.57 ~ ( ord_less_nat @ X2 @ X2 ) ). 0.41/0.57 0.41/0.57 thf(fact_64_less__asym_H,axiom, 0.41/0.57 ! [A: nat,B: nat] : 0.41/0.57 ( ~ ( ord_less_nat @ B @ A ) 0.41/0.57 <= ( ord_less_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_124_le__less,axiom, 0.41/0.57 ( ord_less_eq_nat 0.41/0.57 = ( ^ [X3: nat,Y3: nat] : 0.41/0.57 ( ( ord_less_nat @ X3 @ Y3 ) 0.41/0.57 | ( X3 = Y3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_228_Suc__diff__diff,axiom, 0.41/0.57 ! [M2: nat,N: nat,K: nat] : 0.41/0.57 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K ) ) 0.41/0.57 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K ) ) ). 0.41/0.57 0.41/0.57 thf(fact_97_dual__order_Ostrict__implies__order,axiom, 0.41/0.57 ! [B: nat,A: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ B @ A ) 0.41/0.57 <= ( ord_less_nat @ B @ A ) ) ). 0.41/0.57 0.41/0.57 thf(fact_249_diff__le__mono,axiom, 0.41/0.57 ! [M2: nat,N: nat,L: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_175_Suc__le__mono,axiom, 0.41/0.57 ! [N: nat,M2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) ) 0.41/0.57 = ( ord_less_eq_nat @ N @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_204_less__SucE,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ M2 @ ( suc @ N ) ) 0.41/0.57 => ( ( M2 = N ) 0.41/0.57 <= ~ ( ord_less_nat @ M2 @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_201_less__Suc__eq,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ M2 @ ( suc @ N ) ) 0.41/0.57 = ( ( ord_less_nat @ M2 @ N ) 0.41/0.57 | ( M2 = N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_148_pinf_I7_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ord_less_nat @ T @ X5 ) 0.41/0.57 <= ( ord_less_nat @ Z3 @ X5 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_123_less__le,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [X3: nat,Y3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ X3 @ Y3 ) 0.41/0.57 & ( X3 != Y3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_227_list__ex__length,axiom, 0.41/0.57 ( list_ex_nat 0.41/0.57 = ( ^ [P3: nat > $o,Xs2: list_nat] : 0.41/0.57 ? [N2: nat] : 0.41/0.57 ( ( P3 @ ( nth_nat @ Xs2 @ N2 ) ) 0.41/0.57 & ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_195_less__trans__Suc,axiom, 0.41/0.57 ! [I3: nat,J2: nat,K: nat] : 0.41/0.57 ( ( ord_less_nat @ I3 @ J2 ) 0.41/0.57 => ( ( ord_less_nat @ J2 @ K ) 0.41/0.57 => ( ord_less_nat @ ( suc @ I3 ) @ K ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_69_neqE,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 <= ~ ( ord_less_nat @ X2 @ Y2 ) ) 0.41/0.57 <= ( X2 != Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_172_Suc__less__eq,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) 0.41/0.57 = ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_119_order__less__le__subst2,axiom, 0.41/0.57 ! [A: nat,B: nat,F: nat > nat,C: nat] : 0.41/0.57 ( ( ord_less_nat @ A @ B ) 0.41/0.57 => ( ( ( ord_less_nat @ ( F @ A ) @ C ) 0.41/0.57 <= ! [X4: nat,Y4: nat] : 0.41/0.57 ( ( ord_less_nat @ X4 @ Y4 ) 0.41/0.57 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y4 ) ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ ( F @ B ) @ C ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_131_list__asc__trans,axiom, 0.41/0.57 ( list_asc_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [J: nat] : 0.41/0.57 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) 0.41/0.57 => ! [I2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) 0.41/0.57 <= ( ord_less_nat @ I2 @ J ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_29_order__class_Oorder_Oeq__iff,axiom, 0.41/0.57 ( ( ^ [Y: nat,Z: nat] : ( Y = Z ) ) 0.41/0.57 = ( ^ [A2: nat,B2: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ B2 @ A2 ) 0.41/0.57 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_113_less__imp__le,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( ord_less_eq_nat @ X2 @ Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_218_inc__induct,axiom, 0.41/0.57 ! [I3: nat,J2: nat,P: nat > $o] : 0.41/0.57 ( ( ord_less_eq_nat @ I3 @ J2 ) 0.41/0.57 => ( ( ( P @ I3 ) 0.41/0.57 <= ! [N3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ I3 @ N3 ) 0.41/0.57 => ( ( ( P @ N3 ) 0.41/0.57 <= ( P @ ( suc @ N3 ) ) ) 0.41/0.57 <= ( ord_less_nat @ N3 @ J2 ) ) ) ) 0.41/0.57 <= ( P @ J2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(conj_2,conjecture, 0.41/0.57 ! [I: nat] : 0.41/0.57 ( ( ( nth_a @ xs @ I ) 0.41/0.57 = ( nth_a @ ys @ I ) ) 0.41/0.57 | ~ ( ord_less_nat @ I @ ( size_size_list_a @ xs ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_49_order_Ostrict__trans,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_nat @ A @ C ) 0.41/0.57 <= ( ord_less_nat @ B @ C ) ) 0.41/0.57 <= ( ord_less_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_179_le__SucE,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) 0.41/0.57 => ( ~ ( ord_less_eq_nat @ M2 @ N ) 0.41/0.57 => ( M2 0.41/0.57 = ( suc @ N ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_168_rev__is__rev__conv,axiom, 0.41/0.57 ! [Xs: list_nat,Ys: list_nat] : 0.41/0.57 ( ( ( rev_nat @ Xs ) 0.41/0.57 = ( rev_nat @ Ys ) ) 0.41/0.57 = ( Xs = Ys ) ) ). 0.41/0.57 0.41/0.57 thf(fact_136_less__ge__neq__conv,axiom, 0.41/0.57 ( ord_less_nat 0.41/0.57 = ( ^ [N2: nat,A2: nat] : 0.41/0.57 ! [X3: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A2 @ X3 ) 0.41/0.57 => ( N2 != X3 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_3_i__append__nth1,axiom, 0.41/0.57 ! [N: nat,Xs: list_a,F: nat > a] : 0.41/0.57 ( ( ( listIn1312259492pend_a @ Xs @ F @ N ) 0.41/0.57 = ( nth_a @ Xs @ N ) ) 0.41/0.57 <= ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_244_less__imp__diff__less,axiom, 0.41/0.57 ! [J2: nat,K: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K ) 0.41/0.57 <= ( ord_less_nat @ J2 @ K ) ) ). 0.41/0.57 0.41/0.57 thf(fact_130_list__strict__asc__trans,axiom, 0.41/0.57 ( list_strict_asc_nat 0.41/0.57 = ( ^ [Xs2: list_nat] : 0.41/0.57 ! [J: nat] : 0.41/0.57 ( ! [I2: nat] : 0.41/0.57 ( ( ord_less_nat @ I2 @ J ) 0.41/0.57 => ( ord_less_nat @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_nat @ Xs2 @ J ) ) ) 0.41/0.57 <= ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_239_nat__diff__left__cancel__less,axiom, 0.41/0.57 ! [K: nat,M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_nat @ ( minus_minus_nat @ K @ M2 ) @ ( minus_minus_nat @ K @ N ) ) 0.41/0.57 => ( ord_less_nat @ N @ M2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_200_not__less__eq,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ~ ( ord_less_nat @ M2 @ N ) ) 0.41/0.57 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_178_Suc__leD,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) 0.41/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_140_minf_I8_J,axiom, 0.41/0.57 ! [T: nat] : 0.41/0.57 ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ~ ( ord_less_eq_nat @ T @ X5 ) 0.41/0.57 <= ( ord_less_nat @ X5 @ Z3 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_158_sorted__nth__mono,axiom, 0.41/0.57 ! [Xs: list_nat,I3: nat,J2: nat] : 0.41/0.57 ( ( linorder_sorted_nat @ Xs ) 0.41/0.57 => ( ( ord_less_eq_nat @ I3 @ J2 ) 0.41/0.57 => ( ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J2 ) ) 0.41/0.57 <= ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs ) ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_149_minf_I1_J,axiom, 0.41/0.57 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] : 0.41/0.57 ( ( ? [Z3: nat] : 0.41/0.57 ! [X5: nat] : 0.41/0.57 ( ( ( ( Q @ X5 ) 0.41/0.57 & ( P @ X5 ) ) 0.41/0.57 = ( ( Q2 @ X5 ) 0.41/0.57 & ( P4 @ X5 ) ) ) 0.41/0.57 <= ( ord_less_nat @ X5 @ Z3 ) ) 0.41/0.57 <= ? [Z4: nat] : 0.41/0.57 ! [X4: nat] : 0.41/0.57 ( ( ord_less_nat @ X4 @ Z4 ) 0.41/0.57 => ( ( Q @ X4 ) 0.41/0.57 = ( Q2 @ X4 ) ) ) ) 0.41/0.57 <= ? [Z4: nat] : 0.41/0.57 ! [X4: nat] : 0.41/0.57 ( ( ord_less_nat @ X4 @ Z4 ) 0.41/0.57 => ( ( P @ X4 ) 0.41/0.57 = ( P4 @ X4 ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_105_order_Ostrict__trans2,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ B @ C ) 0.41/0.57 => ( ord_less_nat @ A @ C ) ) 0.41/0.57 <= ( ord_less_nat @ A @ B ) ) ). 