TSTP Solution File: ITP125^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP125^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:27 EDT 2023
% Result : Theorem 0.90s 1.12s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.16 % Problem : ITP125^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.17 % Command : do_cvc5 %s %d
% 0.16/0.38 % Computer : n003.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sun Aug 27 16:50:09 EDT 2023
% 0.25/0.38 % CPUTime :
% 0.25/0.55 %----Proving TH0
% 0.25/0.55 %------------------------------------------------------------------------------
% 0.25/0.55 % File : ITP125^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.55 % Domain : Interactive Theorem Proving
% 0.25/0.55 % Problem : Sledgehammer Monitor problem prob_453__6453916_1
% 0.25/0.55 % Version : Especial.
% 0.25/0.55 % English :
% 0.25/0.55
% 0.25/0.55 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.55 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.55 % Source : [Des21]
% 0.25/0.55 % Names : Monitor/prob_453__6453916_1 [Des21]
% 0.25/0.55
% 0.25/0.55 % Status : Theorem
% 0.25/0.55 % Rating : 0.23 v8.1.0, 0.27 v7.5.0
% 0.25/0.55 % Syntax : Number of formulae : 315 ( 83 unt; 31 typ; 0 def)
% 0.25/0.55 % Number of atoms : 823 ( 183 equ; 0 cnn)
% 0.25/0.55 % Maximal formula atoms : 12 ( 2 avg)
% 0.25/0.55 % Number of connectives : 2451 ( 87 ~; 25 |; 40 &;1887 @)
% 0.25/0.55 % ( 0 <=>; 412 =>; 0 <=; 0 <~>)
% 0.25/0.55 % Maximal formula depth : 18 ( 8 avg)
% 0.25/0.55 % Number of types : 7 ( 6 usr)
% 0.25/0.55 % Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% 0.25/0.55 % Number of symbols : 26 ( 25 usr; 14 con; 0-4 aty)
% 0.25/0.55 % Number of variables : 866 ( 67 ^; 764 !; 35 ?; 866 :)
% 0.25/0.55 % SPC : TH0_THM_EQU_NAR
% 0.25/0.55
% 0.25/0.55 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:11.449
% 0.25/0.55 %------------------------------------------------------------------------------
% 0.25/0.55 % Could-be-implicit typings (6)
% 0.25/0.55 thf(ty_n_t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.25/0.55 prefix1027212443list_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__Trace__Otrace_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.25/0.55 trace_1367752404list_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__Interval__O__092__060I__062,type,
% 0.25/0.55 i: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__MFOTL__Oformula_Itf__a_J,type,
% 0.25/0.55 formula_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.25/0.55 list_a: $tType ).
% 0.25/0.55
% 0.25/0.55 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.55 nat: $tType ).
% 0.25/0.55
% 0.25/0.55 % Explicit typings (25)
% 0.25/0.55 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.25/0.55 one_one_nat: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.25/0.55 plus_plus_nat: nat > nat > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_MFOTL_Oformula_OUntil_001tf__a,type,
% 0.25/0.55 until_a: formula_a > i > formula_a > formula_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_MFOTL_Osat_001tf__a,type,
% 0.25/0.55 sat_a: trace_1367752404list_a > list_a > nat > formula_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Monitor__Mirabelle__prbptmgypa_Oprogress_001tf__a,type,
% 0.25/0.55 monito1457594016ress_a: trace_1367752404list_a > formula_a > nat > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.25/0.55 ord_less_nat: nat > nat > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.25/0.55 ord_le887097159list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.25/0.55 ord_less_eq_nat: nat > nat > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Trace__Oprefix_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J_J,type,
% 0.25/0.55 ord_le699472955list_a: prefix1027212443list_a > prefix1027212443list_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Trace_O_092_060tau_062_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.25/0.55 tau_Pr257024512list_a: trace_1367752404list_a > nat > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Trace_Oplen_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.25/0.55 plen_P694648887list_a: prefix1027212443list_a > nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_c_Trace_Oprefix__of_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_Itf__a_J_J,type,
% 0.25/0.55 prefix1041802747list_a: prefix1027212443list_a > trace_1367752404list_a > $o ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_I____,type,
% 0.25/0.55 i2: i ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v__092_060phi_062,type,
% 0.25/0.55 phi: formula_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v__092_060phi_0621____,type,
% 0.25/0.55 phi_1: formula_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v__092_060phi_0622____,type,
% 0.25/0.55 phi_2: formula_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v__092_060pi_062,type,
% 0.25/0.55 pi: prefix1027212443list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v__092_060sigma_062,type,
% 0.25/0.55 sigma: trace_1367752404list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v__092_060sigma_062_H,type,
% 0.25/0.55 sigma2: trace_1367752404list_a ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_b____,type,
% 0.25/0.55 b: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_i,type,
% 0.25/0.55 i3: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_ia____,type,
% 0.25/0.55 ia: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_j____,type,
% 0.25/0.55 j: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_ja____,type,
% 0.25/0.55 ja: nat ).
% 0.25/0.55
% 0.25/0.55 thf(sy_v_k____,type,
% 0.25/0.55 k: nat ).
% 0.25/0.55
% 0.25/0.55 % Relevant facts (283)
% 0.25/0.55 thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.25/0.55 ord_less_nat @ k @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.55
% 0.25/0.55 % \<open>k < Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>1 (plen \<pi>)\<close>
% 0.25/0.55 thf(fact_1_assms_I3_J,axiom,
% 0.25/0.55 ord_less_nat @ i3 @ ( monito1457594016ress_a @ sigma @ phi @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.55
% 0.25/0.55 % assms(3)
% 0.25/0.55 thf(fact_2_assms_I1_J,axiom,
% 0.25/0.55 prefix1041802747list_a @ pi @ sigma ).
% 0.25/0.55
% 0.25/0.55 % assms(1)
% 0.25/0.55 thf(fact_3_nat__neq__iff,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( M != N )
% 0.25/0.55 = ( ( ord_less_nat @ M @ N )
% 0.25/0.55 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % nat_neq_iff
% 0.25/0.55 thf(fact_4_less__not__refl,axiom,
% 0.25/0.55 ! [N: nat] :
% 0.25/0.55 ~ ( ord_less_nat @ N @ N ) ).
% 0.25/0.55
% 0.25/0.55 % less_not_refl
% 0.25/0.55 thf(fact_5_less__not__refl2,axiom,
% 0.25/0.55 ! [N: nat,M: nat] :
% 0.25/0.55 ( ( ord_less_nat @ N @ M )
% 0.25/0.55 => ( M != N ) ) ).
% 0.25/0.55
% 0.25/0.55 % less_not_refl2
% 0.25/0.55 thf(fact_6_less__not__refl3,axiom,
% 0.25/0.55 ! [S: nat,T: nat] :
% 0.25/0.55 ( ( ord_less_nat @ S @ T )
% 0.25/0.55 => ( S != T ) ) ).
% 0.25/0.55
% 0.25/0.55 % less_not_refl3
% 0.25/0.55 thf(fact_7_less__irrefl__nat,axiom,
% 0.25/0.55 ! [N: nat] :
% 0.25/0.55 ~ ( ord_less_nat @ N @ N ) ).
% 0.25/0.55
% 0.25/0.55 % less_irrefl_nat
% 0.25/0.55 thf(fact_8_nat__less__induct,axiom,
% 0.25/0.55 ! [P: nat > $o,N: nat] :
% 0.25/0.55 ( ! [N2: nat] :
% 0.25/0.55 ( ! [M2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.55 => ( P @ M2 ) )
% 0.25/0.55 => ( P @ N2 ) )
% 0.25/0.55 => ( P @ N ) ) ).
% 0.25/0.55
% 0.25/0.55 % nat_less_induct
% 0.25/0.55 thf(fact_9_infinite__descent,axiom,
% 0.25/0.55 ! [P: nat > $o,N: nat] :
% 0.25/0.55 ( ! [N2: nat] :
% 0.25/0.55 ( ~ ( P @ N2 )
% 0.25/0.55 => ? [M2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.55 & ~ ( P @ M2 ) ) )
% 0.25/0.55 => ( P @ N ) ) ).
% 0.25/0.55
% 0.25/0.55 % infinite_descent
% 0.25/0.55 thf(fact_10_linorder__neqE__nat,axiom,
% 0.25/0.55 ! [X: nat,Y: nat] :
% 0.25/0.55 ( ( X != Y )
% 0.25/0.55 => ( ~ ( ord_less_nat @ X @ Y )
% 0.25/0.55 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % linorder_neqE_nat
% 0.25/0.55 thf(fact_11__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.25/0.55 ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.55
% 0.25/0.55 % \<open>j__ \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>1 (plen \<pi>)\<close>
% 0.25/0.55 thf(fact_12_assms_I2_J,axiom,
% 0.25/0.55 prefix1041802747list_a @ pi @ sigma2 ).
% 0.25/0.55
% 0.25/0.55 % assms(2)
% 0.25/0.55 thf(fact_13__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.25/0.55 ord_less_eq_nat @ j @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.55
% 0.25/0.55 % \<open>j__ \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>2 (plen \<pi>)\<close>
% 0.25/0.55 thf(fact_14_le__refl,axiom,
% 0.25/0.55 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.25/0.55
% 0.25/0.55 % le_refl
% 0.25/0.55 thf(fact_15_le__trans,axiom,
% 0.25/0.55 ! [I: nat,J: nat,K: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.55 => ( ( ord_less_eq_nat @ J @ K )
% 0.25/0.55 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % le_trans
% 0.25/0.55 thf(fact_16_eq__imp__le,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( M = N )
% 0.25/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.25/0.55
% 0.25/0.55 % eq_imp_le
% 0.25/0.55 thf(fact_17_le__antisym,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.25/0.55 => ( ( ord_less_eq_nat @ N @ M )
% 0.25/0.55 => ( M = N ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % le_antisym
% 0.25/0.55 thf(fact_18_nat__le__linear,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.25/0.55 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.25/0.55
% 0.25/0.55 % nat_le_linear
% 0.25/0.55 thf(fact_19_Nat_Oex__has__greatest__nat,axiom,
% 0.25/0.55 ! [P: nat > $o,K: nat,B: nat] :
% 0.25/0.55 ( ( P @ K )
% 0.25/0.55 => ( ! [Y2: nat] :
% 0.25/0.55 ( ( P @ Y2 )
% 0.25/0.55 => ( ord_less_eq_nat @ Y2 @ B ) )
% 0.25/0.55 => ? [X2: nat] :
% 0.25/0.55 ( ( P @ X2 )
% 0.25/0.55 & ! [Y3: nat] :
% 0.25/0.55 ( ( P @ Y3 )
% 0.25/0.55 => ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % Nat.ex_has_greatest_nat
% 0.25/0.55 thf(fact_20_progress__le,axiom,
% 0.25/0.55 ! [Sigma: trace_1367752404list_a,Phi: formula_a,J: nat] : ( ord_less_eq_nat @ ( monito1457594016ress_a @ Sigma @ Phi @ J ) @ J ) ).
% 0.25/0.55
% 0.25/0.55 % progress_le
% 0.25/0.55 thf(fact_21_progress__mono,axiom,
% 0.25/0.55 ! [J: nat,J2: nat,Sigma: trace_1367752404list_a,Phi: formula_a] :
% 0.25/0.55 ( ( ord_less_eq_nat @ J @ J2 )
% 0.25/0.55 => ( ord_less_eq_nat @ ( monito1457594016ress_a @ Sigma @ Phi @ J ) @ ( monito1457594016ress_a @ Sigma @ Phi @ J2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % progress_mono
% 0.25/0.55 thf(fact_22_pinf_I6_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ X3 @ T ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(6)
% 0.25/0.55 thf(fact_23_pinf_I8_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ( ord_less_eq_nat @ T @ X3 ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(8)
% 0.25/0.55 thf(fact_24_minf_I6_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ( ord_less_eq_nat @ X3 @ T ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(6)
% 0.25/0.55 thf(fact_25_minf_I8_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ T @ X3 ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(8)
% 0.25/0.55 thf(fact_26_less__mono__imp__le__mono,axiom,
% 0.25/0.55 ! [F: nat > nat,I: nat,J: nat] :
% 0.25/0.55 ( ! [I2: nat,J3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ I2 @ J3 )
% 0.25/0.55 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J3 ) ) )
% 0.25/0.55 => ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % less_mono_imp_le_mono
% 0.25/0.55 thf(fact_27_le__neq__implies__less,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.25/0.55 => ( ( M != N )
% 0.25/0.55 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % le_neq_implies_less
% 0.25/0.55 thf(fact_28_less__or__eq__imp__le,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( ( ord_less_nat @ M @ N )
% 0.25/0.55 | ( M = N ) )
% 0.25/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.25/0.55
% 0.25/0.55 % less_or_eq_imp_le
% 0.25/0.55 thf(fact_29_le__eq__less__or__eq,axiom,
% 0.25/0.55 ( ord_less_eq_nat
% 0.25/0.55 = ( ^ [M3: nat,N3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ M3 @ N3 )
% 0.25/0.55 | ( M3 = N3 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % le_eq_less_or_eq
% 0.25/0.55 thf(fact_30_less__imp__le__nat,axiom,
% 0.25/0.55 ! [M: nat,N: nat] :
% 0.25/0.55 ( ( ord_less_nat @ M @ N )
% 0.25/0.55 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.25/0.55
% 0.25/0.55 % less_imp_le_nat
% 0.25/0.55 thf(fact_31_nat__less__le,axiom,
% 0.25/0.55 ( ord_less_nat
% 0.25/0.55 = ( ^ [M3: nat,N3: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.25/0.55 & ( M3 != N3 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % nat_less_le
% 0.25/0.55 thf(fact_32_progress__prefix__conv,axiom,
% 0.25/0.55 ! [Pi: prefix1027212443list_a,Sigma: trace_1367752404list_a,Sigma2: trace_1367752404list_a,Phi: formula_a] :
% 0.25/0.55 ( ( prefix1041802747list_a @ Pi @ Sigma )
% 0.25/0.55 => ( ( prefix1041802747list_a @ Pi @ Sigma2 )
% 0.25/0.55 => ( ( monito1457594016ress_a @ Sigma @ Phi @ ( plen_P694648887list_a @ Pi ) )
% 0.25/0.55 = ( monito1457594016ress_a @ Sigma2 @ Phi @ ( plen_P694648887list_a @ Pi ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % progress_prefix_conv
% 0.25/0.55 thf(fact_33_pinf_I1_J,axiom,
% 0.25/0.55 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.25/0.55 ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z2 @ X2 )
% 0.25/0.55 => ( ( P @ X2 )
% 0.25/0.55 = ( P2 @ X2 ) ) )
% 0.25/0.55 => ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z2 @ X2 )
% 0.25/0.55 => ( ( Q @ X2 )
% 0.25/0.55 = ( Q2 @ X2 ) ) )
% 0.25/0.55 => ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ( ( ( P @ X3 )
% 0.25/0.55 & ( Q @ X3 ) )
% 0.25/0.55 = ( ( P2 @ X3 )
% 0.25/0.55 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(1)
% 0.25/0.55 thf(fact_34_pinf_I2_J,axiom,
% 0.25/0.55 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.25/0.55 ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z2 @ X2 )
% 0.25/0.55 => ( ( P @ X2 )
% 0.25/0.55 = ( P2 @ X2 ) ) )
% 0.25/0.55 => ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z2 @ X2 )
% 0.25/0.55 => ( ( Q @ X2 )
% 0.25/0.55 = ( Q2 @ X2 ) ) )
% 0.25/0.55 => ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ( ( ( P @ X3 )
% 0.25/0.55 | ( Q @ X3 ) )
% 0.25/0.55 = ( ( P2 @ X3 )
% 0.25/0.55 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(2)
% 0.25/0.55 thf(fact_35_pinf_I3_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ( X3 != T ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(3)
% 0.25/0.55 thf(fact_36_pinf_I4_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ( X3 != T ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(4)
% 0.25/0.55 thf(fact_37_pinf_I5_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ~ ( ord_less_nat @ X3 @ T ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(5)
% 0.25/0.55 thf(fact_38_pinf_I7_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ Z @ X3 )
% 0.25/0.55 => ( ord_less_nat @ T @ X3 ) ) ).