0.41/0.57 0.41/0.57 thf(fact_234_i__append__nth2,axiom, 0.41/0.57 ! [Xs: list_a,N: nat,F: nat > a] : 0.41/0.57 ( ( ( listIn1312259492pend_a @ Xs @ F @ N ) 0.41/0.57 = ( F @ ( minus_minus_nat @ N @ ( size_size_list_a @ Xs ) ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_116_le__neq__trans,axiom, 0.41/0.57 ! [A: nat,B: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ A @ B ) 0.41/0.57 => ( ( ord_less_nat @ A @ B ) 0.41/0.57 <= ( A != B ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_118_not__le,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ~ ( ord_less_eq_nat @ X2 @ Y2 ) ) 0.41/0.57 = ( ord_less_nat @ Y2 @ X2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_217_Suc__le__lessD,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) 0.41/0.57 => ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_60_ord__eq__less__trans,axiom, 0.41/0.57 ! [A: nat,B: nat,C: nat] : 0.41/0.57 ( ( A = B ) 0.41/0.57 => ( ( ord_less_nat @ A @ C ) 0.41/0.57 <= ( ord_less_nat @ B @ C ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_62_less__linear,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 | ( ord_less_nat @ Y2 @ X2 ) 0.41/0.57 | ( X2 = Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_82_nat__neq__iff,axiom, 0.41/0.57 ! [M2: nat,N: nat] : 0.41/0.57 ( ( M2 != N ) 0.41/0.57 = ( ( ord_less_nat @ N @ M2 ) 0.41/0.57 | ( ord_less_nat @ M2 @ N ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_191_rev__swap,axiom, 0.41/0.57 ! [Xs: list_a,Ys: list_a] : 0.41/0.57 ( ( ( rev_a @ Xs ) 0.41/0.57 = Ys ) 0.41/0.57 = ( Xs 0.41/0.57 = ( rev_a @ Ys ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_183_Suc__n__not__le__n,axiom, 0.41/0.57 ! [N: nat] : 0.41/0.57 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ). 0.41/0.57 0.41/0.57 thf(fact_93_Ex__list__of__length,axiom, 0.41/0.57 ! [N: nat] : 0.41/0.57 ? [Xs3: list_a] : 0.41/0.57 ( ( size_size_list_a @ Xs3 ) 0.41/0.57 = N ) ). 0.41/0.57 0.41/0.57 thf(fact_90_size__neq__size__imp__neq,axiom, 0.41/0.57 ! [X2: list_nat,Y2: list_nat] : 0.41/0.57 ( ( ( size_size_list_nat @ X2 ) 0.41/0.57 != ( size_size_list_nat @ Y2 ) ) 0.41/0.57 => ( X2 != Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_171_rev__rev__ident,axiom, 0.41/0.57 ! [Xs: list_a] : 0.41/0.57 ( ( rev_a @ ( rev_a @ Xs ) ) 0.41/0.57 = Xs ) ). 0.41/0.57 0.41/0.57 thf(fact_24_dual__order_Orefl,axiom, 0.41/0.57 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ). 0.41/0.57 0.41/0.57 thf(fact_57_less__imp__not__eq,axiom, 0.41/0.57 ! [X2: nat,Y2: nat] : 0.41/0.57 ( ( ord_less_nat @ X2 @ Y2 ) 0.41/0.57 => ( X2 != Y2 ) ) ). 0.41/0.57 0.41/0.57 thf(fact_188_n__not__Suc__n,axiom, 0.41/0.57 ! [N: nat] : 0.41/0.57 ( N 0.41/0.57 != ( suc @ N ) ) ). 0.41/0.57 0.41/0.57 thf(fact_164_sorted__rev__iff__nth__mono,axiom, 0.41/0.57 ! [Xs: list_nat] : 0.41/0.57 ( ( linorder_sorted_nat @ ( rev_nat @ Xs ) ) 0.41/0.57 = ( ! [I2: nat,J: nat] : 0.41/0.57 ( ( ( ord_less_eq_nat @ ( nth_nat @ Xs @ J ) @ ( nth_nat @ Xs @ I2 ) ) 0.41/0.57 <= ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) ) ) 0.41/0.57 <= ( ord_less_eq_nat @ I2 @ J ) ) ) ) ). 0.41/0.57 0.41/0.57 thf(fact_45_dual__order_Ostrict__trans,axiom, 0.41/0.57 ! [B: nat,A: nat,C: nat] : 0.41/0.57 ( ( ( ord_less_nat @ C @ A ) 0.41/0.57 <= ( ord_less_nat @ C @ B ) ) 0.41/0.57 <= ( ord_less_nat @ B @ A ) ) ). 0.41/0.57 0.41/0.57 thf(fact_8_list__eq__iff__nth__eq,axiom, 0.41/0.63 ( ( ^ [Y: list_nat,Z: list_nat] : ( Y = Z ) ) 0.41/0.63 = ( ^ [Xs2: list_nat,Ys2: list_nat] : 0.41/0.63 ( ( ( size_size_list_nat @ Xs2 ) 0.41/0.63 = ( size_size_list_nat @ Ys2 ) ) 0.41/0.63 & ! [I2: nat] : 0.41/0.63 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) ) 0.41/0.63 => ( ( nth_nat @ Xs2 @ I2 ) 0.41/0.63 = ( nth_nat @ Ys2 @ I2 ) ) ) ) ) ) ). 0.41/0.63 0.41/0.63 thf(fact_96_order_Onot__eq__order__implies__strict,axiom, 0.41/0.63 ! [A: nat,B: nat] : 0.41/0.63 ( ( ( ord_less_nat @ A @ B ) 0.41/0.63 <= ( ord_less_eq_nat @ A @ B ) ) 0.41/0.63 <= ( A != B ) ) ). 0.41/0.63 0.41/0.63 thf(fact_89_size__neq__size__imp__neq,axiom, 0.41/0.63 ! [X2: list_a,Y2: list_a] : 0.41/0.63 ( ( X2 != Y2 ) 0.41/0.63 <= ( ( size_size_list_a @ X2 ) 0.41/0.63 != ( size_size_list_a @ Y2 ) ) ) ). 0.41/0.63 0.41/0.63 thf(fact_137_list__strict__asc__imp__list__asc,axiom, 0.41/0.63 ! [Xs: list_nat] : 0.41/0.63 ( ( list_asc_nat @ Xs ) 0.41/0.63 <= ( list_strict_asc_nat @ Xs ) ) ). 0.41/0.63 0.41/0.63 thf(fact_160_verit__la__disequality,axiom, 0.41/0.63 ! [A: nat,B: nat] : 0.41/0.63 ( ~ ( ord_less_eq_nat @ A @ B ) 0.41/0.63 | ~ ( ord_less_eq_nat @ B @ A ) 0.41/0.63 | ( A = B ) ) ). 0.41/0.63 0.41/0.63 thf(fact_27_ord__le__eq__trans,axiom, 0.41/0.63 ! [A: nat,B: nat,C: nat] : 0.41/0.63 ( ( ( B = C ) 0.41/0.63 => ( ord_less_eq_nat @ A @ C ) ) 0.41/0.63 <= ( ord_less_eq_nat @ A @ B ) ) ). 0.41/0.63 0.41/0.63 thf(fact_147_pinf_I5_J,axiom, 0.41/0.63 ! [T: nat] : 0.41/0.63 ? [Z3: nat] : 0.41/0.63 ! [X5: nat] : 0.41/0.63 ( ( ord_less_nat @ Z3 @ X5 ) 0.41/0.63 => ~ ( ord_less_nat @ X5 @ T ) ) ). 0.41/0.63 0.41/0.63 thf(fact_143_pinf_I1_J,axiom, 0.41/0.63 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] : 0.41/0.63 ( ? [Z4: nat] : 0.41/0.63 ! [X4: nat] : 0.41/0.63 ( ( ( P @ X4 ) 0.41/0.63 = ( P4 @ X4 ) ) 0.41/0.63 <= ( ord_less_nat @ Z4 @ X4 ) ) 0.41/0.63 => ( ? [Z3: nat] : 0.41/0.63 ! [X5: nat] : 0.41/0.63 ( ( ord_less_nat @ Z3 @ X5 ) 0.41/0.63 => ( ( ( P @ X5 ) 0.41/0.63 & ( Q @ X5 ) ) 0.41/0.63 = ( ( Q2 @ X5 ) 0.41/0.63 & ( P4 @ X5 ) ) ) ) 0.41/0.63 <= ? [Z4: nat] : 0.41/0.63 ! [X4: nat] : 0.41/0.63 ( ( ord_less_nat @ Z4 @ X4 ) 0.41/0.63 => ( ( Q @ X4 ) 0.41/0.63 = ( Q2 @ X4 ) ) ) ) ) ). 0.41/0.63 0.41/0.63 thf(fact_199_All__less__Suc,axiom, 0.41/0.63 ! [N: nat,P: nat > $o] : 0.41/0.63 ( ( ! [I2: nat] : 0.41/0.63 ( ( ord_less_nat @ I2 @ ( suc @ N ) ) 0.41/0.63 => ( P @ I2 ) ) ) 0.41/0.63 = ( ! [I2: nat] : 0.41/0.63 ( ( P @ I2 ) 0.41/0.63 <= ( ord_less_nat @ I2 @ N ) ) 0.41/0.63 & ( P @ N ) ) ) ). 0.41/0.63 0.41/0.63 thf(fact_36_antisym,axiom, 0.41/0.63 ! [X2: nat,Y2: nat] : 0.41/0.63 ( ( ord_less_eq_nat @ X2 @ Y2 ) 0.41/0.63 => ( ( ord_less_eq_nat @ Y2 @ X2 ) 0.41/0.63 => ( X2 = Y2 ) ) ) ). 0.41/0.63 0.41/0.63 thf(fact_207_Suc__lessD,axiom, 0.41/0.63 ! [M2: nat,N: nat] : 0.41/0.63 ( ( ord_less_nat @ ( suc @ M2 ) @ N ) 0.41/0.63 => ( ord_less_nat @ M2 @ N ) ) ). 0.41/0.63 0.41/0.63 thf(conj_0,hypothesis, 0.41/0.63 ! [X5: nat] : 0.41/0.63 ( ( listIn1312259492pend_a @ xs @ f @ X5 ) 0.41/0.63 = ( listIn1312259492pend_a @ ys @ g @ X5 ) ) ). 0.41/0.63 0.41/0.63 thf(fact_184_not__less__eq__eq,axiom, 0.41/0.63 ! [M2: nat,N: nat] : 0.41/0.63 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) ) 0.41/0.63 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ). 0.41/0.63 0.41/0.63 thf(fact_211_lift__Suc__antimono__le,axiom, 0.41/0.63 ! [F: nat > nat,N: nat,N4: nat] : 0.41/0.63 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) ) 0.41/0.63 => ( ( ord_less_eq_nat @ N @ N4 ) 0.41/0.63 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ). 0.41/0.63 0.41/0.63 thf(fact_152_minf_I4_J,axiom, 0.41/0.63 ! [T: nat] : 0.41/0.63 ? [Z3: nat] : 0.41/0.63 ! [X5: nat] : 0.41/0.63 ( ( ord_less_nat @ X5 @ Z3 ) 0.41/0.63 => ( X5 != T ) ) ). 0.41/0.63 0.41/0.63 thf(fact_185_full__nat__induct,axiom, 0.41/0.63 ! [P: nat > $o,N: nat] : 0.41/0.63 ( ! [N3: nat] : 0.41/0.63 ( ( P @ N3 ) 0.41/0.63 <= ! [M3: nat] : 0.41/0.63 ( ( P @ M3 ) 0.41/0.63 <= ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 ) ) ) 0.41/0.63 => ( P @ N ) ) ). 