% 0.25/0.55
% 0.25/0.55 % pinf(7)
% 0.25/0.55 thf(fact_39_minf_I1_J,axiom,
% 0.25/0.55 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.25/0.55 ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X2 @ Z2 )
% 0.25/0.55 => ( ( P @ X2 )
% 0.25/0.55 = ( P2 @ X2 ) ) )
% 0.25/0.55 => ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X2 @ Z2 )
% 0.25/0.55 => ( ( Q @ X2 )
% 0.25/0.55 = ( Q2 @ X2 ) ) )
% 0.25/0.55 => ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ( ( ( P @ X3 )
% 0.25/0.55 & ( Q @ X3 ) )
% 0.25/0.55 = ( ( P2 @ X3 )
% 0.25/0.55 & ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(1)
% 0.25/0.55 thf(fact_40_minf_I2_J,axiom,
% 0.25/0.55 ! [P: nat > $o,P2: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.25/0.55 ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X2 @ Z2 )
% 0.25/0.55 => ( ( P @ X2 )
% 0.25/0.55 = ( P2 @ X2 ) ) )
% 0.25/0.55 => ( ? [Z2: nat] :
% 0.25/0.55 ! [X2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X2 @ Z2 )
% 0.25/0.55 => ( ( Q @ X2 )
% 0.25/0.55 = ( Q2 @ X2 ) ) )
% 0.25/0.55 => ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ( ( ( P @ X3 )
% 0.25/0.55 | ( Q @ X3 ) )
% 0.25/0.55 = ( ( P2 @ X3 )
% 0.25/0.55 | ( Q2 @ X3 ) ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(2)
% 0.25/0.55 thf(fact_41_minf_I3_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ( X3 != T ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(3)
% 0.25/0.55 thf(fact_42_minf_I4_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ( X3 != T ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(4)
% 0.25/0.55 thf(fact_43_minf_I5_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ( ord_less_nat @ X3 @ T ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(5)
% 0.25/0.55 thf(fact_44_minf_I7_J,axiom,
% 0.25/0.55 ! [T: nat] :
% 0.25/0.55 ? [Z: nat] :
% 0.25/0.55 ! [X3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ X3 @ Z )
% 0.25/0.55 => ~ ( ord_less_nat @ T @ X3 ) ) ).
% 0.25/0.55
% 0.25/0.55 % minf(7)
% 0.25/0.55 thf(fact_45__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.25/0.55 ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.55
% 0.25/0.55 % \<open>j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>1 (plen \<pi>)\<close>
% 0.25/0.55 thf(fact_46_order__refl,axiom,
% 0.25/0.55 ! [X: prefix1027212443list_a] : ( ord_le699472955list_a @ X @ X ) ).
% 0.25/0.55
% 0.25/0.55 % order_refl
% 0.25/0.55 thf(fact_47_order__refl,axiom,
% 0.25/0.55 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.25/0.55
% 0.25/0.55 % order_refl
% 0.25/0.55 thf(fact_48_Until_OIH_I1_J,axiom,
% 0.25/0.55 ! [I: nat,V: list_a] :
% 0.25/0.55 ( ( ord_less_nat @ I @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.25/0.55 => ( ( sat_a @ sigma @ V @ I @ phi_1 )
% 0.25/0.55 = ( sat_a @ sigma2 @ V @ I @ phi_1 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % Until.IH(1)
% 0.25/0.55 thf(fact_49_nat__descend__induct,axiom,
% 0.25/0.55 ! [N: nat,P: nat > $o,M: nat] :
% 0.25/0.55 ( ! [K2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ N @ K2 )
% 0.25/0.55 => ( P @ K2 ) )
% 0.25/0.55 => ( ! [K2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ K2 @ N )
% 0.25/0.55 => ( ! [I3: nat] :
% 0.25/0.55 ( ( ord_less_nat @ K2 @ I3 )
% 0.25/0.55 => ( P @ I3 ) )
% 0.25/0.55 => ( P @ K2 ) ) )
% 0.25/0.55 => ( P @ M ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % nat_descend_induct
% 0.25/0.55 thf(fact_50_complete__interval,axiom,
% 0.25/0.55 ! [A: nat,B: nat,P: nat > $o] :
% 0.25/0.55 ( ( ord_less_nat @ A @ B )
% 0.25/0.55 => ( ( P @ A )
% 0.25/0.55 => ( ~ ( P @ B )
% 0.25/0.55 => ? [C: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A @ C )
% 0.25/0.55 & ( ord_less_eq_nat @ C @ B )
% 0.25/0.55 & ! [X3: nat] :
% 0.25/0.55 ( ( ( ord_less_eq_nat @ A @ X3 )
% 0.25/0.55 & ( ord_less_nat @ X3 @ C ) )
% 0.25/0.55 => ( P @ X3 ) )
% 0.25/0.55 & ! [D: nat] :
% 0.25/0.55 ( ! [X2: nat] :
% 0.25/0.55 ( ( ( ord_less_eq_nat @ A @ X2 )
% 0.25/0.55 & ( ord_less_nat @ X2 @ D ) )
% 0.25/0.55 => ( P @ X2 ) )
% 0.25/0.55 => ( ord_less_eq_nat @ D @ C ) ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % complete_interval
% 0.25/0.55 thf(fact_51_order_Onot__eq__order__implies__strict,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.25/0.55 ( ( A != B )
% 0.25/0.55 => ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( ord_le887097159list_a @ A @ B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order.not_eq_order_implies_strict
% 0.25/0.55 thf(fact_52_order_Onot__eq__order__implies__strict,axiom,
% 0.25/0.55 ! [A: nat,B: nat] :
% 0.25/0.55 ( ( A != B )
% 0.25/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order.not_eq_order_implies_strict
% 0.25/0.55 thf(fact_53_dual__order_Ostrict__implies__order,axiom,
% 0.25/0.55 ! [B: prefix1027212443list_a,A: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le887097159list_a @ B @ A )
% 0.25/0.55 => ( ord_le699472955list_a @ B @ A ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.strict_implies_order
% 0.25/0.55 thf(fact_54_dual__order_Ostrict__implies__order,axiom,
% 0.25/0.55 ! [B: nat,A: nat] :
% 0.25/0.55 ( ( ord_less_nat @ B @ A )
% 0.25/0.55 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.strict_implies_order
% 0.25/0.55 thf(fact_55_dual__order_Ostrict__iff__order,axiom,
% 0.25/0.55 ( ord_le887097159list_a
% 0.25/0.55 = ( ^ [B2: prefix1027212443list_a,A2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ B2 @ A2 )
% 0.25/0.55 & ( A2 != B2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.strict_iff_order
% 0.25/0.55 thf(fact_56_dual__order_Ostrict__iff__order,axiom,
% 0.25/0.55 ( ord_less_nat
% 0.25/0.55 = ( ^ [B2: nat,A2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.25/0.55 & ( A2 != B2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.strict_iff_order
% 0.25/0.55 thf(fact_57_dual__order_Oorder__iff__strict,axiom,
% 0.25/0.55 ( ord_le699472955list_a
% 0.25/0.55 = ( ^ [B2: prefix1027212443list_a,A2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le887097159list_a @ B2 @ A2 )
% 0.25/0.55 | ( A2 = B2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.order_iff_strict
% 0.25/0.55 thf(fact_58_dual__order_Oorder__iff__strict,axiom,
% 0.25/0.55 ( ord_less_eq_nat
% 0.25/0.55 = ( ^ [B2: nat,A2: nat] :
% 0.25/0.55 ( ( ord_less_nat @ B2 @ A2 )
% 0.25/0.55 | ( A2 = B2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.order_iff_strict
% 0.25/0.55 thf(fact_59_order_Ostrict__implies__order,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le887097159list_a @ A @ B )
% 0.25/0.55 => ( ord_le699472955list_a @ A @ B ) ) ).
% 0.25/0.55
% 0.25/0.55 % order.strict_implies_order
% 0.25/0.55 thf(fact_60_order_Ostrict__implies__order,axiom,
% 0.25/0.55 ! [A: nat,B: nat] :
% 0.25/0.55 ( ( ord_less_nat @ A @ B )
% 0.25/0.55 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.25/0.55
% 0.25/0.55 % order.strict_implies_order
% 0.25/0.55 thf(fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.25/0.55 ord_less_eq_nat @ ja @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.55
% 0.25/0.55 % \<open>j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>2 (plen \<pi>)\<close>
% 0.25/0.55 thf(fact_62_Until_OIH_I2_J,axiom,
% 0.25/0.55 ! [I: nat,V: list_a] :
% 0.25/0.55 ( ( ord_less_nat @ I @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) )
% 0.25/0.55 => ( ( sat_a @ sigma @ V @ I @ phi_2 )
% 0.25/0.55 = ( sat_a @ sigma2 @ V @ I @ phi_2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % Until.IH(2)
% 0.25/0.55 thf(fact_63_dual__order_Oantisym,axiom,
% 0.25/0.55 ! [B: prefix1027212443list_a,A: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ B @ A )
% 0.25/0.55 => ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( A = B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.antisym
% 0.25/0.55 thf(fact_64_dual__order_Oantisym,axiom,
% 0.25/0.55 ! [B: nat,A: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( A = B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.antisym
% 0.25/0.55 thf(fact_65_dual__order_Oeq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.25/0.55 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ B2 @ A2 )
% 0.25/0.55 & ( ord_le699472955list_a @ A2 @ B2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.eq_iff
% 0.25/0.55 thf(fact_66_dual__order_Oeq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.25/0.55 = ( ^ [A2: nat,B2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ B2 @ A2 )
% 0.25/0.55 & ( ord_less_eq_nat @ A2 @ B2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.eq_iff
% 0.25/0.55 thf(fact_67_dual__order_Otrans,axiom,
% 0.25/0.55 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ B @ A )
% 0.25/0.55 => ( ( ord_le699472955list_a @ C2 @ B )
% 0.25/0.55 => ( ord_le699472955list_a @ C2 @ A ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.trans
% 0.25/0.55 thf(fact_68_dual__order_Otrans,axiom,
% 0.25/0.55 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.55 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.25/0.55 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.trans
% 0.25/0.55 thf(fact_69_linorder__wlog,axiom,
% 0.25/0.55 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.25/0.55 ( ! [A3: nat,B3: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.25/0.55 => ( P @ A3 @ B3 ) )
% 0.25/0.55 => ( ! [A3: nat,B3: nat] :
% 0.25/0.55 ( ( P @ B3 @ A3 )
% 0.25/0.55 => ( P @ A3 @ B3 ) )
% 0.25/0.55 => ( P @ A @ B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % linorder_wlog
% 0.25/0.55 thf(fact_70_dual__order_Orefl,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a] : ( ord_le699472955list_a @ A @ A ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.refl
% 0.25/0.55 thf(fact_71_dual__order_Orefl,axiom,
% 0.25/0.55 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.25/0.55
% 0.25/0.55 % dual_order.refl
% 0.25/0.55 thf(fact_72_order__trans,axiom,
% 0.25/0.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.55 => ( ( ord_le699472955list_a @ Y @ Z4 )
% 0.25/0.55 => ( ord_le699472955list_a @ X @ Z4 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order_trans
% 0.25/0.55 thf(fact_73_order__trans,axiom,
% 0.25/0.55 ! [X: nat,Y: nat,Z4: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.55 => ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.25/0.55 => ( ord_less_eq_nat @ X @ Z4 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order_trans
% 0.25/0.55 thf(fact_74_order__class_Oorder_Oantisym,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( ( ord_le699472955list_a @ B @ A )
% 0.25/0.55 => ( A = B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order_class.order.antisym
% 0.25/0.55 thf(fact_75_order__class_Oorder_Oantisym,axiom,
% 0.25/0.55 ! [A: nat,B: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.55 => ( A = B ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order_class.order.antisym
% 0.25/0.55 thf(fact_76_ord__le__eq__trans,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( ( B = C2 )
% 0.25/0.55 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_le_eq_trans
% 0.25/0.55 thf(fact_77_ord__le__eq__trans,axiom,
% 0.25/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( ( B = C2 )
% 0.25/0.55 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_le_eq_trans
% 0.25/0.55 thf(fact_78_ord__eq__le__trans,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( A = B )
% 0.25/0.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.55 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_eq_le_trans
% 0.25/0.55 thf(fact_79_ord__eq__le__trans,axiom,
% 0.25/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.55 ( ( A = B )
% 0.25/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.55 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_eq_le_trans
% 0.25/0.55 thf(fact_80_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.25/0.55 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ A2 @ B2 )
% 0.25/0.55 & ( ord_le699472955list_a @ B2 @ A2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order_class.order.eq_iff
% 0.25/0.55 thf(fact_81_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.25/0.55 = ( ^ [A2: nat,B2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.25/0.55 & ( ord_less_eq_nat @ B2 @ A2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order_class.order.eq_iff
% 0.25/0.55 thf(fact_82_antisym__conv,axiom,
% 0.25/0.55 ! [Y: prefix1027212443list_a,X: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ Y @ X )
% 0.25/0.55 => ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.55 = ( X = Y ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % antisym_conv
% 0.25/0.55 thf(fact_83_antisym__conv,axiom,
% 0.25/0.55 ! [Y: nat,X: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ Y @ X )
% 0.25/0.55 => ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.55 = ( X = Y ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % antisym_conv
% 0.25/0.55 thf(fact_84_le__cases3,axiom,
% 0.25/0.55 ! [X: nat,Y: nat,Z4: nat] :
% 0.25/0.55 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ Y @ Z4 ) )
% 0.25/0.55 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ X @ Z4 ) )
% 0.25/0.55 => ( ( ( ord_less_eq_nat @ X @ Z4 )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ Z4 @ Y ) )
% 0.25/0.55 => ( ( ( ord_less_eq_nat @ Z4 @ Y )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.25/0.55 => ( ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ Z4 @ X ) )
% 0.25/0.55 => ~ ( ( ord_less_eq_nat @ Z4 @ X )
% 0.25/0.55 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % le_cases3
% 0.25/0.55 thf(fact_85_order_Otrans,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.55 => ( ord_le699472955list_a @ A @ C2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order.trans
% 0.25/0.55 thf(fact_86_order_Otrans,axiom,
% 0.25/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.55 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % order.trans
% 0.25/0.55 thf(fact_87_le__cases,axiom,
% 0.25/0.55 ! [X: nat,Y: nat] :
% 0.25/0.55 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.25/0.55 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.25/0.55
% 0.25/0.55 % le_cases
% 0.25/0.55 thf(fact_88_eq__refl,axiom,
% 0.25/0.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.25/0.55 ( ( X = Y )
% 0.25/0.55 => ( ord_le699472955list_a @ X @ Y ) ) ).