0.41/0.63 0.41/0.63 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XuPZ0FQ13a/cvc5---1.0.5_19331.p... 0.41/0.63 (declare-sort $$unsorted 0) 0.41/0.63 (declare-sort tptp.list_nat 0) 0.41/0.63 (declare-sort tptp.list_a 0) 0.41/0.63 (declare-sort tptp.nat 0) 0.41/0.63 (declare-sort tptp.a 0) 0.41/0.63 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat) 0.41/0.63 (declare-fun tptp.list_asc_nat (tptp.list_nat) Bool) 0.41/0.63 (declare-fun tptp.list_desc_nat (tptp.list_nat) Bool) 0.41/0.63 (declare-fun tptp.list_strict_asc_nat (tptp.list_nat) Bool) 0.41/0.63 (declare-fun tptp.list_strict_desc_nat (tptp.list_nat) Bool) 0.41/0.63 (declare-fun tptp.listIn923761578nd_nat (tptp.list_nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat) 0.41/0.63 (declare-fun tptp.listIn1312259492pend_a (tptp.list_a (-> tptp.nat tptp.a) tptp.nat) tptp.a) 0.41/0.63 (declare-fun tptp.linorder_sorted_nat (tptp.list_nat) Bool) 0.41/0.63 (declare-fun tptp.list_ex_nat ((-> tptp.nat Bool) tptp.list_nat) Bool) 0.41/0.63 (declare-fun tptp.list_ex_a ((-> tptp.a Bool) tptp.list_a) Bool) 0.41/0.63 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat) 0.41/0.63 (declare-fun tptp.nth_a (tptp.list_a tptp.nat) tptp.a) 0.41/0.63 (declare-fun tptp.rev_nat (tptp.list_nat) tptp.list_nat) 0.41/0.63 (declare-fun tptp.rev_a (tptp.list_a) tptp.list_a) 0.41/0.63 (declare-fun tptp.suc (tptp.nat) tptp.nat) 0.41/0.63 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat) 0.41/0.63 (declare-fun tptp.size_size_list_a (tptp.list_a) tptp.nat) 0.41/0.63 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool) 0.41/0.63 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool) 0.41/0.63 (declare-fun tptp.f (tptp.nat) tptp.a) 0.41/0.63 (declare-fun tptp.g (tptp.nat) tptp.a) 0.41/0.63 (declare-fun tptp.xs () tptp.list_a) 0.41/0.63 (declare-fun tptp.ys () tptp.list_a) 0.41/0.63 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M2) (not (= M2 N))))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0)))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.list_ex_nat P))) (= (@ _let_1 (@ tptp.rev_nat Xs)) (@ _let_1 Xs))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M2) N)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N)))) 0.41/0.63 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ P M2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N)))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (or (@ (@ tptp.ord_less_nat Y2) X2) (= X2 Y2))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2))))))))))))))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2)))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_desc_nat Xs) (@ tptp.list_desc_nat Xs)))) 0.41/0.63 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y2) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2))))) 0.41/0.63 (assert (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2)))))))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I) (@ (@ tptp.nth_a Ys) I)))) (= Xs Ys))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C)))))) 0.41/0.63 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M2) (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat N) M6) (= M2 (@ tptp.suc M6))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat C2) B) (forall ((D tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat X4) D) (@ (@ tptp.ord_less_eq_nat A) X4)) (@ P X4))) (@ (@ tptp.ord_less_eq_nat D) C2))) (forall ((X5 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X5) (@ (@ tptp.ord_less_nat X5) C2)) (@ P X5)))))))))) 0.41/0.63 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (=> (@ _let_1 (@ tptp.suc M2)) (= M2 N)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= M2 N))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_eq_nat T) X5)))))) 0.41/0.63 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M2) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N)))))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X5))) (=> (@ _let_1 Z3) (@ _let_1 T))))))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A))))) 0.41/0.63 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ P I2) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)))) (or (@ P N) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P I2))))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (N0 tptp.nat) (N tptp.nat)) (=> (@ P N0) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N0) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_eq_nat N0) N) (@ P N)))))) 0.41/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A2) (= A2 B2))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) N)) M2))) 0.41/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C)))))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J2)) (@ _let_1 I3)))))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ tptp.rev_nat Xs) Ys) (= Xs (@ tptp.rev_nat Ys))))) 0.41/0.63 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M2 tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I4) (@ P I4))) (@ P K2)))) (@ P M2))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2))))) 0.41/0.63 (assert (forall ((N tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5)))))) 0.41/0.63 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X tptp.nat)) (@ P2 X))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ P3 M)))) (@ P3 N2)))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (@ P M3))) (@ P N3))) (@ P N)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N) K)) (=> (@ (@ tptp.ord_less_nat K) M2) (= M2 N))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat M2) N)))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs)) (@ tptp.size_size_list_nat Xs)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_nat Y2) X2) (@ (@ tptp.ord_less_nat X2) Y2))))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A)))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 _let_2)) (@ _let_1 I2))))))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (forall ((I tptp.nat)) (@ (@ P I) (@ tptp.suc I))) (=> (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I))) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (@ (@ tptp.ord_less_nat J3) K2) (=> (@ _let_1 J3) (=> (@ (@ P J3) K2) (@ _let_1 K2))))))) (@ (@ P I3) J2)))))) 0.41/0.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (I3 tptp.nat) (J2 tptp.nat)) (=> (forall ((I tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (@ (@ tptp.ord_less_nat (@ F I)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ F J2)))))) 0.41/0.63 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A)))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ P I3) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J2)))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N) K)) (=> (@ (@ tptp.ord_less_nat K) N) (= M2 N))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2)))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) (@ tptp.rev_a Ys)) (= Xs Ys)))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C)))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (N tptp.nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ (@ tptp.listIn923761578nd_nat Xs) F) N) (@ F (@ (@ tptp.minus_minus_nat N) _let_1))))))) 0.41/0.63 (assert (= (lambda ((Y tptp.list_a) (Z tptp.list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs2)) (= (@ (@ tptp.nth_a Xs2) I2) (@ (@ tptp.nth_a Ys2) I2)))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ (@ tptp.ord_less_nat X2) Z2))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2))))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (and (not (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N)))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (= (= (@ (@ tptp.listIn923761578nd_nat Xs) F) (@ (@ tptp.listIn923761578nd_nat Ys) G)) (and (= F G) (= Xs Ys)))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C)))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I) (@ (@ tptp.nth_nat Ys) I)))) (= Xs Ys))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N)))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C))))) 0.41/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C)))))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I3)) K) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (not (= K (@ tptp.suc J3))))))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N)))) 0.41/0.63 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys3)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs)))) 0.41/0.63 (assert (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2)))))))))) 0.41/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N2) (= M N2))))) 0.41/0.