% 0.25/0.55
% 0.25/0.55 % eq_refl
% 0.25/0.55 thf(fact_89_eq__refl,axiom,
% 0.25/0.55 ! [X: nat,Y: nat] :
% 0.25/0.55 ( ( X = Y )
% 0.25/0.55 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.25/0.55
% 0.25/0.55 % eq_refl
% 0.25/0.55 thf(fact_90_linear,axiom,
% 0.25/0.55 ! [X: nat,Y: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.55 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.25/0.55
% 0.25/0.55 % linear
% 0.25/0.55 thf(fact_91_antisym,axiom,
% 0.25/0.55 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.55 => ( ( ord_le699472955list_a @ Y @ X )
% 0.25/0.55 => ( X = Y ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % antisym
% 0.25/0.55 thf(fact_92_antisym,axiom,
% 0.25/0.55 ! [X: nat,Y: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.55 => ( ( ord_less_eq_nat @ Y @ X )
% 0.25/0.55 => ( X = Y ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % antisym
% 0.25/0.55 thf(fact_93_eq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y4: prefix1027212443list_a,Z3: prefix1027212443list_a] : ( Y4 = Z3 ) )
% 0.25/0.55 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.25/0.55 & ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % eq_iff
% 0.25/0.55 thf(fact_94_eq__iff,axiom,
% 0.25/0.55 ( ( ^ [Y4: nat,Z3: nat] : ( Y4 = Z3 ) )
% 0.25/0.55 = ( ^ [X4: nat,Y5: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.25/0.55 & ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % eq_iff
% 0.25/0.55 thf(fact_95_ord__le__eq__subst,axiom,
% 0.25/0.55 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( ( ( F @ B )
% 0.25/0.55 = C2 )
% 0.25/0.55 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_le_eq_subst
% 0.25/0.55 thf(fact_96_ord__le__eq__subst,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.25/0.55 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( ( ( F @ B )
% 0.25/0.55 = C2 )
% 0.25/0.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_le_eq_subst
% 0.25/0.55 thf(fact_97_ord__le__eq__subst,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.55 => ( ( ( F @ B )
% 0.25/0.55 = C2 )
% 0.25/0.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_le_eq_subst
% 0.25/0.55 thf(fact_98_ord__le__eq__subst,axiom,
% 0.25/0.55 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.55 => ( ( ( F @ B )
% 0.25/0.55 = C2 )
% 0.25/0.55 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_le_eq_subst
% 0.25/0.55 thf(fact_99_ord__eq__le__subst,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.25/0.55 ( ( A
% 0.25/0.55 = ( F @ B ) )
% 0.25/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.55 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_eq_le_subst
% 0.25/0.55 thf(fact_100_ord__eq__le__subst,axiom,
% 0.25/0.55 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( A
% 0.25/0.55 = ( F @ B ) )
% 0.25/0.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_eq_le_subst
% 0.25/0.55 thf(fact_101_ord__eq__le__subst,axiom,
% 0.25/0.55 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.55 ( ( A
% 0.25/0.55 = ( F @ B ) )
% 0.25/0.55 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.55 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.55 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.55 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.55 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.55
% 0.25/0.55 % ord_eq_le_subst
% 0.25/0.55 thf(fact_102_ord__eq__le__subst,axiom,
% 0.25/0.55 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.25/0.55 ( ( A
% 0.25/0.55 = ( F @ B ) )
% 0.25/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.55 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.55 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.55 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_le_subst
% 0.25/0.56 thf(fact_103_order__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_104_order__subst2,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_105_order__subst2,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.56 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_106_order__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst2
% 0.25/0.56 thf(fact_107_order__subst1,axiom,
% 0.25/0.56 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_108_order__subst1,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_109_order__subst1,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le699472955list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_110_order__subst1,axiom,
% 0.25/0.56 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_subst1
% 0.25/0.56 thf(fact_111_ord__eq__less__subst,axiom,
% 0.25/0.56 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( A
% 0.25/0.56 = ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_subst
% 0.25/0.56 thf(fact_112_ord__less__eq__subst,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ( F @ B )
% 0.25/0.56 = C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_subst
% 0.25/0.56 thf(fact_113_order__less__subst1,axiom,
% 0.25/0.56 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst1
% 0.25/0.56 thf(fact_114_order__less__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_subst2
% 0.25/0.56 thf(fact_115_gt__ex,axiom,
% 0.25/0.56 ! [X: nat] :
% 0.25/0.56 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.25/0.56
% 0.25/0.56 % gt_ex
% 0.25/0.56 thf(fact_116_neqE,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( X != Y )
% 0.25/0.56 => ( ~ ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neqE
% 0.25/0.56 thf(fact_117_neq__iff,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( X != Y )
% 0.25/0.56 = ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % neq_iff
% 0.25/0.56 thf(fact_118_order_Oasym,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.asym
% 0.25/0.56 thf(fact_119_less__imp__neq,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( X != Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_neq
% 0.25/0.56 thf(fact_120_less__asym,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_asym
% 0.25/0.56 thf(fact_121_less__asym_H,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_asym'
% 0.25/0.56 thf(fact_122_less__trans,axiom,
% 0.25/0.56 ! [X: nat,Y: nat,Z4: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ( ord_less_nat @ Y @ Z4 )
% 0.25/0.56 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_trans
% 0.25/0.56 thf(fact_123_less__linear,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 | ( X = Y )
% 0.25/0.56 | ( ord_less_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_linear
% 0.25/0.56 thf(fact_124_less__irrefl,axiom,
% 0.25/0.56 ! [X: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ X @ X ) ).
% 0.25/0.56
% 0.25/0.56 % less_irrefl
% 0.25/0.56 thf(fact_125_ord__eq__less__trans,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_eq_less_trans
% 0.25/0.56 thf(fact_126_ord__less__eq__trans,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( B = C2 )
% 0.25/0.56 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ord_less_eq_trans
% 0.25/0.56 thf(fact_127_dual__order_Oasym,axiom,
% 0.25/0.56 ! [B: nat,A: nat] :
% 0.25/0.56 ( ( ord_less_nat @ B @ A )
% 0.25/0.56 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.asym
% 0.25/0.56 thf(fact_128_less__imp__not__eq,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( X != Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_eq
% 0.25/0.56 thf(fact_129_less__not__sym,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_not_sym
% 0.25/0.56 thf(fact_130_less__induct,axiom,
% 0.25/0.56 ! [P: nat > $o,A: nat] :
% 0.25/0.56 ( ! [X2: nat] :
% 0.25/0.56 ( ! [Y3: nat] :
% 0.25/0.56 ( ( ord_less_nat @ Y3 @ X2 )
% 0.25/0.56 => ( P @ Y3 ) )
% 0.25/0.56 => ( P @ X2 ) )
% 0.25/0.56 => ( P @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_induct
% 0.25/0.56 thf(fact_131_antisym__conv3,axiom,
% 0.25/0.56 ! [Y: nat,X: nat] :
% 0.25/0.56 ( ~ ( ord_less_nat @ Y @ X )
% 0.25/0.56 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv3
% 0.25/0.56 thf(fact_132_less__imp__not__eq2,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( Y != X ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_eq2
% 0.25/0.56 thf(fact_133_less__imp__triv,axiom,
% 0.25/0.56 ! [X: nat,Y: nat,P: $o] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ( ord_less_nat @ Y @ X )
% 0.25/0.56 => P ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_triv
% 0.25/0.56 thf(fact_134_linorder__cases,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ~ ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ( X != Y )
% 0.25/0.56 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_cases
% 0.25/0.56 thf(fact_135_dual__order_Oirrefl,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.irrefl
% 0.25/0.56 thf(fact_136_order_Ostrict__trans,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans
% 0.25/0.56 thf(fact_137_less__imp__not__less,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_not_less
% 0.25/0.56 thf(fact_138_exists__least__iff,axiom,
% 0.25/0.56 ( ( ^ [P3: nat > $o] :
% 0.25/0.56 ? [X5: nat] : ( P3 @ X5 ) )
% 0.25/0.56 = ( ^ [P4: nat > $o] :
% 0.25/0.56 ? [N3: nat] :
% 0.25/0.56 ( ( P4 @ N3 )
% 0.25/0.56 & ! [M3: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M3 @ N3 )
% 0.25/0.56 => ~ ( P4 @ M3 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % exists_least_iff
% 0.25/0.56 thf(fact_139_linorder__less__wlog,axiom,
% 0.25/0.56 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.25/0.56 ( ! [A3: nat,B3: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A3 @ B3 )
% 0.25/0.56 => ( P @ A3 @ B3 ) )
% 0.25/0.56 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 0.25/0.56 => ( ! [A3: nat,B3: nat] :
% 0.25/0.56 ( ( P @ B3 @ A3 )
% 0.25/0.56 => ( P @ A3 @ B3 ) )
% 0.25/0.56 => ( P @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % linorder_less_wlog
% 0.25/0.56 thf(fact_140_dual__order_Ostrict__trans,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ B @ A )
% 0.25/0.56 => ( ( ord_less_nat @ C2 @ B )
% 0.25/0.56 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans
% 0.25/0.56 thf(fact_141_not__less__iff__gr__or__eq,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.25/0.56 = ( ( ord_less_nat @ Y @ X )
% 0.25/0.56 | ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_less_iff_gr_or_eq
% 0.25/0.56 thf(fact_142_order_Ostrict__implies__not__eq,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( A != B ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_implies_not_eq
% 0.25/0.56 thf(fact_143_dual__order_Ostrict__implies__not__eq,axiom,
% 0.25/0.56 ! [B: nat,A: nat] :
% 0.25/0.56 ( ( ord_less_nat @ B @ A )
% 0.25/0.56 => ( A != B ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_implies_not_eq
% 0.25/0.56 thf(fact_144_leD,axiom,
% 0.25/0.56 ! [Y: prefix1027212443list_a,X: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ Y @ X )
% 0.25/0.56 => ~ ( ord_le887097159list_a @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % leD
% 0.25/0.56 thf(fact_145_leD,axiom,
% 0.25/0.56 ! [Y: nat,X: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ Y @ X )
% 0.25/0.56 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % leD
% 0.25/0.56 thf(fact_146_leI,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ~ ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % leI
% 0.25/0.56 thf(fact_147_le__less,axiom,
% 0.25/0.56 ( ord_le699472955list_a
% 0.25/0.56 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ X4 @ Y5 )
% 0.25/0.56 | ( X4 = Y5 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less
% 0.25/0.56 thf(fact_148_le__less,axiom,
% 0.25/0.56 ( ord_less_eq_nat
% 0.25/0.56 = ( ^ [X4: nat,Y5: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X4 @ Y5 )
% 0.25/0.56 | ( X4 = Y5 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less
% 0.25/0.56 thf(fact_149_less__le,axiom,
% 0.25/0.56 ( ord_le887097159list_a
% 0.25/0.56 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.25/0.56 & ( X4 != Y5 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le
% 0.25/0.56 thf(fact_150_less__le,axiom,
% 0.25/0.56 ( ord_less_nat
% 0.25/0.56 = ( ^ [X4: nat,Y5: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.25/0.56 & ( X4 != Y5 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le
% 0.25/0.56 thf(fact_151_order__le__less__subst1,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le887097159list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst1
% 0.25/0.56 thf(fact_152_order__le__less__subst1,axiom,
% 0.25/0.56 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst1
% 0.25/0.56 thf(fact_153_order__le__less__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_le887097159list_a @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst2
% 0.25/0.56 thf(fact_154_order__le__less__subst2,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > nat,C2: nat] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst2
% 0.25/0.56 thf(fact_155_order__le__less__subst2,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.56 => ( ( ord_le887097159list_a @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst2
% 0.25/0.56 thf(fact_156_order__le__less__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_le_less_subst2
% 0.25/0.56 thf(fact_157_order__less__le__subst1,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,F: nat > prefix1027212443list_a,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_le887097159list_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_le_subst1
% 0.25/0.56 thf(fact_158_order__less__le__subst1,axiom,
% 0.25/0.56 ! [A: nat,F: prefix1027212443list_a > nat,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_le_subst1
% 0.25/0.56 thf(fact_159_order__less__le__subst1,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,F: prefix1027212443list_a > prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.56 => ( ! [X2: prefix1027212443list_a,Y2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le699472955list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le887097159list_a @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_le_subst1
% 0.25/0.56 thf(fact_160_order__less__le__subst1,axiom,
% 0.25/0.56 ! [A: nat,F: nat > nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.25/0.56 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_le_subst1
% 0.25/0.56 thf(fact_161_order__less__le__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_le699472955list_a @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_le887097159list_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_le887097159list_a @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_le_subst2
% 0.25/0.56 thf(fact_162_order__less__le__subst2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,F: nat > nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.25/0.56 => ( ! [X2: nat,Y2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X2 @ Y2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.25/0.56 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order_less_le_subst2
% 0.25/0.56 thf(fact_163_not__le,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.25/0.56 = ( ord_less_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_le
% 0.25/0.56 thf(fact_164_not__less,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.25/0.56 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_less
% 0.25/0.56 thf(fact_165_le__neq__trans,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.56 => ( ( A != B )
% 0.25/0.56 => ( ord_le887097159list_a @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_neq_trans
% 0.25/0.56 thf(fact_166_le__neq__trans,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( A != B )
% 0.25/0.56 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_neq_trans
% 0.25/0.56 thf(fact_167_antisym__conv1,axiom,
% 0.25/0.56 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.25/0.56 ( ~ ( ord_le887097159list_a @ X @ Y )
% 0.25/0.56 => ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv1
% 0.25/0.56 thf(fact_168_antisym__conv1,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ~ ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv1
% 0.25/0.56 thf(fact_169_antisym__conv2,axiom,
% 0.25/0.56 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.56 => ( ( ~ ( ord_le887097159list_a @ X @ Y ) )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv2
% 0.25/0.56 thf(fact_170_antisym__conv2,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.56 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.25/0.56 = ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % antisym_conv2
% 0.25/0.56 thf(fact_171_less__imp__le,axiom,
% 0.25/0.56 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ X @ Y )
% 0.25/0.56 => ( ord_le699472955list_a @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_le
% 0.25/0.56 thf(fact_172_less__imp__le,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_imp_le
% 0.25/0.56 thf(fact_173_le__less__trans,axiom,
% 0.25/0.56 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.56 => ( ( ord_le887097159list_a @ Y @ Z4 )
% 0.25/0.56 => ( ord_le887097159list_a @ X @ Z4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less_trans
% 0.25/0.56 thf(fact_174_le__less__trans,axiom,
% 0.25/0.56 ! [X: nat,Y: nat,Z4: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.56 => ( ( ord_less_nat @ Y @ Z4 )
% 0.25/0.56 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less_trans
% 0.25/0.56 thf(fact_175_less__le__trans,axiom,
% 0.25/0.56 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a,Z4: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ X @ Y )
% 0.25/0.56 => ( ( ord_le699472955list_a @ Y @ Z4 )
% 0.25/0.56 => ( ord_le887097159list_a @ X @ Z4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le_trans
% 0.25/0.56 thf(fact_176_less__le__trans,axiom,
% 0.25/0.56 ! [X: nat,Y: nat,Z4: nat] :
% 0.25/0.56 ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 => ( ( ord_less_eq_nat @ Y @ Z4 )
% 0.25/0.56 => ( ord_less_nat @ X @ Z4 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le_trans
% 0.25/0.56 thf(fact_177_le__less__linear,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.56 | ( ord_less_nat @ Y @ X ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_less_linear
% 0.25/0.56 thf(fact_178_le__imp__less__or__eq,axiom,
% 0.25/0.56 ! [X: prefix1027212443list_a,Y: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X @ Y )
% 0.25/0.56 => ( ( ord_le887097159list_a @ X @ Y )
% 0.25/0.56 | ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_imp_less_or_eq
% 0.25/0.56 thf(fact_179_le__imp__less__or__eq,axiom,
% 0.25/0.56 ! [X: nat,Y: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X @ Y )
% 0.25/0.56 => ( ( ord_less_nat @ X @ Y )
% 0.25/0.56 | ( X = Y ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_imp_less_or_eq
% 0.25/0.56 thf(fact_180_less__le__not__le,axiom,
% 0.25/0.56 ( ord_le887097159list_a
% 0.25/0.56 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.25/0.56 & ~ ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le_not_le
% 0.25/0.56 thf(fact_181_less__le__not__le,axiom,
% 0.25/0.56 ( ord_less_nat
% 0.25/0.56 = ( ^ [X4: nat,Y5: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ X4 @ Y5 )
% 0.25/0.56 & ~ ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_le_not_le
% 0.25/0.56 thf(fact_182_not__le__imp__less,axiom,
% 0.25/0.56 ! [Y: nat,X: nat] :
% 0.25/0.56 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.25/0.56 => ( ord_less_nat @ X @ Y ) ) ).
% 0.25/0.56
% 0.25/0.56 % not_le_imp_less
% 0.25/0.56 thf(fact_183_order_Ostrict__trans1,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A @ B )
% 0.25/0.56 => ( ( ord_le887097159list_a @ B @ C2 )
% 0.25/0.56 => ( ord_le887097159list_a @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans1
% 0.25/0.56 thf(fact_184_order_Ostrict__trans1,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ B @ C2 )
% 0.25/0.56 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans1
% 0.25/0.56 thf(fact_185_order_Ostrict__trans2,axiom,
% 0.25/0.56 ! [A: prefix1027212443list_a,B: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ A @ B )
% 0.25/0.56 => ( ( ord_le699472955list_a @ B @ C2 )
% 0.25/0.56 => ( ord_le887097159list_a @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans2
% 0.25/0.56 thf(fact_186_order_Ostrict__trans2,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.25/0.56 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_trans2
% 0.25/0.56 thf(fact_187_order_Oorder__iff__strict,axiom,
% 0.25/0.56 ( ord_le699472955list_a
% 0.25/0.56 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ A2 @ B2 )
% 0.25/0.56 | ( A2 = B2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.order_iff_strict
% 0.25/0.56 thf(fact_188_order_Oorder__iff__strict,axiom,
% 0.25/0.56 ( ord_less_eq_nat
% 0.25/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A2 @ B2 )
% 0.25/0.56 | ( A2 = B2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.order_iff_strict
% 0.25/0.56 thf(fact_189_order_Ostrict__iff__order,axiom,
% 0.25/0.56 ( ord_le887097159list_a
% 0.25/0.56 = ( ^ [A2: prefix1027212443list_a,B2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ A2 @ B2 )
% 0.25/0.56 & ( A2 != B2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_iff_order
% 0.25/0.56 thf(fact_190_order_Ostrict__iff__order,axiom,
% 0.25/0.56 ( ord_less_nat
% 0.25/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A2 @ B2 )
% 0.25/0.56 & ( A2 != B2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % order.strict_iff_order
% 0.25/0.56 thf(fact_191_dual__order_Ostrict__trans1,axiom,
% 0.25/0.56 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ B @ A )
% 0.25/0.56 => ( ( ord_le887097159list_a @ C2 @ B )
% 0.25/0.56 => ( ord_le887097159list_a @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans1
% 0.25/0.56 thf(fact_192_dual__order_Ostrict__trans1,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ B @ A )
% 0.25/0.56 => ( ( ord_less_nat @ C2 @ B )
% 0.25/0.56 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans1
% 0.25/0.56 thf(fact_193_dual__order_Ostrict__trans2,axiom,
% 0.25/0.56 ! [B: prefix1027212443list_a,A: prefix1027212443list_a,C2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le887097159list_a @ B @ A )
% 0.25/0.56 => ( ( ord_le699472955list_a @ C2 @ B )
% 0.25/0.56 => ( ord_le887097159list_a @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans2
% 0.25/0.56 thf(fact_194_dual__order_Ostrict__trans2,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ B @ A )
% 0.25/0.56 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.25/0.56 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % dual_order.strict_trans2
% 0.25/0.56 thf(fact_195_Until_Oprems,axiom,
% 0.25/0.56 ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.56
% 0.25/0.56 % Until.prems
% 0.25/0.56 thf(fact_196_plen__mono,axiom,
% 0.25/0.56 ! [Pi: prefix1027212443list_a,Pi2: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plen_P694648887list_a @ Pi ) @ ( plen_P694648887list_a @ Pi2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % plen_mono
% 0.25/0.56 thf(fact_197_verit__comp__simplify1_I3_J,axiom,
% 0.25/0.56 ! [B4: nat,A4: nat] :
% 0.25/0.56 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 0.25/0.56 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 0.25/0.56
% 0.25/0.56 % verit_comp_simplify1(3)
% 0.25/0.56 thf(fact_198__092_060open_062i_A_060_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.25/0.56 ord_less_nat @ ia @ ( monito1457594016ress_a @ sigma2 @ ( until_a @ phi_1 @ i2 @ phi_2 ) @ ( plen_P694648887list_a @ pi ) ) ).
% 0.25/0.56
% 0.25/0.56 % \<open>i < Monitor_Mirabelle_prbptmgypa.progress \<sigma>' (formula.Until \<phi>1 I \<phi>2) (plen \<pi>)\<close>
% 0.25/0.56 thf(fact_199_less__prefix__def,axiom,
% 0.25/0.56 ( ord_le887097159list_a
% 0.25/0.56 = ( ^ [X4: prefix1027212443list_a,Y5: prefix1027212443list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ X4 @ Y5 )
% 0.25/0.56 & ~ ( ord_le699472955list_a @ Y5 @ X4 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_prefix_def
% 0.25/0.56 thf(fact_200_verit__la__disequality,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( A = B )
% 0.25/0.56 | ~ ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.25/0.56
% 0.25/0.56 % verit_la_disequality
% 0.25/0.56 thf(fact_201_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.56 ! [A: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ A @ A ) ).
% 0.25/0.56
% 0.25/0.56 % verit_comp_simplify1(1)
% 0.25/0.56 thf(fact_202_ex__prefix__of,axiom,
% 0.25/0.56 ! [P5: prefix1027212443list_a] :
% 0.25/0.56 ? [X_1: trace_1367752404list_a] : ( prefix1041802747list_a @ P5 @ X_1 ) ).
% 0.25/0.56
% 0.25/0.56 % ex_prefix_of
% 0.25/0.56 thf(fact_203_prefix__of__antimono,axiom,
% 0.25/0.56 ! [Pi: prefix1027212443list_a,Pi2: prefix1027212443list_a,S: trace_1367752404list_a] :
% 0.25/0.56 ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.25/0.56 => ( ( prefix1041802747list_a @ Pi2 @ S )
% 0.25/0.56 => ( prefix1041802747list_a @ Pi @ S ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prefix_of_antimono
% 0.25/0.56 thf(fact_204_prefix__of__imp__linear,axiom,
% 0.25/0.56 ! [Pi: prefix1027212443list_a,Sigma: trace_1367752404list_a,Pi2: prefix1027212443list_a] :
% 0.25/0.56 ( ( prefix1041802747list_a @ Pi @ Sigma )
% 0.25/0.56 => ( ( prefix1041802747list_a @ Pi2 @ Sigma )
% 0.25/0.56 => ( ( ord_le699472955list_a @ Pi @ Pi2 )
% 0.25/0.56 | ( ord_le699472955list_a @ Pi2 @ Pi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % prefix_of_imp_linear
% 0.25/0.56 thf(fact_205_formula_Oinject_I9_J,axiom,
% 0.25/0.56 ! [X91: formula_a,X92: i,X93: formula_a,Y91: formula_a,Y92: i,Y93: formula_a] :
% 0.25/0.56 ( ( ( until_a @ X91 @ X92 @ X93 )
% 0.25/0.56 = ( until_a @ Y91 @ Y92 @ Y93 ) )
% 0.25/0.56 = ( ( X91 = Y91 )
% 0.25/0.56 & ( X92 = Y92 )
% 0.25/0.56 & ( X93 = Y93 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % formula.inject(9)
% 0.25/0.56 thf(fact_206__C21_C,axiom,
% 0.25/0.56 ! [K: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
% 0.25/0.56 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "21"
% 0.25/0.56 thf(fact_207__C11_C,axiom,
% 0.25/0.56 ! [K: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) )
% 0.25/0.56 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "11"
% 0.25/0.56 thf(fact_208_that,axiom,
% 0.25/0.56 ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma2 @ k ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) ).
% 0.25/0.56
% 0.25/0.56 % that
% 0.25/0.56 thf(fact_209_nat__add__left__cancel__less,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.25/0.56 = ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_add_left_cancel_less
% 0.25/0.56 thf(fact_210_nat__add__left__cancel__le,axiom,
% 0.25/0.56 ! [K: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.25/0.56 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_add_left_cancel_le
% 0.25/0.56 thf(fact_211__C3_C,axiom,
% 0.25/0.56 ! [K: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.25/0.56 => ( ord_less_nat @ K @ ( plen_P694648887list_a @ pi ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "3"
% 0.25/0.56 thf(fact_212__C1_C,axiom,
% 0.25/0.56 ! [K: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.25/0.56 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "1"
% 0.25/0.56 thf(fact_213__C2_C,axiom,
% 0.25/0.56 ! [K: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ sigma @ K ) @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) )
% 0.25/0.56 => ( ord_less_nat @ K @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % "2"
% 0.25/0.56 thf(fact_214__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062,axiom,
% 0.25/0.56 ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ j ) ).
% 0.25/0.56
% 0.25/0.56 % \<open>\<tau> \<sigma> i + b + 1 \<le> \<tau> \<sigma> j__\<close>
% 0.25/0.56 thf(fact_215__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062,axiom,
% 0.25/0.56 ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ ja ) ).
% 0.25/0.56
% 0.25/0.56 % \<open>\<tau> \<sigma>' i + b + 1 \<le> \<tau> \<sigma>' j\<close>
% 0.25/0.56 thf(fact_216_less___092_060tau_062D,axiom,
% 0.25/0.56 ! [Sigma: trace_1367752404list_a,I: nat,J: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( tau_Pr257024512list_a @ Sigma @ I ) @ ( tau_Pr257024512list_a @ Sigma @ J ) )
% 0.25/0.56 => ( ord_less_nat @ I @ J ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_\<tau>D
% 0.25/0.56 thf(fact_217_ex__le___092_060tau_062,axiom,
% 0.25/0.56 ! [I: nat,X: nat,S: trace_1367752404list_a] :
% 0.25/0.56 ? [J3: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ I @ J3 )
% 0.25/0.56 & ( ord_less_eq_nat @ X @ ( tau_Pr257024512list_a @ S @ J3 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ex_le_\<tau>
% 0.25/0.56 thf(fact_218__092_060tau_062__mono,axiom,
% 0.25/0.56 ! [I: nat,J: nat,S: trace_1367752404list_a] :
% 0.25/0.56 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 => ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ S @ I ) @ ( tau_Pr257024512list_a @ S @ J ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % \<tau>_mono
% 0.25/0.56 thf(fact_219_less__add__eq__less,axiom,
% 0.25/0.56 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_nat @ K @ L )
% 0.25/0.56 => ( ( ( plus_plus_nat @ M @ L )
% 0.25/0.56 = ( plus_plus_nat @ K @ N ) )
% 0.25/0.56 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_add_eq_less
% 0.25/0.56 thf(fact_220_trans__less__add2,axiom,
% 0.25/0.56 ! [I: nat,J: nat,M: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I @ J )
% 0.25/0.56 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % trans_less_add2
% 0.25/0.56 thf(fact_221_trans__less__add1,axiom,
% 0.25/0.56 ! [I: nat,J: nat,M: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I @ J )
% 0.25/0.56 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % trans_less_add1
% 0.25/0.56 thf(fact_222_add__less__mono1,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I @ J )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_mono1
% 0.25/0.56 thf(fact_223_not__add__less2,axiom,
% 0.25/0.56 ! [J: nat,I: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.25/0.56
% 0.25/0.56 % not_add_less2
% 0.25/0.56 thf(fact_224_not__add__less1,axiom,
% 0.25/0.56 ! [I: nat,J: nat] :
% 0.25/0.56 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.25/0.56
% 0.25/0.56 % not_add_less1
% 0.25/0.56 thf(fact_225_add__less__mono,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I @ J )
% 0.25/0.56 => ( ( ord_less_nat @ K @ L )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_mono
% 0.25/0.56 thf(fact_226_add__lessD1,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.25/0.56 => ( ord_less_nat @ I @ K ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_lessD1
% 0.25/0.56 thf(fact_227_add__leE,axiom,
% 0.25/0.56 ! [M: nat,K: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.25/0.56 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.25/0.56 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_leE
% 0.25/0.56 thf(fact_228_le__add1,axiom,
% 0.25/0.56 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_add1
% 0.25/0.56 thf(fact_229_le__add2,axiom,
% 0.25/0.56 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_add2
% 0.25/0.56 thf(fact_230_add__leD1,axiom,
% 0.25/0.56 ! [M: nat,K: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.25/0.56 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_leD1
% 0.25/0.56 thf(fact_231_add__leD2,axiom,
% 0.25/0.56 ! [M: nat,K: nat,N: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.25/0.56 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_leD2
% 0.25/0.56 thf(fact_232_le__Suc__ex,axiom,
% 0.25/0.56 ! [K: nat,L: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ K @ L )
% 0.25/0.56 => ? [N2: nat] :
% 0.25/0.56 ( L
% 0.25/0.56 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_Suc_ex
% 0.25/0.56 thf(fact_233_add__le__mono,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 => ( ( ord_less_eq_nat @ K @ L )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_mono
% 0.25/0.56 thf(fact_234_add__le__mono1,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_mono1
% 0.25/0.56 thf(fact_235_trans__le__add1,axiom,
% 0.25/0.56 ! [I: nat,J: nat,M: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % trans_le_add1
% 0.25/0.56 thf(fact_236_trans__le__add2,axiom,
% 0.25/0.56 ! [I: nat,J: nat,M: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % trans_le_add2
% 0.25/0.56 thf(fact_237_nat__le__iff__add,axiom,
% 0.25/0.56 ( ord_less_eq_nat
% 0.25/0.56 = ( ^ [M3: nat,N3: nat] :
% 0.25/0.56 ? [K3: nat] :
% 0.25/0.56 ( N3
% 0.25/0.56 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % nat_le_iff_add
% 0.25/0.56 thf(fact_238_mono__nat__linear__lb,axiom,
% 0.25/0.56 ! [F: nat > nat,M: nat,K: nat] :
% 0.25/0.56 ( ! [M4: nat,N2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ M4 @ N2 )
% 0.25/0.56 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % mono_nat_linear_lb
% 0.25/0.56 thf(fact_239_progress__time__conv,axiom,
% 0.25/0.56 ! [J: nat,Sigma: trace_1367752404list_a,Sigma2: trace_1367752404list_a,Phi: formula_a] :
% 0.25/0.56 ( ! [I2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ I2 @ J )
% 0.25/0.56 => ( ( tau_Pr257024512list_a @ Sigma @ I2 )
% 0.25/0.56 = ( tau_Pr257024512list_a @ Sigma2 @ I2 ) ) )
% 0.25/0.56 => ( ( monito1457594016ress_a @ Sigma @ Phi @ J )
% 0.25/0.56 = ( monito1457594016ress_a @ Sigma2 @ Phi @ J ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % progress_time_conv
% 0.25/0.56 thf(fact_240_le___092_060tau_062__less,axiom,
% 0.25/0.56 ! [Sigma: trace_1367752404list_a,I: nat,J: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( tau_Pr257024512list_a @ Sigma @ I ) @ ( tau_Pr257024512list_a @ Sigma @ J ) )
% 0.25/0.56 => ( ( ord_less_nat @ J @ I )
% 0.25/0.56 => ( ( tau_Pr257024512list_a @ Sigma @ I )
% 0.25/0.56 = ( tau_Pr257024512list_a @ Sigma @ J ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_\<tau>_less
% 0.25/0.56 thf(fact_241__092_060tau_062__prefix__conv,axiom,
% 0.25/0.56 ! [P5: prefix1027212443list_a,S: trace_1367752404list_a,S2: trace_1367752404list_a,I: nat] :
% 0.25/0.56 ( ( prefix1041802747list_a @ P5 @ S )
% 0.25/0.56 => ( ( prefix1041802747list_a @ P5 @ S2 )
% 0.25/0.56 => ( ( ord_less_nat @ I @ ( plen_P694648887list_a @ P5 ) )
% 0.25/0.56 => ( ( tau_Pr257024512list_a @ S @ I )
% 0.25/0.56 = ( tau_Pr257024512list_a @ S2 @ I ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % \<tau>_prefix_conv
% 0.25/0.56 thf(fact_242__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.25/0.56 ~ ! [J3: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma2 @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma2 @ J3 ) )
% 0.25/0.56 => ( ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma2 @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.25/0.56 => ~ ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma2 @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % \<open>\<And>thesis. (\<And>j. \<lbrakk>\<tau> \<sigma>' i + b + 1 \<le> \<tau> \<sigma>' j; j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>1 (plen \<pi>); j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma>' \<phi>2 (plen \<pi>)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.25/0.56 thf(fact_243__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__prbptmgypa_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.25/0.56 ~ ! [J3: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( tau_Pr257024512list_a @ sigma @ ia ) @ b ) @ one_one_nat ) @ ( tau_Pr257024512list_a @ sigma @ J3 ) )
% 0.25/0.56 => ( ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma @ phi_1 @ ( plen_P694648887list_a @ pi ) ) )
% 0.25/0.56 => ~ ( ord_less_eq_nat @ J3 @ ( monito1457594016ress_a @ sigma @ phi_2 @ ( plen_P694648887list_a @ pi ) ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % \<open>\<And>thesis. (\<And>j. \<lbrakk>\<tau> \<sigma> i + b + 1 \<le> \<tau> \<sigma> j; j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>1 (plen \<pi>); j \<le> Monitor_Mirabelle_prbptmgypa.progress \<sigma> \<phi>2 (plen \<pi>)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.25/0.56 thf(fact_244_add__less__cancel__right,axiom,
% 0.25/0.56 ! [A: nat,C2: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.25/0.56 = ( ord_less_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_cancel_right
% 0.25/0.56 thf(fact_245_add__left__cancel,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ( plus_plus_nat @ A @ B )
% 0.25/0.56 = ( plus_plus_nat @ A @ C2 ) )
% 0.25/0.56 = ( B = C2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_left_cancel
% 0.25/0.56 thf(fact_246_add__right__cancel,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.56 ( ( ( plus_plus_nat @ B @ A )
% 0.25/0.56 = ( plus_plus_nat @ C2 @ A ) )
% 0.25/0.56 = ( B = C2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_right_cancel
% 0.25/0.56 thf(fact_247_add__le__cancel__left,axiom,
% 0.25/0.56 ! [C2: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.25/0.56 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_cancel_left
% 0.25/0.56 thf(fact_248_add__le__cancel__right,axiom,
% 0.25/0.56 ! [A: nat,C2: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.25/0.56 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_cancel_right
% 0.25/0.56 thf(fact_249_add__less__cancel__left,axiom,
% 0.25/0.56 ! [C2: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.25/0.56 = ( ord_less_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_cancel_left
% 0.25/0.56 thf(fact_250_one__reorient,axiom,
% 0.25/0.56 ! [X: nat] :
% 0.25/0.56 ( ( one_one_nat = X )
% 0.25/0.56 = ( X = one_one_nat ) ) ).