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4)))))) 0.41/0.63 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2)))))) 0.41/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A) (@ F C))))))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B))))) 0.41/0.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4)))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.rev_nat (@ tptp.rev_nat Xs)) Xs))) 0.41/0.63 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.nat)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_nat)) (and (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs2) I2)))) (= (@ tptp.size_size_list_nat Xs2) K)))))) 0.41/0.63 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) A2))))) 0.41/0.63 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ tptp.listIn923761578nd_nat Xs) F) N) (@ (@ tptp.nth_nat Xs) N))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (@ (@ tptp.ord_less_eq_nat X5) T)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (= M2 N) (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_eq_nat M2) N)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N)))) 0.41/0.63 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A)))) 0.41/0.63 (assert (= tptp.list_strict_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 J)) (@ _let_1 I2)))))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A)))))))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C)))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T))))))) 0.41/0.63 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2)))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (not (= A2 B2)))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I3))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat J2) M2)) (@ _let_1 J2))))) 0.41/0.63 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y2) X2)) (@ (@ tptp.ord_less_nat X2) Y2)))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (=> (not (= K (@ tptp.suc I3))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (not (= K (@ tptp.suc J3)))))))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat N) M2)))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4))))))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J4) (@ tptp.size_size_list_nat Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J4) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J4)))))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= Y2 X2))))) 0.41/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (or (= A2 B2) (@ (@ tptp.ord_less_nat A2) B2))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (forall ((I tptp.nat)) (=> (= J2 (@ tptp.suc I)) (@ P I))) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (@ P (@ tptp.suc I)) (@ P I)))) (@ P I3)))))) 0.41/0.63 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat Y3) X3) (@ (@ tptp.ord_less_eq_nat X3) Y3))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X4) (@ P Y5))) (@ P X4))) (@ P A)))) 0.41/0.63 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I3 tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I3)))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))) 0.41/0.63 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M2) N))))))) 0.41/0.63 (assert (forall ((P (-> tptp.a Bool)) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.list_ex_a P))) (= (@ _let_1 (@ tptp.rev_a Xs)) (@ _let_1 Xs))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ Q2 X5) (@ P4 X5)))))))))) 0.41/0.63 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_a)) (and (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_a Xs2) I2)))) (= (@ tptp.size_size_list_a Xs2) K)))))) 0.41/0.63 (assert (= tptp.linorder_sorted_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))) 0.41/0.63 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (not (@ (@ tptp.ord_less_nat X2) Y2))))) 0.41/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C)))))))) 0.41/0.63 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a tptp.xs)) (@ tptp.size_size_list_a tptp.ys))) 0.41/0.63 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (= (= (@ (@ tptp.listIn1312259492pend_a Xs) F) (@ (@ tptp.listIn1312259492pend_a Ys) G)) (and (= Xs Ys) (= F G)))))) 0.41/0.63 (assert (forall ((N tptp.nat) (K tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.ord_less_nat N) M2)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat Y2) X2) (@ (@ tptp.ord_less_eq_nat X2) Y2)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N))))) 0.41/0.63 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat K))) (=> (= (@ _let_1 M2) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat M2) K) (= M2 N)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (or (= M2 _let_2) (@ _let_1 N))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A) (@ F C))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2))))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (not (@ (@ tptp.ord_less_eq_nat Y3) X3)))))) 0.41/0.63 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rev_nat Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N)))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C)))))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B))))) 0.41/0.63 (assert (= tptp.list_ex_a (lambda ((P3 (-> tptp.a Bool)) (Xs2 tptp.list_a)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs2)) (@ P3 (@ (@ tptp.nth_a Xs2) N2))))))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (N2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) A2) (not (= N2 X3))))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M2) N)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.size_size_list_a (@ tptp.rev_a Xs)) (@ tptp.size_size_list_a Xs)))) 0.41/0.63 (assert (= tptp.linorder_sorted_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))) 0.41/0.63 (assert (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J)))))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ _let_1 Z2)))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T))))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N)))))) 0.41/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (A2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) X3) (not (= N2 X3))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B)))) 0.41/0.63 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4)))) 0.41/0.63 (assert (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z3) (@ _let_1 Z3))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M2) N))))))) 0.41/0.