% 0.25/0.56
% 0.25/0.56 % one_reorient
% 0.25/0.56 thf(fact_251_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.25/0.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % ab_semigroup_add_class.add_ac(1)
% 0.25/0.56 thf(fact_252_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( I = J )
% 0.25/0.56 & ( K = L ) )
% 0.25/0.56 => ( ( plus_plus_nat @ I @ K )
% 0.25/0.56 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(4)
% 0.25/0.56 thf(fact_253_group__cancel_Oadd1,axiom,
% 0.25/0.56 ! [A5: nat,K: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( A5
% 0.25/0.56 = ( plus_plus_nat @ K @ A ) )
% 0.25/0.56 => ( ( plus_plus_nat @ A5 @ B )
% 0.25/0.56 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % group_cancel.add1
% 0.25/0.56 thf(fact_254_group__cancel_Oadd2,axiom,
% 0.25/0.56 ! [B5: nat,K: nat,B: nat,A: nat] :
% 0.25/0.56 ( ( B5
% 0.25/0.56 = ( plus_plus_nat @ K @ B ) )
% 0.25/0.56 => ( ( plus_plus_nat @ A @ B5 )
% 0.25/0.56 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % group_cancel.add2
% 0.25/0.56 thf(fact_255_add_Oassoc,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.25/0.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add.assoc
% 0.25/0.56 thf(fact_256_add_Ocommute,axiom,
% 0.25/0.56 ( plus_plus_nat
% 0.25/0.56 = ( ^ [A2: nat,B2: nat] : ( plus_plus_nat @ B2 @ A2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add.commute
% 0.25/0.56 thf(fact_257_add_Oleft__commute,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.56 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 0.25/0.56 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add.left_commute
% 0.25/0.56 thf(fact_258_add__left__imp__eq,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ( plus_plus_nat @ A @ B )
% 0.25/0.56 = ( plus_plus_nat @ A @ C2 ) )
% 0.25/0.56 => ( B = C2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_left_imp_eq
% 0.25/0.56 thf(fact_259_add__right__imp__eq,axiom,
% 0.25/0.56 ! [B: nat,A: nat,C2: nat] :
% 0.25/0.56 ( ( ( plus_plus_nat @ B @ A )
% 0.25/0.56 = ( plus_plus_nat @ C2 @ A ) )
% 0.25/0.56 => ( B = C2 ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_right_imp_eq
% 0.25/0.56 thf(fact_260_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 & ( K = L ) )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(3)
% 0.25/0.56 thf(fact_261_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( I = J )
% 0.25/0.56 & ( ord_less_eq_nat @ K @ L ) )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(2)
% 0.25/0.56 thf(fact_262_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 & ( ord_less_eq_nat @ K @ L ) )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_semiring(1)
% 0.25/0.56 thf(fact_263_add__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono
% 0.25/0.56 thf(fact_264_add__left__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_left_mono
% 0.25/0.56 thf(fact_265_less__eqE,axiom,
% 0.25/0.56 ! [A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ~ ! [C: nat] :
% 0.25/0.56 ( B
% 0.25/0.56 != ( plus_plus_nat @ A @ C ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % less_eqE
% 0.25/0.56 thf(fact_266_add__right__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_right_mono
% 0.25/0.56 thf(fact_267_le__iff__add,axiom,
% 0.25/0.56 ( ord_less_eq_nat
% 0.25/0.56 = ( ^ [A2: nat,B2: nat] :
% 0.25/0.56 ? [C3: nat] :
% 0.25/0.56 ( B2
% 0.25/0.56 = ( plus_plus_nat @ A2 @ C3 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % le_iff_add
% 0.25/0.56 thf(fact_268_add__le__imp__le__left,axiom,
% 0.25/0.56 ! [C2: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.25/0.56 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_imp_le_left
% 0.25/0.56 thf(fact_269_add__le__imp__le__right,axiom,
% 0.25/0.56 ! [A: nat,C2: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.25/0.56 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_imp_le_right
% 0.25/0.56 thf(fact_270_add__mono__thms__linordered__field_I5_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( ord_less_nat @ I @ J )
% 0.25/0.56 & ( ord_less_nat @ K @ L ) )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_field(5)
% 0.25/0.56 thf(fact_271_add__mono__thms__linordered__field_I2_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( I = J )
% 0.25/0.56 & ( ord_less_nat @ K @ L ) )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_field(2)
% 0.25/0.56 thf(fact_272_add__mono__thms__linordered__field_I1_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( ord_less_nat @ I @ J )
% 0.25/0.56 & ( K = L ) )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_field(1)
% 0.25/0.56 thf(fact_273_add__strict__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ C2 @ D2 )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_strict_mono
% 0.25/0.56 thf(fact_274_add__strict__left__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_strict_left_mono
% 0.25/0.56 thf(fact_275_add__strict__right__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_strict_right_mono
% 0.25/0.56 thf(fact_276_add__less__imp__less__left,axiom,
% 0.25/0.56 ! [C2: nat,A: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.25/0.56 => ( ord_less_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_imp_less_left
% 0.25/0.56 thf(fact_277_add__less__imp__less__right,axiom,
% 0.25/0.56 ! [A: nat,C2: nat,B: nat] :
% 0.25/0.56 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.25/0.56 => ( ord_less_nat @ A @ B ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_imp_less_right
% 0.25/0.56 thf(fact_278_add__less__le__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.25/0.56 ( ( ord_less_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_eq_nat @ C2 @ D2 )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_less_le_mono
% 0.25/0.56 thf(fact_279_add__le__less__mono,axiom,
% 0.25/0.56 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 0.25/0.56 ( ( ord_less_eq_nat @ A @ B )
% 0.25/0.56 => ( ( ord_less_nat @ C2 @ D2 )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_le_less_mono
% 0.25/0.56 thf(fact_280_add__mono__thms__linordered__field_I3_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( ord_less_nat @ I @ J )
% 0.25/0.56 & ( ord_less_eq_nat @ K @ L ) )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_field(3)
% 0.25/0.56 thf(fact_281_add__mono__thms__linordered__field_I4_J,axiom,
% 0.25/0.56 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.56 ( ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.56 & ( ord_less_nat @ K @ L ) )
% 0.25/0.56 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.56
% 0.25/0.56 % add_mono_thms_linordered_field(4)
% 0.25/0.56 thf(fact_282_discrete,axiom,
% 0.25/0.56 ( ord_less_nat
% 0.25/0.62 = ( ^ [A2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ) ) ).
% 0.25/0.62
% 0.25/0.62 % discrete
% 0.25/0.62
% 0.25/0.62 % Conjectures (1)
% 0.25/0.62 thf(conj_0,conjecture,
% 0.25/0.62 ord_less_nat @ k @ ( plen_P694648887list_a @ pi ) ).
% 0.25/0.62
% 0.25/0.62 %------------------------------------------------------------------------------
% 0.25/0.62 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.BpyJIsMUUR/cvc5---1.0.5_4513.p...
% 0.25/0.62 (declare-sort $$unsorted 0)
% 0.25/0.62 (declare-sort tptp.prefix1027212443list_a 0)
% 0.25/0.62 (declare-sort tptp.trace_1367752404list_a 0)
% 0.25/0.62 (declare-sort tptp.i 0)
% 0.25/0.62 (declare-sort tptp.formula_a 0)
% 0.25/0.62 (declare-sort tptp.list_a 0)
% 0.25/0.62 (declare-sort tptp.nat 0)
% 0.25/0.62 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.25/0.62 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.25/0.62 (declare-fun tptp.until_a (tptp.formula_a tptp.i tptp.formula_a) tptp.formula_a)
% 0.25/0.62 (declare-fun tptp.sat_a (tptp.trace_1367752404list_a tptp.list_a tptp.nat tptp.formula_a) Bool)
% 0.25/0.62 (declare-fun tptp.monito1457594016ress_a (tptp.trace_1367752404list_a tptp.formula_a tptp.nat) tptp.nat)
% 0.25/0.62 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.62 (declare-fun tptp.ord_le887097159list_a (tptp.prefix1027212443list_a tptp.prefix1027212443list_a) Bool)
% 0.25/0.62 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.62 (declare-fun tptp.ord_le699472955list_a (tptp.prefix1027212443list_a tptp.prefix1027212443list_a) Bool)
% 0.25/0.62 (declare-fun tptp.tau_Pr257024512list_a (tptp.trace_1367752404list_a tptp.nat) tptp.nat)
% 0.25/0.62 (declare-fun tptp.plen_P694648887list_a (tptp.prefix1027212443list_a) tptp.nat)
% 0.25/0.62 (declare-fun tptp.prefix1041802747list_a (tptp.prefix1027212443list_a tptp.trace_1367752404list_a) Bool)
% 0.25/0.62 (declare-fun tptp.i2 () tptp.i)
% 0.25/0.62 (declare-fun tptp.phi () tptp.formula_a)
% 0.25/0.62 (declare-fun tptp.phi_1 () tptp.formula_a)
% 0.25/0.62 (declare-fun tptp.phi_2 () tptp.formula_a)
% 0.25/0.62 (declare-fun tptp.pi () tptp.prefix1027212443list_a)
% 0.25/0.62 (declare-fun tptp.sigma () tptp.trace_1367752404list_a)
% 0.25/0.62 (declare-fun tptp.sigma2 () tptp.trace_1367752404list_a)
% 0.25/0.62 (declare-fun tptp.b () tptp.nat)
% 0.25/0.62 (declare-fun tptp.i3 () tptp.nat)
% 0.25/0.62 (declare-fun tptp.ia () tptp.nat)
% 0.25/0.62 (declare-fun tptp.j () tptp.nat)
% 0.25/0.62 (declare-fun tptp.ja () tptp.nat)
% 0.25/0.62 (declare-fun tptp.k () tptp.nat)
% 0.25/0.62 (assert (@ (@ tptp.ord_less_nat tptp.k) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_nat tptp.i3) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (@ (@ tptp.prefix1041802747list_a tptp.pi) tptp.sigma))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.25/0.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.25/0.62 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_eq_nat tptp.j) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (@ (@ tptp.prefix1041802747list_a tptp.pi) tptp.sigma2))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_eq_nat tptp.j) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y2 tptp.nat)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_nat Y2) B))) (exists ((X2 tptp.nat)) (and (@ P X2) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))))))
% 0.25/0.62 (assert (forall ((Sigma tptp.trace_1367752404list_a) (Phi tptp.formula_a) (J tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) J)) J)))
% 0.25/0.62 (assert (forall ((J tptp.nat) (J2 tptp.nat) (Sigma tptp.trace_1367752404list_a) (Phi tptp.formula_a)) (let ((_let_1 (@ (@ tptp.monito1457594016ress_a Sigma) Phi))) (=> (@ (@ tptp.ord_less_eq_nat J) J2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 J)) (@ _let_1 J2))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (not (@ (@ tptp.ord_less_eq_nat X3) T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (@ (@ tptp.ord_less_eq_nat T) X3))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (@ (@ tptp.ord_less_eq_nat X3) T))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (not (@ (@ tptp.ord_less_eq_nat T) X3)))))))
% 0.25/0.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J3) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J3)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.25/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N3) (= M3 N3)))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.25/0.62 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N3) (not (= M3 N3))))))
% 0.25/0.62 (assert (forall ((Pi tptp.prefix1027212443list_a) (Sigma tptp.trace_1367752404list_a) (Sigma2 tptp.trace_1367752404list_a) (Phi tptp.formula_a)) (let ((_let_1 (@ tptp.plen_P694648887list_a Pi))) (let ((_let_2 (@ tptp.prefix1041802747list_a Pi))) (=> (@ _let_2 Sigma) (=> (@ _let_2 Sigma2) (= (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) _let_1) (@ (@ (@ tptp.monito1457594016ress_a Sigma2) Phi) _let_1))))))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (@ P X2) (@ P2 X2))))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (@ Q X2) (@ Q2 X2))))) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P2 X3) (@ Q2 X3))))))))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (@ P X2) (@ P2 X2))))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (@ Q X2) (@ Q2 X2))))) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P2 X3) (@ Q2 X3))))))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (not (= X3 T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (not (= X3 T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (not (@ (@ tptp.ord_less_nat X3) T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z) X3) (@ (@ tptp.ord_less_nat T) X3))))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= (@ P X2) (@ P2 X2))))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= (@ Q X2) (@ Q2 X2))))) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (= (and (@ P X3) (@ Q X3)) (and (@ P2 X3) (@ Q2 X3))))))))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (P2 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= (@ P X2) (@ P2 X2))))) (=> (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= (@ Q X2) (@ Q2 X2))))) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (= (or (@ P X3) (@ Q X3)) (or (@ P2 X3) (@ Q2 X3))))))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (not (= X3 T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (not (= X3 T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Z) (@ _let_1 T)))))))
% 0.25/0.62 (assert (forall ((T tptp.nat)) (exists ((Z tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z) (not (@ (@ tptp.ord_less_nat T) X3)))))))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_eq_nat tptp.ja) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma2) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a)) (@ (@ tptp.ord_le699472955list_a X) X)))
% 0.25/0.62 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 0.25/0.62 (assert (forall ((I tptp.nat) (V tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi))) (= (@ (@ (@ (@ tptp.sat_a tptp.sigma) V) I) tptp.phi_1) (@ (@ (@ (@ tptp.sat_a tptp.sigma2) V) I) tptp.phi_1)))))
% 0.25/0.62 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M 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 ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I3) (@ P I3))) (@ P K2)))) (@ P M)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat C) B) (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X3) (@ (@ tptp.ord_less_nat X3) C)) (@ P X3))) (forall ((D tptp.nat)) (=> (forall ((X2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X2) (@ (@ tptp.ord_less_nat X2) D)) (@ P X2))) (@ (@ tptp.ord_less_eq_nat D) C))))))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a)) (=> (not (= A B)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (@ (@ tptp.ord_le887097159list_a A) B)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 0.25/0.62 (assert (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le887097159list_a B) A) (@ (@ tptp.ord_le699472955list_a B) A))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 0.25/0.62 (assert (= tptp.ord_le887097159list_a (lambda ((B2 tptp.prefix1027212443list_a) (A2 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a B2) A2) (not (= A2 B2))))))
% 0.25/0.62 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (not (= A2 B2))))))
% 0.25/0.62 (assert (= tptp.ord_le699472955list_a (lambda ((B2 tptp.prefix1027212443list_a) (A2 tptp.prefix1027212443list_a)) (or (@ (@ tptp.ord_le887097159list_a B2) A2) (= A2 B2)))))
% 0.25/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A2 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A2) (= A2 B2)))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le887097159list_a A) B) (@ (@ tptp.ord_le699472955list_a A) B))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_eq_nat tptp.ja) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma2) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (V tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi))) (= (@ (@ (@ (@ tptp.sat_a tptp.sigma) V) I) tptp.phi_2) (@ (@ (@ (@ tptp.sat_a tptp.sigma2) V) I) tptp.phi_2)))))
% 0.25/0.62 (assert (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a B) A) (=> (@ (@ tptp.ord_le699472955list_a A) B) (= A B)))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 0.25/0.62 (assert (= (lambda ((Y4 tptp.prefix1027212443list_a) (Z3 tptp.prefix1027212443list_a)) (= Y4 Z3)) (lambda ((A2 tptp.prefix1027212443list_a) (B2 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a B2) A2) (@ (@ tptp.ord_le699472955list_a A2) B2)))))
% 0.25/0.62 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A2) (@ (@ tptp.ord_less_eq_nat A2) B2)))))
% 0.25/0.62 (assert (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le699472955list_a C2))) (=> (@ (@ tptp.ord_le699472955list_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.62 (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)))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a)) (@ (@ tptp.ord_le699472955list_a A) A)))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a) (Z4 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le699472955list_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le699472955list_a Y) Z4) (@ _let_1 Z4))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z4) (@ _let_1 Z4))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le699472955list_a B) A) (= A B)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le699472955list_a A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (= A B) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (@ (@ tptp.ord_le699472955list_a A) C2)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ (@ tptp.ord_less_eq_nat A) C2)))))
% 0.25/0.62 (assert (= (lambda ((Y4 tptp.prefix1027212443list_a) (Z3 tptp.prefix1027212443list_a)) (= Y4 Z3)) (lambda ((A2 tptp.prefix1027212443list_a) (B2 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a A2) B2) (@ (@ tptp.ord_le699472955list_a B2) A2)))))
% 0.25/0.62 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (@ (@ tptp.ord_less_eq_nat B2) A2)))))
% 0.25/0.62 (assert (forall ((Y tptp.prefix1027212443list_a) (X tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a Y) X) (= (@ (@ tptp.ord_le699472955list_a X) Y) (= X Y)))))
% 0.25/0.62 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z4))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z4))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z4))) (=> (=> _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)))))))))))))))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le699472955list_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (= X Y) (@ (@ tptp.ord_le699472955list_a X) Y))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (=> (@ (@ tptp.ord_le699472955list_a Y) X) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 0.25/0.62 (assert (= (lambda ((Y4 tptp.prefix1027212443list_a) (Z3 tptp.prefix1027212443list_a)) (= Y4 Z3)) (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (@ (@ tptp.ord_le699472955list_a Y5) X4)))))
% 0.25/0.62 (assert (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.prefix1027212443list_a tptp.nat)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le699472955list_a (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le699472955list_a (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.prefix1027212443list_a tptp.nat)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le699472955list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le699472955list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z4) (@ _let_1 Z4))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 0.25/0.62 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X2 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X2) (@ P Y3))) (@ P X2))) (@ P A))))
% 0.25/0.62 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.62 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P3 X5))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P4 N3) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (not (@ P4 M3)))))))))
% 0.25/0.62 (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))))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 0.25/0.62 (assert (forall ((Y tptp.prefix1027212443list_a) (X tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a Y) X) (not (@ (@ tptp.ord_le887097159list_a X) Y)))))
% 0.25/0.62 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.25/0.62 (assert (= tptp.ord_le699472955list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (or (@ (@ tptp.ord_le887097159list_a X4) Y5) (= X4 Y5)))))
% 0.25/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y5) (= X4 Y5)))))
% 0.25/0.62 (assert (= tptp.ord_le887097159list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (not (= X4 Y5))))))
% 0.25/0.62 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (= X4 Y5))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_le887097159list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le887097159list_a (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le887097159list_a (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le887097159list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.prefix1027212443list_a tptp.nat)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_le699472955list_a (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_le887097159list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (not (= A B)) (@ (@ tptp.ord_le887097159list_a A) B)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (not (@ (@ tptp.ord_le887097159list_a X) Y)) (= (@ (@ tptp.ord_le699472955list_a X) Y) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (= (not (@ (@ tptp.ord_le887097159list_a X) Y)) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le887097159list_a X) Y) (@ (@ tptp.ord_le699472955list_a X) Y))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a) (Z4 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (=> (@ (@ tptp.ord_le887097159list_a Y) Z4) (@ (@ tptp.ord_le887097159list_a X) Z4)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z4) (@ (@ tptp.ord_less_nat X) Z4)))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a) (Z4 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le699472955list_a Y) Z4) (@ _let_1 Z4))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z4) (@ _let_1 Z4))))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 0.25/0.62 (assert (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (or (@ (@ tptp.ord_le887097159list_a X) Y) (= X Y)))))
% 0.25/0.62 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 0.25/0.62 (assert (= tptp.ord_le887097159list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (not (@ (@ tptp.ord_le699472955list_a Y5) X4))))))
% 0.25/0.62 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X4))))))
% 0.25/0.62 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le887097159list_a B) C2) (@ (@ tptp.ord_le887097159list_a A) C2)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))))
% 0.25/0.62 (assert (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))))
% 0.25/0.62 (assert (= tptp.ord_le699472955list_a (lambda ((A2 tptp.prefix1027212443list_a) (B2 tptp.prefix1027212443list_a)) (or (@ (@ tptp.ord_le887097159list_a A2) B2) (= A2 B2)))))
% 0.25/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A2) B2) (= A2 B2)))))
% 0.25/0.62 (assert (= tptp.ord_le887097159list_a (lambda ((A2 tptp.prefix1027212443list_a) (B2 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a A2) B2) (not (= A2 B2))))))
% 0.25/0.62 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (not (= A2 B2))))))
% 0.25/0.62 (assert (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a C2))) (=> (@ (@ tptp.ord_le699472955list_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.62 (assert (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le887097159list_a B) A) (=> (@ (@ tptp.ord_le699472955list_a C2) B) (@ (@ tptp.ord_le887097159list_a C2) A)))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_nat C2) A)))))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_nat tptp.ia) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) (@ (@ (@ tptp.until_a tptp.phi_1) tptp.i2) tptp.phi_2)) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (forall ((Pi tptp.prefix1027212443list_a) (Pi2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a Pi) Pi2) (@ (@ tptp.ord_less_eq_nat (@ tptp.plen_P694648887list_a Pi)) (@ tptp.plen_P694648887list_a Pi2)))))
% 0.25/0.62 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 0.25/0.62 (assert (@ (@ tptp.ord_less_nat tptp.ia) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma2) (@ (@ (@ tptp.until_a tptp.phi_1) tptp.i2) tptp.phi_2)) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.25/0.62 (assert (= tptp.ord_le887097159list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (not (@ (@ tptp.ord_le699472955list_a Y5) X4))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 0.25/0.62 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.25/0.62 (assert (forall ((P5 tptp.prefix1027212443list_a)) (exists ((X_1 tptp.trace_1367752404list_a)) (@ (@ tptp.prefix1041802747list_a P5) X_1))))
% 0.25/0.62 (assert (forall ((Pi tptp.prefix1027212443list_a) (Pi2 tptp.prefix1027212443list_a) (S tptp.trace_1367752404list_a)) (=> (@ (@ tptp.ord_le699472955list_a Pi) Pi2) (=> (@ (@ tptp.prefix1041802747list_a Pi2) S) (@ (@ tptp.prefix1041802747list_a Pi) S)))))
% 0.25/0.62 (assert (forall ((Pi tptp.prefix1027212443list_a) (Sigma tptp.trace_1367752404list_a) (Pi2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.prefix1041802747list_a Pi) Sigma) (=> (@ (@ tptp.prefix1041802747list_a Pi2) Sigma) (or (@ (@ tptp.ord_le699472955list_a Pi) Pi2) (@ (@ tptp.ord_le699472955list_a Pi2) Pi))))))
% 0.25/0.62 (assert (forall ((X91 tptp.formula_a) (X92 tptp.i) (X93 tptp.formula_a) (Y91 tptp.formula_a) (Y92 tptp.i) (Y93 tptp.formula_a)) (= (= (@ (@ (@ tptp.until_a X91) X92) X93) (@ (@ (@ tptp.until_a Y91) Y92) Y93)) (and (= X91 Y91) (= X92 Y92) (= X93 Y93)))))
% 0.25/0.62 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi)))))))
% 0.25/0.62 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi)))))))
% 0.25/0.62 (assert (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 tptp.k)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b))))
% 0.25/0.62 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.25/0.62 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.25/0.62 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ tptp.plen_P694648887list_a tptp.pi))))))
% 0.25/0.62 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi)))))))
% 0.25/0.62 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi)))))))
% 0.25/0.62 (assert (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_1 tptp.j))))
% 0.25/0.62 (assert (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_1 tptp.ja))))
% 0.25/0.62 (assert (forall ((Sigma tptp.trace_1367752404list_a) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a Sigma))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)) (@ (@ tptp.ord_less_nat I) J)))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (X tptp.nat) (S tptp.trace_1367752404list_a)) (exists ((J3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) J3) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.tau_Pr257024512list_a S) J3))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (S tptp.trace_1367752404list_a)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a S))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))))
% 0.25/0.62 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.25/0.62 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 0.25/0.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.25/0.62 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.25/0.62 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 0.25/0.62 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.25/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (exists ((K3 tptp.nat)) (= N3 (@ (@ tptp.plus_plus_nat M3) K3))))))
% 0.25/0.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N2) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 0.25/0.62 (assert (forall ((J tptp.nat) (Sigma tptp.trace_1367752404list_a) (Sigma2 tptp.trace_1367752404list_a) (Phi tptp.formula_a)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.tau_Pr257024512list_a Sigma) I2) (@ (@ tptp.tau_Pr257024512list_a Sigma2) I2)))) (= (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) J) (@ (@ (@ tptp.monito1457594016ress_a Sigma2) Phi) J)))))
% 0.25/0.62 (assert (forall ((Sigma tptp.trace_1367752404list_a) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a Sigma))) (let ((_let_2 (@ _let_1 J))) (let ((_let_3 (@ _let_1 I))) (=> (@ (@ tptp.ord_less_eq_nat _let_3) _let_2) (=> (@ (@ tptp.ord_less_nat J) I) (= _let_3 _let_2))))))))
% 0.25/0.62 (assert (forall ((P5 tptp.prefix1027212443list_a) (S tptp.trace_1367752404list_a) (S2 tptp.trace_1367752404list_a) (I tptp.nat)) (let ((_let_1 (@ tptp.prefix1041802747list_a P5))) (=> (@ _let_1 S) (=> (@ _let_1 S2) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.plen_P694648887list_a P5)) (= (@ (@ tptp.tau_Pr257024512list_a S) I) (@ (@ tptp.tau_Pr257024512list_a S2) I))))))))
% 0.25/0.62 (assert (not (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.plen_P694648887list_a tptp.pi))) (let ((_let_2 (@ tptp.monito1457594016ress_a tptp.sigma2))) (let ((_let_3 (@ tptp.ord_less_eq_nat J3))) (let ((_let_4 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_4 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_4 J3)) (=> (@ _let_3 (@ (@ _let_2 tptp.phi_1) _let_1)) (not (@ _let_3 (@ (@ _let_2 tptp.phi_2) _let_1))))))))))))
% 0.25/0.62 (assert (not (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.plen_P694648887list_a tptp.pi))) (let ((_let_2 (@ tptp.monito1457594016ress_a tptp.sigma))) (let ((_let_3 (@ tptp.ord_less_eq_nat J3))) (let ((_let_4 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_4 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_4 J3)) (=> (@ _let_3 (@ (@ _let_2 tptp.phi_1) _let_1)) (not (@ _let_3 (@ (@ _let_2 tptp.phi_2) _let_1))))))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))))
% 0.25/0.62 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.25/0.62 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 0.25/0.62 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.62 (assert (forall ((A5 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A5 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A5) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 0.25/0.62 (assert (forall ((B5 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))))
% 0.25/0.62 (assert (= tptp.plus_plus_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A2))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))))
% 0.25/0.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.62 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C))))))))
% 0.25/0.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))))
% 0.25/0.62 (assert (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (exists ((C3 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A2) C3))))))
% 0.90/1.12 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.90/1.12 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.90/1.12 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.90/1.12 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))))
% 0.90/1.12 (assert (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 0.90/1.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 0.90/1.12 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.90/1.12 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.90/1.12 (assert (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) __flatten_var_0))))
% 0.90/1.12 (assert (not (@ (@ tptp.ord_less_nat tptp.k) (@ tptp.plen_P694648887list_a tptp.pi))))
% 0.90/1.12 (set-info :filename cvc5---1.0.5_4513)
% 0.90/1.12 (check-sat-assuming ( true ))
% 0.90/1.12 ------- get file name : TPTP file name is ITP125^1
% 0.90/1.12 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4513.smt2...
% 0.90/1.12 --- Run --ho-elim --full-saturate-quant at 10...