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (or (@ Q X5) (@ P X5)) (or (@ P4 X5) (@ Q2 X5)))))))))) 0.41/0.63 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2)))) 0.41/0.63 (assert (= tptp.linorder_sorted_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (let ((_let_2 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_eq_nat (@ _let_2 I2)) (@ _let_2 _let_1))))))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 N) (@ (@ tptp.ord_less_eq_nat M2) N)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_nat Y2) X2))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) X2) P)))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C)))))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A)))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ _let_1 (@ _let_1 I3)) I3))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_nat T) X5))))))) 0.41/0.63 (assert (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1)))) 0.41/0.63 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (forall ((Xs3 tptp.list_a)) (=> (forall ((Ys3 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Ys3)) (@ tptp.size_size_list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs)))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T))))))) 0.41/0.63 (assert (forall ((N tptp.nat) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_a (@ tptp.rev_a Xs)) N) (@ (@ tptp.nth_a Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N)))))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2)))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2)))))))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= A2 B2)))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I3))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J2))))) 0.41/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (N2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) A2) (not (= N2 X3))))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N)))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2)))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (or (= X2 Y2) (@ (@ tptp.ord_less_nat X2) Y2))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys))) (not (= Xs Ys))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3)))))) (@ P N)))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K)))))) 0.41/0.63 (assert (= tptp.list_asc_nat tptp.linorder_sorted_nat)) 0.41/0.63 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat K))) (=> (= (@ _let_1 M2) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat N) K) (= M2 N)))))) 0.41/0.63 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2)))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A))))) 0.41/0.63 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y3) (= X3 Y3))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N)) K)))) 0.41/0.63 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N) L))))) 0.41/0.63 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N) M2)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N)))))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_nat T) X5)))))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (not (= X3 Y3)))))) 0.41/0.63 (assert (= tptp.list_ex_nat (lambda ((P3 (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (exists ((N2 tptp.nat)) (and (@ P3 (@ (@ tptp.nth_nat Xs2) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2))))))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I3)) K))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N)))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C)))))) 0.41/0.63 (assert (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J)))))))))) 0.41/0.63 (assert (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2)))) 0.41/0.63 (assert (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ P J2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I3)))))) 0.41/0.63 (assert (not (forall ((I tptp.nat)) (or (= (@ (@ tptp.nth_a tptp.xs) I) (@ (@ tptp.nth_a tptp.ys) I)) (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a tptp.xs))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C)))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M2 _let_1))))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ tptp.rev_nat Xs) (@ tptp.rev_nat Ys)) (= Xs Ys)))) 0.41/0.63 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (A2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X3) (not (= N2 X3))))))) 0.41/0.63 (assert (forall ((N tptp.nat) (Xs tptp.list_a) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (= (@ (@ (@ tptp.listIn1312259492pend_a Xs) F) N) (@ (@ tptp.nth_a Xs) N))))) 0.41/0.63 (assert (forall ((J2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K)))) 0.41/0.63 (assert (= tptp.list_strict_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))))) 0.41/0.63 (assert (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat K))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2))))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_eq_nat M2) N)))) 0.41/0.63 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X5))))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ tptp.linorder_sorted_nat Xs) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I3)) (@ _let_1 J2)))))))) 0.41/0.63 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (and (@ Q X5) (@ P X5)) (and (@ Q2 X5) (@ P4 X5)))))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C)))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a) (N tptp.nat) (F (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ (@ tptp.listIn1312259492pend_a Xs) F) N) (@ F (@ (@ tptp.minus_minus_nat N) _let_1))))))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N)))) 0.41/0.63 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C))))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2) (= X2 Y2)))) 0.41/0.63 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.ord_less_nat M2) N))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) Ys) (= Xs (@ tptp.rev_a Ys))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N)))) 0.41/0.63 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_a)) (= (@ tptp.size_size_list_a Xs3) N)))) 0.41/0.63 (assert (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y2))) (not (= X2 Y2))))) 0.41/0.63 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.rev_a (@ tptp.rev_a Xs)) Xs))) 0.41/0.63 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A))) 0.41/0.63 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2))))) 0.41/0.63 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N))))) 0.41/0.63 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs)) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))) 11.51/11.72 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A)))))) 11.51/11.72 (assert (= (lambda ((Y tptp.list_nat) (Z tptp.list_nat)) (= Y Z)) (lambda ((Xs2 tptp.list_nat) (Ys2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys2) I2)))))))) 11.51/11.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B))))) 11.51/11.72 (assert (forall ((X2 tptp.list_a) (Y2 tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a X2) (@ tptp.size_size_list_a Y2))) (not (= X2 Y2))))) 11.51/11.72 (assert (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (@ tptp.list_asc_nat Xs)))) 11.51/11.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)) (= A B)))) 11.51/11.72 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C)))))) 11.51/11.72 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_nat X5) T))))))) 11.51/11.72 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ Q2 X5) (@ P4 X5)))))))))) 11.51/11.72 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2))) (@ P N))))) 11.51/11.72 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= X2 Y2))))) 11.51/11.72 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N)))) 11.51/11.72 (assert (forall ((X5 tptp.nat)) (= (@ (@ (@ tptp.listIn1312259492pend_a tptp.xs) tptp.f) X5) (@ (@ (@ tptp.listIn1312259492pend_a tptp.ys) tptp.g) X5)))) 11.51/11.72 (assert (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2)))) 11.51/11.72 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N)))))) 11.51/11.72 (assert (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T))))))) 11.51/11.72 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N3) (@ P M3))) (@ P N3))) (@ P N)))) 11.51/11.72 (set-info :filename cvc5---1.0.5_19331) 11.51/11.72 (check-sat-assuming ( true )) 11.51/11.72 ------- get file name : TPTP file name is 11.51/11.72 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19331.smt2... 