% 0.90/1.12 % SZS status Theorem for ITP125^1
% 0.90/1.12 % SZS output start Proof for ITP125^1
% 0.90/1.12 (
% 0.90/1.12 (let ((_let_1 (@ tptp.plen_P694648887list_a tptp.pi))) (let ((_let_2 (@ tptp.ord_less_nat tptp.k))) (let ((_let_3 (not (@ _let_2 _let_1)))) (let ((_let_4 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (let ((_let_5 (@ (@ tptp.plus_plus_nat (@ _let_4 tptp.ia)) tptp.b))) (let ((_let_6 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (let ((_let_7 (@ (@ (@ tptp.until_a tptp.phi_1) tptp.i2) tptp.phi_2))) (let ((_let_8 (@ tptp.monito1457594016ress_a tptp.sigma2))) (let ((_let_9 (@ tptp.ord_less_nat tptp.ia))) (let ((_let_10 (@ tptp.monito1457594016ress_a tptp.sigma))) (let ((_let_11 (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X4))))))) (let ((_let_12 (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))) (let ((_let_13 (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))) (let ((_let_14 (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))) (let ((_let_15 (@ tptp.ord_less_eq_nat tptp.ja))) (let ((_let_16 (= tptp.ord_le887097159list_a (lambda ((B2 tptp.prefix1027212443list_a) (A2 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a B2) A2) (not (= A2 B2))))))) (let ((_let_17 (forall ((Pi tptp.prefix1027212443list_a) (Sigma tptp.trace_1367752404list_a) (Sigma2 tptp.trace_1367752404list_a) (Phi tptp.formula_a)) (let ((_let_1 (@ tptp.plen_P694648887list_a Pi))) (let ((_let_2 (@ tptp.prefix1041802747list_a Pi))) (=> (@ _let_2 Sigma) (=> (@ _let_2 Sigma2) (= (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) _let_1) (@ (@ (@ tptp.monito1457594016ress_a Sigma2) Phi) _let_1))))))))) (let ((_let_18 (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N3) (= M3 N3)))))) (let ((_let_19 (forall ((Sigma tptp.trace_1367752404list_a) (Phi tptp.formula_a) (J tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) J)) J)))) (let ((_let_20 (@ tptp.ord_less_eq_nat tptp.j))) (let ((_let_21 (@ tptp.prefix1041802747list_a tptp.pi))) (let ((_let_22 (@ _let_21 tptp.sigma2))) (let ((_let_23 (@ (@ _let_10 tptp.phi_1) _let_1))) (let ((_let_24 (@ _let_21 tptp.sigma))) (let ((_let_25 (@ _let_2 _let_23))) (let ((_let_26 (ho_83 k_82 tptp.pi))) (let ((_let_27 (ho_42 (ho_86 (ho_85 k_84 tptp.sigma) tptp.phi_1) _let_26))) (let ((_let_28 (= _let_26 _let_27))) (let ((_let_29 (ho_38 k_43 _let_27))) (let ((_let_30 (ho_39 _let_29 _let_26))) (let ((_let_31 (or _let_30 _let_28))) (let ((_let_32 (forall ((Sigma tptp.trace_1367752404list_a) (Phi tptp.formula_a) (J tptp.nat)) (let ((_let_1 (ho_42 (ho_86 (ho_85 k_84 Sigma) Phi) J))) (or (ho_39 (ho_38 k_43 _let_1) J) (= J _let_1)))))) (let ((_let_33 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_18))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_19)) (TRANS (MACRO_SR_EQ_INTRO _let_33 :args (_let_19 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Sigma tptp.trace_1367752404list_a) (Phi tptp.formula_a) (J tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) J))) (or (@ (@ tptp.ord_less_nat _let_1) J) (= J _let_1)))) _let_32))))))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.sigma tptp.phi_1 _let_26 QUANTIFIERS_INST_E_MATCHING ((ho_42 (ho_86 (ho_85 k_84 Sigma) Phi) J)))) :args (_let_32))) _let_34 :args (_let_31 false _let_32)))) (let ((_let_36 (= tptp.k _let_27))) (let ((_let_37 (= tptp.k _let_26))) (let ((_let_38 (not _let_28))) (let ((_let_39 (ho_38 k_43 tptp.k))) (let ((_let_40 (ho_39 _let_39 _let_27))) (let ((_let_41 (not _let_40))) (let ((_let_42 (= _let_41 _let_36))) (let ((_let_43 (not _let_36))) (let ((_let_44 (or _let_41 _let_42))) (let ((_let_45 (forall ((BOUND_VARIABLE_10218 tptp.nat) (BOUND_VARIABLE_10220 tptp.nat)) (let ((_let_1 (not (ho_39 (ho_38 k_43 BOUND_VARIABLE_10218) BOUND_VARIABLE_10220)))) (or _let_1 (= (= BOUND_VARIABLE_10218 BOUND_VARIABLE_10220) _let_1)))))) (let ((_let_46 (0))) (let ((_let_47 (_let_45))) (let ((_let_48 (forall ((u |u_(-> tptp.formula_a Bool)|) (e Bool) (i tptp.formula_a)) (not (forall ((v |u_(-> tptp.formula_a Bool)|)) (not (forall ((ii tptp.formula_a)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.formula_a Bool)|) (y |u_(-> tptp.formula_a Bool)|)) (or (not (forall ((z tptp.formula_a)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_42 v ii) (ite (= i ii) e (ho_42 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_42 x z) (ho_42 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.prefix1027212443list_a tptp.trace_1367752404list_a Bool)|) (e |u_(-> tptp.trace_1367752404list_a Bool)|) (i tptp.prefix1027212443list_a)) (not (forall ((v |u_(-> tptp.prefix1027212443list_a tptp.trace_1367752404list_a Bool)|)) (not (forall ((ii tptp.prefix1027212443list_a)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.prefix1027212443list_a tptp.trace_1367752404list_a Bool)|) (y |u_(-> tptp.prefix1027212443list_a tptp.trace_1367752404list_a Bool)|)) (or (not (forall ((z tptp.prefix1027212443list_a)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.trace_1367752404list_a Bool)|) (e Bool) (i tptp.trace_1367752404list_a)) (not (forall ((v |u_(-> tptp.trace_1367752404list_a Bool)|)) (not (forall ((ii tptp.trace_1367752404list_a)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.trace_1367752404list_a Bool)|) (y |u_(-> tptp.trace_1367752404list_a Bool)|)) (or (not (forall ((z tptp.trace_1367752404list_a)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.trace_1367752404list_a tptp.formula_a tptp.nat tptp.nat)|) (e |u_(-> tptp.formula_a tptp.nat tptp.nat)|) (i tptp.trace_1367752404list_a)) (not (forall ((v |u_(-> tptp.trace_1367752404list_a tptp.formula_a tptp.nat tptp.nat)|)) (not (forall ((ii tptp.trace_1367752404list_a)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.trace_1367752404list_a tptp.formula_a tptp.nat tptp.nat)|) (y |u_(-> tptp.trace_1367752404list_a tptp.formula_a tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.trace_1367752404list_a)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> tptp.prefix1027212443list_a tptp.nat)|) (e tptp.nat) (i tptp.prefix1027212443list_a)) (not (forall ((v |u_(-> tptp.prefix1027212443list_a tptp.nat)|)) (not (forall ((ii tptp.prefix1027212443list_a)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> tptp.prefix1027212443list_a tptp.nat)|) (y |u_(-> tptp.prefix1027212443list_a tptp.nat)|)) (or (not (forall ((z tptp.prefix1027212443list_a)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> tptp.formula_a tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.formula_a)) (not (forall ((v |u_(-> tptp.formula_a tptp.nat tptp.nat)|)) (not (forall ((ii tptp.formula_a)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> tptp.formula_a tptp.nat tptp.nat)|) (y |u_(-> tptp.formula_a tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.formula_a)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.nat tptp.formula_a Bool)|) (e |u_(-> tptp.formula_a Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.formula_a Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.nat tptp.formula_a Bool)|) (y |u_(-> tptp.nat tptp.formula_a Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.trace_1367752404list_a tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.trace_1367752404list_a)) (not (forall ((v |u_(-> tptp.trace_1367752404list_a tptp.nat tptp.nat)|)) (not (forall ((ii tptp.trace_1367752404list_a)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.trace_1367752404list_a tptp.nat tptp.nat)|) (y |u_(-> tptp.trace_1367752404list_a tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.trace_1367752404list_a)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a Bool)|) (e |u_(-> tptp.prefix1027212443list_a Bool)|) (i tptp.prefix1027212443list_a)) (not (forall ((v |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a Bool)|)) (not (forall ((ii tptp.prefix1027212443list_a)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a Bool)|) (y |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a Bool)|)) (or (not (forall ((z tptp.prefix1027212443list_a)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> tptp.i tptp.formula_a tptp.formula_a)|) (e |u_(-> tptp.formula_a tptp.formula_a)|) (i tptp.i)) (not (forall ((v |u_(-> tptp.i tptp.formula_a tptp.formula_a)|)) (not (forall ((ii tptp.i)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.i tptp.formula_a tptp.formula_a)|) (y |u_(-> tptp.i tptp.formula_a tptp.formula_a)|)) (or (not (forall ((z tptp.i)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.prefix1027212443list_a Bool)|) (e Bool) (i tptp.prefix1027212443list_a)) (not (forall ((v |u_(-> tptp.prefix1027212443list_a Bool)|)) (not (forall ((ii tptp.prefix1027212443list_a)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.prefix1027212443list_a Bool)|) (y |u_(-> tptp.prefix1027212443list_a Bool)|)) (or (not (forall ((z tptp.prefix1027212443list_a)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.list_a tptp.nat tptp.formula_a Bool)|) (e |u_(-> tptp.nat tptp.formula_a Bool)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.nat tptp.formula_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.list_a tptp.nat tptp.formula_a Bool)|) (y |u_(-> tptp.list_a tptp.nat tptp.formula_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> tptp.trace_1367752404list_a tptp.list_a tptp.nat tptp.formula_a Bool)|) (e |u_(-> tptp.list_a tptp.nat tptp.formula_a Bool)|) (i tptp.trace_1367752404list_a)) (not (forall ((v |u_(-> tptp.trace_1367752404list_a tptp.list_a tptp.nat tptp.formula_a Bool)|)) (not (forall ((ii tptp.trace_1367752404list_a)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.trace_1367752404list_a tptp.list_a tptp.nat tptp.formula_a Bool)|) (y |u_(-> tptp.trace_1367752404list_a tptp.list_a tptp.nat tptp.formula_a Bool)|)) (or (not (forall ((z tptp.trace_1367752404list_a)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> tptp.nat tptp.prefix1027212443list_a)|) (e tptp.prefix1027212443list_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.prefix1027212443list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.nat tptp.prefix1027212443list_a)|) (y |u_(-> tptp.nat tptp.prefix1027212443list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)|) (e tptp.prefix1027212443list_a) (i tptp.prefix1027212443list_a)) (not (forall ((v |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)|)) (not (forall ((ii tptp.prefix1027212443list_a)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)|) (y |u_(-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)|)) (or (not (forall ((z tptp.prefix1027212443list_a)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.formula_a tptp.formula_a)|) (e tptp.formula_a) (i tptp.formula_a)) (not (forall ((v |u_(-> tptp.formula_a tptp.formula_a)|)) (not (forall ((ii tptp.formula_a)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.formula_a tptp.formula_a)|) (y |u_(-> tptp.formula_a tptp.formula_a)|)) (or (not (forall ((z tptp.formula_a)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.formula_a tptp.i tptp.formula_a tptp.formula_a)|) (e |u_(-> tptp.i tptp.formula_a tptp.formula_a)|) (i tptp.formula_a)) (not (forall ((v |u_(-> tptp.formula_a tptp.i tptp.formula_a tptp.formula_a)|)) (not (forall ((ii tptp.formula_a)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.formula_a tptp.i tptp.formula_a tptp.formula_a)|) (y |u_(-> tptp.formula_a tptp.i tptp.formula_a tptp.formula_a)|)) (or (not (forall ((z tptp.formula_a)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_92 (forall ((BOUND_VARIABLE_13797 tptp.nat) (BOUND_VARIABLE_13798 tptp.nat)) (let ((_let_1 (ho_42 (ho_41 k_40 BOUND_VARIABLE_13797) tptp.one_one_nat))) (= (ho_39 (ho_38 k_37 BOUND_VARIABLE_13797) BOUND_VARIABLE_13798) (or (ho_39 (ho_38 k_43 _let_1) BOUND_VARIABLE_13798) (= BOUND_VARIABLE_13798 _let_1))))))) (let ((_let_93 (forall ((BOUND_VARIABLE_13785 tptp.nat) (BOUND_VARIABLE_13786 tptp.nat)) (= (ho_39 (ho_38 k_44 BOUND_VARIABLE_13785) BOUND_VARIABLE_13786) (not (forall ((C3 tptp.nat)) (not (= BOUND_VARIABLE_13786 (ho_42 (ho_41 k_40 BOUND_VARIABLE_13785) C3))))))))) (let ((_let_94 (forall ((BOUND_VARIABLE_13777 tptp.nat) (BOUND_VARIABLE_13778 tptp.nat)) (= (ho_42 (ho_41 k_45 BOUND_VARIABLE_13777) BOUND_VARIABLE_13778) (ho_42 (ho_41 k_40 BOUND_VARIABLE_13778) BOUND_VARIABLE_13777))))) (let ((_let_95 (forall ((BOUND_VARIABLE_13765 tptp.nat) (BOUND_VARIABLE_13766 tptp.nat)) (= (ho_39 (ho_38 k_46 BOUND_VARIABLE_13765) BOUND_VARIABLE_13766) (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_13766 (ho_42 (ho_41 k_40 BOUND_VARIABLE_13765) K3))))))))) (let ((_let_96 (forall ((BOUND_VARIABLE_13753 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13754 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_47 BOUND_VARIABLE_13753) BOUND_VARIABLE_13754) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13753) BOUND_VARIABLE_13754) (not (ho_49 (ho_48 k_50 BOUND_VARIABLE_13754) BOUND_VARIABLE_13753))))))) (let ((_let_97 (forall ((BOUND_VARIABLE_13741 tptp.nat) (BOUND_VARIABLE_13742 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13741 BOUND_VARIABLE_13742))) (= (ho_39 (ho_38 k_51 BOUND_VARIABLE_13741) BOUND_VARIABLE_13742) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13741) BOUND_VARIABLE_13742) _let_1) (not _let_1))))))) (let ((_let_98 (forall ((BOUND_VARIABLE_13730 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13731 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_52 BOUND_VARIABLE_13730) BOUND_VARIABLE_13731) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13730) BOUND_VARIABLE_13731) (not (= BOUND_VARIABLE_13730 BOUND_VARIABLE_13731))))))) (let ((_let_99 (forall ((BOUND_VARIABLE_13720 tptp.nat) (BOUND_VARIABLE_13721 tptp.nat)) (= (ho_39 (ho_38 k_53 BOUND_VARIABLE_13720) BOUND_VARIABLE_13721) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13720) BOUND_VARIABLE_13721) (= BOUND_VARIABLE_13720 BOUND_VARIABLE_13721)))))) (let ((_let_100 (forall ((BOUND_VARIABLE_13708 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13709 tptp.prefix1027212443list_a)) (let ((_let_1 (= BOUND_VARIABLE_13708 BOUND_VARIABLE_13709))) (= (ho_49 (ho_48 k_54 BOUND_VARIABLE_13708) BOUND_VARIABLE_13709) (or (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13708) BOUND_VARIABLE_13709) (not _let_1)) _let_1)))))) (let ((_let_101 (forall ((BOUND_VARIABLE_13693 tptp.nat) (BOUND_VARIABLE_13694 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13693 BOUND_VARIABLE_13694))) (= (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13693) BOUND_VARIABLE_13694) _let_1) (not (ho_39 (ho_38 k_43 BOUND_VARIABLE_13694) BOUND_VARIABLE_13693)) (not _let_1)) (ho_39 (ho_38 k_55 BOUND_VARIABLE_13693) BOUND_VARIABLE_13694)))))) (let ((_let_102 (forall ((BOUND_VARIABLE_13681 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13682 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_56 BOUND_VARIABLE_13681) BOUND_VARIABLE_13682) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13681) BOUND_VARIABLE_13682) (not (ho_49 (ho_48 k_50 BOUND_VARIABLE_13682) BOUND_VARIABLE_13681))))))) (let ((_let_103 (forall ((BOUND_VARIABLE_13669 tptp.nat) (BOUND_VARIABLE_13670 