11.51/11.72 --- Run --ho-elim --full-saturate-quant at 10... 11.51/11.72 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 11.51/11.72 % SZS status Theorem for 11.51/11.72 % SZS output start Proof for 11.51/11.72 ( 11.51/11.72 (let ((_let_1 (forall ((X5 tptp.nat)) (= (@ (@ (@ tptp.listIn1312259492pend_a tptp.xs) tptp.f) X5) (@ (@ (@ tptp.listIn1312259492pend_a tptp.ys) tptp.g) X5))))) (let ((_let_2 (= tptp.list_strict_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_3 (forall ((N tptp.nat) (Xs tptp.list_a) (F (-> tptp.nat tptp.a))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_a Xs)) (= (@ (@ (@ tptp.listIn1312259492pend_a Xs) F) N) (@ (@ tptp.nth_a Xs) N)))))) (let ((_let_4 (not (forall ((I tptp.nat)) (or (= (@ (@ tptp.nth_a tptp.xs) I) (@ (@ tptp.nth_a tptp.ys) I)) (not (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a tptp.xs)))))))) (let ((_let_5 (= tptp.list_ex_nat (lambda ((P3 (-> tptp.nat Bool)) (Xs2 tptp.list_nat)) (exists ((N2 tptp.nat)) (and (@ P3 (@ (@ tptp.nth_nat Xs2) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs2)))))))) (let ((_let_6 (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))) (let ((_let_7 (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_nat M2) (@ tptp.suc N)))))) (let ((_let_8 (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))) (let ((_let_9 (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))))) (let ((_let_10 (= tptp.list_ex_a (lambda ((P3 (-> tptp.a Bool)) (Xs2 tptp.list_a)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs2)) (@ P3 (@ (@ tptp.nth_a Xs2) N2)))))))) (let ((_let_11 (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a tptp.xs)) (@ tptp.size_size_list_a tptp.ys)))) (let ((_let_12 (= tptp.linorder_sorted_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J)))))))))) (let ((_let_13 (= tptp.list_strict_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_14 (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))) (let ((_let_15 (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C))))))))) (let ((_let_16 (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= M2 N)))))) (let ((_let_17 (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))))) (let ((_let_18 (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y2))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z2))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y2))) (let ((_let_6 (@ _let_5 Z2))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y2))) (let ((_let_9 (@ _let_1 Z2))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))) (let ((_let_19 (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))) (let ((_let_20 (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (ho_46 k_45 C))) (or (not (ho_47 (ho_46 k_45 B) A)) (not (ho_47 _let_1 B)) (ho_47 _let_1 A)))))) (let ((_let_21 (ho_82 k_81 tptp.xs))) (let ((_let_22 (ho_82 k_81 tptp.ys))) (let ((_let_23 (ho_46 k_45 _let_22))) (let ((_let_24 (ho_47 _let_23 _let_21))) (let ((_let_25 (ho_41 k_44 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_103))) (let ((_let_26 (ho_47 _let_23 _let_25))) (let ((_let_27 (not _let_26))) (let ((_let_28 (ho_46 k_45 _let_25))) (let ((_let_29 (ho_47 _let_28 _let_21))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_27 _let_24))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_6)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (or (not (@ (@ tptp.ord_less_eq_nat B) A)) (not (@ _let_1 B)) (@ _let_1 A)))) _let_20))))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (forall ((X4 tptp.nat) (Y4 tptp.nat)) (or (not (ho_47 (ho_46 k_45 X4) Y4)) (ho_47 (ho_46 k_45 (ho_41 k_44 X4)) (ho_41 k_44 Y4)))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (ho_47 _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_103))) (let ((_let_37 (not _let_36))) (let ((_let_38 (ho_47 _let_23 (ho_41 k_44 _let_22)))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_35 _let_26))) (let ((_let_41 (forall ((A tptp.nat) (BOUND_VARIABLE_12234 |u_(-> tptp.nat tptp.nat)|) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (ho_46 k_45 A))) (or (not (ho_47 _let_1 (ho_41 BOUND_VARIABLE_12234 B))) (not (ho_47 (ho_46 k_45 B) C)) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (or (not (ho_47 (ho_46 k_45 X4) Y4)) (ho_47 (ho_46 k_45 (ho_41 BOUND_VARIABLE_12234 X4)) (ho_41 BOUND_VARIABLE_12234 Y4))))) (ho_47 _let_1 (ho_41 BOUND_VARIABLE_12234 C))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (or (not (@ _let_1 (@ F B))) (not (@ (@ tptp.ord_less_eq_nat B) C)) (not (forall ((X4 tptp.nat) (Y4 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat X4) Y4)) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4))))) (@ _let_1 (@ F C))))) _let_41))))))) (let ((_let_43 (ho_47 _let_28 _let_22))) (let ((_let_44 (= _let_43 _let_37))) (let ((_let_45 (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (ho_47 (ho_46 k_45 (ho_41 k_44 A4)) B4) (not (ho_47 (ho_46 k_45 B4) A4)))))) (let ((_let_46 (ASSUME :args (_let_19)))) (let ((_let_47 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO _let_46 :args ((= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat) (BOUND_VARIABLE_4499 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (or (not (@ (@ tptp.ord_less_nat J) (@ 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(forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (or (not (@ (@ tptp.ord_less_nat I2) J)) (not (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_49 _let_48 _let_47 _let_46) :args ((= tptp.list_ex_a (lambda ((P3 (-> tptp.a Bool)) (Xs2 tptp.list_a)) (not (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs2))) (not (@ P3 (@ (@ tptp.nth_a Xs2) N2)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_50 _let_49 _let_48 _let_47 _let_46) :args ((= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat) (BOUND_VARIABLE_5760 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N))) (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs)) (@ tptp.size_size_list_nat Xs))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)) (= N M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (not (= M2 N)) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (= X2 Y2)) (or (@ (@ tptp.ord_less_nat Y2) X2) (@ (@ tptp.ord_less_nat X2) Y2)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((Xs tptp.list_nat)) (= (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 _let_2)) (@ _let_1 I2)))))))) (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (forall ((I tptp.nat)) (@ (@ P I) (@ tptp.suc I))) (=> (forall ((I tptp.nat) (J3 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I))) (=> (@ (@ tptp.ord_less_nat I) J3) (=> (@ (@ tptp.ord_less_nat J3) K2) (=> (@ _let_1 J3) (=> (@ (@ P J3) K2) (@ _let_1 K2))))))) (@ (@ P I3) J2))))) (forall ((F (-> tptp.nat tptp.nat)) (I3 tptp.nat) (J2 tptp.nat)) (=> (forall ((I tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J3) (@ (@ tptp.ord_less_nat (@ F I)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ F J2))))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ P I3) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J2))))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((M2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M2) K) (@ (@ tptp.minus_minus_nat N) K)) (=> (@ (@ tptp.ord_less_nat K) N) (= M2 N)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B))))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) (@ tptp.rev_a Ys)) (= Xs Ys))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((Xs tptp.list_nat) (N tptp.nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ (@ tptp.listIn923761578nd_nat Xs) F) N) (@ F (@ (@ tptp.minus_minus_nat N) _let_1)))))) (= (lambda ((Y tptp.list_a) (Z tptp.list_a)) (= Y Z)) (lambda ((Xs2 tptp.list_a) (Ys2 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs2) (@ tptp.size_size_list_a Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs2)) (= (@ (@ tptp.nth_a Xs2) I2) (@ (@ tptp.nth_a Ys2) I2))))))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ (@ tptp.ord_less_nat X2) Z2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= X2 Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) (= tptp.ord_less_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (and (not (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (= (= (@ (@ tptp.listIn923761578nd_nat Xs) F) (@ (@ tptp.listIn923761578nd_nat Ys) G)) (and (= F G) (= Xs Ys))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I) (@ (@ tptp.nth_nat Ys) I)))) (= Xs Ys)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) _let_14 (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((I3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I3)) K) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (not (= K (@ tptp.suc J3)))))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys3)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (= tptp.list_desc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2))))))))) (= tptp.ord_less_eq_nat (lambda ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4))))) (forall ((N tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M2)) (= (@ _let_1 (@ tptp.suc M2)) (= N M2))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4))))) (forall ((Xs tptp.list_nat)) (= (@ tptp.rev_nat (@ tptp.rev_nat Xs)) Xs)) (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.nat)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_nat)) (and (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_nat Xs2) I2)))) (= (@ tptp.size_size_list_nat Xs2) K))))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) A2)))) (forall ((N tptp.nat) (Xs tptp.list_nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (= (@ (@ (@ tptp.listIn923761578nd_nat Xs) F) N) (@ (@ tptp.nth_nat Xs) N)))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (@ (@ tptp.ord_less_eq_nat X5) T))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (or (= M2 N) (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) _let_13 (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T)))))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (not (= A2 B2))))) (forall ((I3 tptp.nat) (J2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I3))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat J2) M2)) (@ _let_1 J2)))) (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y2) X2)) (@ (@ tptp.ord_less_nat X2) Y2))) (forall ((I3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (=> (not (= K (@ tptp.suc I3))) (not (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J3) (not (= K (@ tptp.suc J3))))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat N) M2))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4)))))))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (forall ((J4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J4) (@ tptp.size_size_list_nat Xs)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J4) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J4))))))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= Y2 X2)))) (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (or (= A2 B2) (@ (@ tptp.ord_less_nat A2) B2)))) (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (forall ((I tptp.nat)) (=> (= J2 (@ tptp.suc I)) (@ P I))) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (=> (@ P (@ tptp.suc I)) (@ P I)))) (@ P I3))))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat Y3) X3) (@ (@ tptp.ord_less_eq_nat X3) Y3)))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X4) (@ P Y5))) (@ P X4))) (@ P A))) (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I3 tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I3))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ P A3) B3))) (=> (forall ((A3 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A3) (@ (@ P A3) B3))) (@ (@ P A) B)))) (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M2) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M2) N)))))) (forall ((P (-> tptp.a Bool)) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.list_ex_a P))) (= (@ _let_1 (@ tptp.rev_a Xs)) (@ _let_1 Xs)))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (or (@ P X5) (@ Q X5)) (or (@ Q2 X5) (@ P4 X5))))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.a Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X tptp.a)) (@ (@ P I2) X)))) (exists ((Xs2 tptp.list_a)) (and (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_a Xs2) I2)))) (= (@ tptp.size_size_list_a Xs2) K))))) _let_12 (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (not (@ (@ tptp.ord_less_nat X2) Y2)))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ _let_1 (@ F C))))))) _let_11 (forall ((Xs tptp.list_a) (Ys tptp.list_a) (F (-> tptp.nat tptp.a)) (G (-> tptp.nat tptp.a))) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (= (= (@ (@ tptp.listIn1312259492pend_a Xs) F) (@ (@ tptp.listIn1312259492pend_a Ys) G)) (and (= Xs Ys) (= F G))))) (forall ((N tptp.nat) (K tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M2) K)) (@ (@ tptp.ord_less_nat N) M2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat Y2) X2) (@ (@ tptp.ord_less_eq_nat X2) Y2))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)))) (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat K))) (=> (= (@ _let_1 M2) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat M2) K) (= M2 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M2))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (or (= M2 _let_2) (@ _let_1 N)))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (= (not (@ (@ tptp.ord_less_nat X2) Y2)) (= X2 Y2)))) (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (not (@ (@ tptp.ord_less_eq_nat Y3) X3))))) (forall ((N tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rev_nat Xs)) N) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) _let_10 (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (N2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) A2) (not (= N2 X3)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M2) N))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((Xs tptp.list_a)) (= (@ tptp.size_size_list_a (@ tptp.rev_a Xs)) (@ tptp.size_size_list_a Xs))) (= tptp.linorder_sorted_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J)))))))) _let_9 (forall ((X2 tptp.nat) (Y2 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y2) (=> (@ (@ tptp.ord_less_nat Y2) Z2) (@ _let_1 Z2))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (= X5 T)))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M2))) (=> (@ (@ tptp.ord_less_nat M2) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (A2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) X3) (not (= N2 X3)))))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))) _let_8 (forall ((Y2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y2) (= X2 Y2)))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((M2 tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y4) (=> (@ (@ R Y4) Z3) (@ _let_1 Z3))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M2) N)))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M2)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (or (@ Q X5) (@ P X5)) (or (@ P4 X5) (@ Q2 X5))))))))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) _let_7 (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_eq_nat Y2) X2))) (= tptp.linorder_sorted_nat (lambda ((Xs2 tptp.list_nat)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (let ((_let_2 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.ord_less_eq_nat (@ _let_2 I2)) (@ _let_2 _let_1)))))))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (= M2 N) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (=> (not (= X2 Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (=> (@ (@ tptp.ord_less_nat Y2) X2) P))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) _let_6 (forall ((I3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (= (@ _let_1 (@ _let_1 I3)) I3)))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_nat T) X5)))))) (forall ((X2 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_1))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (forall ((Xs3 tptp.list_a)) (=> (forall ((Ys3 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Ys3)) (@ tptp.size_size_list_a Xs3)) (@ P Ys3))) (@ P Xs3))) (@ P Xs))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T)))))) (forall ((N tptp.nat) (Xs tptp.list_a)) (let ((_let_1 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ (@ tptp.nth_a (@ tptp.rev_a Xs)) N) (@ (@ tptp.nth_a Xs) (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc N))))))) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M2))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M2))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M2))))))) (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= A2 B2))))) (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I3))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J2)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J2)))) (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (N2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) A2) (not (= N2 X3)))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (or (= X2 Y2) (@ (@ tptp.ord_less_nat X2) Y2)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys))) (not (= Xs Ys)))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N3) (not (@ P M3)))))) (@ P N))) (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J2) (=> (@ (@ tptp.ord_less_eq_nat J2) K) (@ _let_1 K))))) (= tptp.list_asc_nat tptp.linorder_sorted_nat) (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat K))) (=> (= (@ _let_1 M2) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat N) K) (= M2 N))))) (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y3) (= X3 Y3)))) (forall ((M2 tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M2)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M2) N)) K))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))) (forall ((M2 tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M2) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((N tptp.nat) (M2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M2)) (@ (@ tptp.ord_less_eq_nat N) M2))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M2 N))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M2))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M2 N))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (@ (@ tptp.ord_less_nat T) X5))))) (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (not (= X3 Y3))))) _let_5 (forall ((I3 tptp.nat) (J2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I3)) K)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (not (= X2 Y2)) (=> (not (@ (@ tptp.ord_less_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M2) N))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y4)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (= tptp.list_asc_nat (lambda ((Xs2 tptp.list_nat)) (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))) (= (lambda ((Y tptp.nat) (Z tptp.nat)) (= Y Z)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat X2) Y2))) (forall ((I3 tptp.nat) (J2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ P J2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N3) (=> (@ (@ tptp.ord_less_nat N3) J2) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I3))))) _let_4 (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))) (forall ((M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M2 _let_1)))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= (@ tptp.rev_nat Xs) (@ tptp.rev_nat Ys)) (= Xs Ys))) (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (A2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) X3) (not (= N2 X3)))))) _let_3 (forall ((J2 tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J2) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J2) N)) K))) _let_2 (forall ((K tptp.nat) (M2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat K))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M2)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M2) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_eq_nat M2) N))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))) (forall ((Xs tptp.list_nat) (I3 tptp.nat) (J2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ tptp.linorder_sorted_nat Xs) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I3)) (@ _let_1 J2))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (and (@ Q X5) (@ P X5)) (and (@ Q2 X5) (@ P4 X5))))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))) (forall ((Xs tptp.list_a) (N tptp.nat) (F (-> tptp.nat tptp.a))) (let ((_let_1 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ (@ tptp.listIn1312259492pend_a Xs) F) N) (@ F (@ (@ tptp.minus_minus_nat N) _let_1)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y2)) (@ (@ tptp.ord_less_nat Y2) X2))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat Y2) X2) (= X2 Y2))) (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (= M2 N)) (or (@ (@ tptp.ord_less_nat N) M2) (@ (@ tptp.ord_less_nat M2) N)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) Ys) (= Xs (@ tptp.rev_a Ys)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))) (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_a)) (= (@ tptp.size_size_list_a Xs3) N))) (forall ((X2 tptp.list_nat) (Y2 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y2))) (not (= X2 Y2)))) (forall ((Xs tptp.list_a)) (= (@ tptp.rev_a (@ tptp.rev_a Xs)) Xs)) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (not (= X2 Y2)))) (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))) (forall ((Xs tptp.list_nat)) (= (@ tptp.linorder_sorted_nat (@ tptp.rev_nat Xs)) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 I2)))))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (= (lambda ((Y tptp.list_nat) (Z tptp.list_nat)) (= Y Z)) (lambda ((Xs2 tptp.list_nat) (Ys2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys2)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I2) (@ (@ tptp.nth_nat Ys2) I2))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((X2 tptp.list_a) (Y2 tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a X2) (@ tptp.size_size_list_a Y2))) (not (= X2 Y2)))) (forall ((Xs tptp.list_nat)) (=> (@ tptp.list_strict_asc_nat Xs) (@ tptp.list_asc_nat Xs))) (forall ((A tptp.nat) (B tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)) (= A B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (not (@ (@ tptp.ord_less_nat X5) T)))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((Z4 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X4) (= (@ Q X4) (@ Q2 X4))))) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (and (@ P X5) (@ Q X5)) (and (@ Q2 X5) (@ P4 X5))))))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2))) (@ P N)))) (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (=> (@ (@ tptp.ord_less_eq_nat Y2) X2) (= X2 Y2)))) (forall ((M2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M2)) N) (@ (@ tptp.ord_less_nat M2) N))) _let_1 (forall ((M2 tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M2) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (not (= X5 T)))))) (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M3)) N3) (@ P M3))) (@ P N3))) (@ P N))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 11.51/11.73 ) 11.51/11.73 % SZS output end Proof for 11.51/11.73 % cvc5---1.0.5 exiting 11.51/11.73 % cvc5---1.0.5 exiting 11.51/11.73 EOF