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13669 BOUND_VARIABLE_13670))) (= (ho_39 (ho_38 k_57 BOUND_VARIABLE_13669) BOUND_VARIABLE_13670) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13669) BOUND_VARIABLE_13670) _let_1) (not _let_1))))))) (let ((_let_104 (forall ((BOUND_VARIABLE_13658 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13659 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_58 BOUND_VARIABLE_13658) BOUND_VARIABLE_13659) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13658) BOUND_VARIABLE_13659) (not (= BOUND_VARIABLE_13658 BOUND_VARIABLE_13659))))))) (let ((_let_105 (forall ((BOUND_VARIABLE_13647 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13648 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_59 BOUND_VARIABLE_13647) BOUND_VARIABLE_13648) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13647) BOUND_VARIABLE_13648) (not (= BOUND_VARIABLE_13647 BOUND_VARIABLE_13648))))))) (let ((_let_106 (forall ((BOUND_VARIABLE_13637 tptp.nat) (BOUND_VARIABLE_13638 tptp.nat)) (= (ho_39 (ho_38 k_60 BOUND_VARIABLE_13637) BOUND_VARIABLE_13638) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13637) BOUND_VARIABLE_13638) (= BOUND_VARIABLE_13637 BOUND_VARIABLE_13638)))))) (let ((_let_107 (forall ((BOUND_VARIABLE_13625 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13626 tptp.prefix1027212443list_a)) (let ((_let_1 (= BOUND_VARIABLE_13625 BOUND_VARIABLE_13626))) (= (ho_49 (ho_48 k_61 BOUND_VARIABLE_13625) BOUND_VARIABLE_13626) (or (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13625) BOUND_VARIABLE_13626) (not _let_1)) _let_1)))))) (let ((_let_108 (forall ((BOUND_VARIABLE_14095 |u_(-> tptp.nat Bool)|)) (= (ho_63 k_62 BOUND_VARIABLE_14095) (not (forall ((X5 tptp.nat)) (not (ho_39 BOUND_VARIABLE_14095 X5)))))))) (let ((_let_109 (forall ((BOUND_VARIABLE_14110 |u_(-> tptp.nat Bool)|)) (= (ho_63 k_64 BOUND_VARIABLE_14110) (not (forall ((N3 tptp.nat)) (or (not (ho_39 BOUND_VARIABLE_14110 N3)) (not (forall ((M3 tptp.nat)) (or (not (ho_39 (ho_38 k_43 M3) N3)) (not (ho_39 BOUND_VARIABLE_14110 M3)))))))))))) (let ((_let_110 (forall ((BOUND_VARIABLE_13594 tptp.nat) (BOUND_VARIABLE_13595 tptp.nat)) (= (= BOUND_VARIABLE_13594 BOUND_VARIABLE_13595) (ho_39 (ho_38 k_65 BOUND_VARIABLE_13594) BOUND_VARIABLE_13595))))) (let ((_let_111 (forall ((BOUND_VARIABLE_13580 tptp.nat) (BOUND_VARIABLE_13581 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13580 BOUND_VARIABLE_13581))) (= (ho_39 (ho_38 k_66 BOUND_VARIABLE_13580) BOUND_VARIABLE_13581) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13580) BOUND_VARIABLE_13581) _let_1) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13581) BOUND_VARIABLE_13580) _let_1))))))) (let ((_let_112 (forall ((BOUND_VARIABLE_13573 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13574 tptp.prefix1027212443list_a)) (= (= BOUND_VARIABLE_13573 BOUND_VARIABLE_13574) (ho_49 (ho_48 k_67 BOUND_VARIABLE_13573) BOUND_VARIABLE_13574))))) (let ((_let_113 (forall ((BOUND_VARIABLE_13562 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13563 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_68 BOUND_VARIABLE_13562) BOUND_VARIABLE_13563) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13562) BOUND_VARIABLE_13563) (ho_49 (ho_48 k_50 BOUND_VARIABLE_13563) BOUND_VARIABLE_13562)))))) (let ((_let_114 (forall ((BOUND_VARIABLE_13555 tptp.nat) (BOUND_VARIABLE_13556 tptp.nat)) (= (= BOUND_VARIABLE_13555 BOUND_VARIABLE_13556) (ho_39 (ho_38 k_69 BOUND_VARIABLE_13555) BOUND_VARIABLE_13556))))) (let ((_let_115 (forall ((BOUND_VARIABLE_13541 tptp.nat) (BOUND_VARIABLE_13542 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13541 BOUND_VARIABLE_13542))) (= (ho_39 (ho_38 k_70 BOUND_VARIABLE_13541) BOUND_VARIABLE_13542) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13541) BOUND_VARIABLE_13542) _let_1) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13542) BOUND_VARIABLE_13541) _let_1))))))) (let ((_let_116 (forall ((BOUND_VARIABLE_13534 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13535 tptp.prefix1027212443list_a)) (= (= BOUND_VARIABLE_13534 BOUND_VARIABLE_13535) (ho_49 (ho_48 k_71 BOUND_VARIABLE_13534) BOUND_VARIABLE_13535))))) (let ((_let_117 (forall ((BOUND_VARIABLE_13523 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13524 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_72 BOUND_VARIABLE_13523) BOUND_VARIABLE_13524) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13523) BOUND_VARIABLE_13524) (ho_49 (ho_48 k_50 BOUND_VARIABLE_13524) BOUND_VARIABLE_13523)))))) (let ((_let_118 (forall ((BOUND_VARIABLE_13516 tptp.nat) (BOUND_VARIABLE_13517 tptp.nat)) (= (= BOUND_VARIABLE_13516 BOUND_VARIABLE_13517) (ho_39 (ho_38 k_73 BOUND_VARIABLE_13516) BOUND_VARIABLE_13517))))) (let ((_let_119 (forall ((BOUND_VARIABLE_13502 tptp.nat) (BOUND_VARIABLE_13503 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13502 BOUND_VARIABLE_13503))) (= (ho_39 (ho_38 k_74 BOUND_VARIABLE_13502) BOUND_VARIABLE_13503) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13503) BOUND_VARIABLE_13502) _let_1) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13502) BOUND_VARIABLE_13503) _let_1))))))) (let ((_let_120 (forall ((BOUND_VARIABLE_13495 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13496 tptp.prefix1027212443list_a)) (= (= BOUND_VARIABLE_13495 BOUND_VARIABLE_13496) (ho_49 (ho_48 k_75 BOUND_VARIABLE_13495) BOUND_VARIABLE_13496))))) (let ((_let_121 (forall ((BOUND_VARIABLE_13484 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13485 tptp.prefix1027212443list_a)) (= (ho_49 (ho_48 k_76 BOUND_VARIABLE_13484) BOUND_VARIABLE_13485) (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13485) BOUND_VARIABLE_13484) (ho_49 (ho_48 k_50 BOUND_VARIABLE_13484) BOUND_VARIABLE_13485)))))) (let ((_let_122 (forall ((BOUND_VARIABLE_13474 tptp.nat) (BOUND_VARIABLE_13475 tptp.nat)) (= (ho_39 (ho_38 k_77 BOUND_VARIABLE_13474) BOUND_VARIABLE_13475) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13474) BOUND_VARIABLE_13475) (= BOUND_VARIABLE_13474 BOUND_VARIABLE_13475)))))) (let ((_let_123 (forall ((BOUND_VARIABLE_13464 tptp.nat) (BOUND_VARIABLE_13465 tptp.nat)) (= (ho_39 (ho_38 k_78 BOUND_VARIABLE_13464) BOUND_VARIABLE_13465) (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13464) BOUND_VARIABLE_13465) (= BOUND_VARIABLE_13464 BOUND_VARIABLE_13465)))))) (let ((_let_124 (forall ((BOUND_VARIABLE_13452 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13453 tptp.prefix1027212443list_a)) (let ((_let_1 (= BOUND_VARIABLE_13452 BOUND_VARIABLE_13453))) (= (ho_49 (ho_48 k_79 BOUND_VARIABLE_13452) BOUND_VARIABLE_13453) (or (and (ho_49 (ho_48 k_50 BOUND_VARIABLE_13452) BOUND_VARIABLE_13453) (not _let_1)) _let_1)))))) (let ((_let_125 (forall ((BOUND_VARIABLE_13440 tptp.nat) (BOUND_VARIABLE_13441 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13440 BOUND_VARIABLE_13441))) (= (ho_39 (ho_38 k_80 BOUND_VARIABLE_13440) BOUND_VARIABLE_13441) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13440) BOUND_VARIABLE_13441) _let_1) (not _let_1))))))) (let ((_let_126 (forall ((BOUND_VARIABLE_13428 tptp.nat) (BOUND_VARIABLE_13429 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13428 BOUND_VARIABLE_13429))) (= (ho_39 (ho_38 k_81 BOUND_VARIABLE_13428) BOUND_VARIABLE_13429) (and (or (ho_39 (ho_38 k_43 BOUND_VARIABLE_13428) BOUND_VARIABLE_13429) _let_1) (not _let_1))))))) (let ((_let_127 (forall ((BOUND_VARIABLE_13797 tptp.nat) (BOUND_VARIABLE_13798 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_13797) tptp.one_one_nat))) (= (or (@ (@ tptp.ord_less_nat _let_1) BOUND_VARIABLE_13798) (= BOUND_VARIABLE_13798 _let_1)) (ll_36 BOUND_VARIABLE_13797 BOUND_VARIABLE_13798)))))) (let ((_let_128 (forall ((BOUND_VARIABLE_13785 tptp.nat) (BOUND_VARIABLE_13786 tptp.nat)) (= (not (forall ((C3 tptp.nat)) (not (= BOUND_VARIABLE_13786 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_13785) C3))))) (ll_35 BOUND_VARIABLE_13785 BOUND_VARIABLE_13786))))) (let ((_let_129 (forall ((BOUND_VARIABLE_13777 tptp.nat) (BOUND_VARIABLE_13778 tptp.nat)) (= (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_13778) BOUND_VARIABLE_13777) (ll_34 BOUND_VARIABLE_13777 BOUND_VARIABLE_13778))))) (let ((_let_130 (forall ((BOUND_VARIABLE_13765 tptp.nat) (BOUND_VARIABLE_13766 tptp.nat)) (= (not (forall ((K3 tptp.nat)) (not (= BOUND_VARIABLE_13766 (@ (@ tptp.plus_plus_nat BOUND_VARIABLE_13765) K3))))) (ll_33 BOUND_VARIABLE_13765 BOUND_VARIABLE_13766))))) (let ((_let_131 (forall ((BOUND_VARIABLE_13753 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13754 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13753) BOUND_VARIABLE_13754) (not (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13754) BOUND_VARIABLE_13753))) (ll_32 BOUND_VARIABLE_13753 BOUND_VARIABLE_13754))))) (let ((_let_132 (forall ((BOUND_VARIABLE_13741 tptp.nat) (BOUND_VARIABLE_13742 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13741 BOUND_VARIABLE_13742))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13741) BOUND_VARIABLE_13742) _let_1) (not _let_1)) (ll_31 BOUND_VARIABLE_13741 BOUND_VARIABLE_13742)))))) (let ((_let_133 (forall ((BOUND_VARIABLE_13730 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13731 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13730) BOUND_VARIABLE_13731) (not (= BOUND_VARIABLE_13730 BOUND_VARIABLE_13731))) (ll_30 BOUND_VARIABLE_13730 BOUND_VARIABLE_13731))))) (let ((_let_134 (forall ((BOUND_VARIABLE_13720 tptp.nat) (BOUND_VARIABLE_13721 tptp.nat)) (= (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13720) BOUND_VARIABLE_13721) (= BOUND_VARIABLE_13720 BOUND_VARIABLE_13721)) (ll_29 BOUND_VARIABLE_13720 BOUND_VARIABLE_13721))))) (let ((_let_135 (forall ((BOUND_VARIABLE_13708 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13709 tptp.prefix1027212443list_a)) (let ((_let_1 (= BOUND_VARIABLE_13708 BOUND_VARIABLE_13709))) (= (or (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13708) BOUND_VARIABLE_13709) (not _let_1)) _let_1) (ll_28 BOUND_VARIABLE_13708 BOUND_VARIABLE_13709)))))) (let ((_let_136 (forall ((BOUND_VARIABLE_13693 tptp.nat) (BOUND_VARIABLE_13694 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13693 BOUND_VARIABLE_13694))) (= (ll_27 BOUND_VARIABLE_13693 BOUND_VARIABLE_13694) (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13693) BOUND_VARIABLE_13694) _let_1) (not (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13694) BOUND_VARIABLE_13693)) (not _let_1))))))) (let ((_let_137 (forall ((BOUND_VARIABLE_13681 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13682 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13681) BOUND_VARIABLE_13682) (not (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13682) BOUND_VARIABLE_13681))) (ll_26 BOUND_VARIABLE_13681 BOUND_VARIABLE_13682))))) (let ((_let_138 (forall ((BOUND_VARIABLE_13669 tptp.nat) (BOUND_VARIABLE_13670 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13669 BOUND_VARIABLE_13670))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13669) BOUND_VARIABLE_13670) _let_1) (not _let_1)) (ll_25 BOUND_VARIABLE_13669 BOUND_VARIABLE_13670)))))) (let ((_let_139 (forall ((BOUND_VARIABLE_13658 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13659 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13658) BOUND_VARIABLE_13659) (not (= BOUND_VARIABLE_13658 BOUND_VARIABLE_13659))) (ll_24 BOUND_VARIABLE_13658 BOUND_VARIABLE_13659))))) (let ((_let_140 (forall ((BOUND_VARIABLE_13647 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13648 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13647) BOUND_VARIABLE_13648) (not (= BOUND_VARIABLE_13647 BOUND_VARIABLE_13648))) (ll_23 BOUND_VARIABLE_13647 BOUND_VARIABLE_13648))))) (let ((_let_141 (forall ((BOUND_VARIABLE_13637 tptp.nat) (BOUND_VARIABLE_13638 tptp.nat)) (= (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13637) BOUND_VARIABLE_13638) (= BOUND_VARIABLE_13637 BOUND_VARIABLE_13638)) (ll_22 BOUND_VARIABLE_13637 BOUND_VARIABLE_13638))))) (let ((_let_142 (forall ((BOUND_VARIABLE_13625 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13626 tptp.prefix1027212443list_a)) (let ((_let_1 (= BOUND_VARIABLE_13625 BOUND_VARIABLE_13626))) (= (or (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13625) BOUND_VARIABLE_13626) (not _let_1)) _let_1) (ll_21 BOUND_VARIABLE_13625 BOUND_VARIABLE_13626)))))) (let ((_let_143 (forall ((BOUND_VARIABLE_13616 (-> tptp.nat Bool))) (= (not (forall ((X5 tptp.nat)) (not (@ BOUND_VARIABLE_13616 X5)))) (ll_20 BOUND_VARIABLE_13616))))) (let ((_let_144 (forall ((BOUND_VARIABLE_13601 (-> tptp.nat Bool))) (= (not (forall ((N3 tptp.nat)) (or (not (@ BOUND_VARIABLE_13601 N3)) (not (forall ((M3 tptp.nat)) (or (not (@ (@ tptp.ord_less_nat M3) N3)) (not (@ BOUND_VARIABLE_13601 M3)))))))) (ll_19 BOUND_VARIABLE_13601))))) (let ((_let_145 (forall ((BOUND_VARIABLE_13594 tptp.nat) (BOUND_VARIABLE_13595 tptp.nat)) (= (= BOUND_VARIABLE_13594 BOUND_VARIABLE_13595) (ll_18 BOUND_VARIABLE_13594 BOUND_VARIABLE_13595))))) (let ((_let_146 (forall ((BOUND_VARIABLE_13580 tptp.nat) (BOUND_VARIABLE_13581 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13580 BOUND_VARIABLE_13581))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13580) BOUND_VARIABLE_13581) _let_1) (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13581) BOUND_VARIABLE_13580) _let_1)) (ll_17 BOUND_VARIABLE_13580 BOUND_VARIABLE_13581)))))) (let ((_let_147 (forall ((BOUND_VARIABLE_13573 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13574 tptp.prefix1027212443list_a)) (= (= BOUND_VARIABLE_13573 BOUND_VARIABLE_13574) (ll_16 BOUND_VARIABLE_13573 BOUND_VARIABLE_13574))))) (let ((_let_148 (forall ((BOUND_VARIABLE_13562 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13563 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13562) BOUND_VARIABLE_13563) (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13563) BOUND_VARIABLE_13562)) (ll_15 BOUND_VARIABLE_13562 BOUND_VARIABLE_13563))))) (let ((_let_149 (forall ((BOUND_VARIABLE_13555 tptp.nat) (BOUND_VARIABLE_13556 tptp.nat)) (= (= BOUND_VARIABLE_13555 BOUND_VARIABLE_13556) (ll_14 BOUND_VARIABLE_13555 BOUND_VARIABLE_13556))))) (let ((_let_150 (forall ((BOUND_VARIABLE_13541 tptp.nat) (BOUND_VARIABLE_13542 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13541 BOUND_VARIABLE_13542))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13541) BOUND_VARIABLE_13542) _let_1) (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13542) BOUND_VARIABLE_13541) _let_1)) (ll_13 BOUND_VARIABLE_13541 BOUND_VARIABLE_13542)))))) (let ((_let_151 (forall ((BOUND_VARIABLE_13534 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13535 tptp.prefix1027212443list_a)) (= (= BOUND_VARIABLE_13534 BOUND_VARIABLE_13535) (ll_12 BOUND_VARIABLE_13534 BOUND_VARIABLE_13535))))) (let ((_let_152 (forall ((BOUND_VARIABLE_13523 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13524 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13523) BOUND_VARIABLE_13524) (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13524) BOUND_VARIABLE_13523)) (ll_11 BOUND_VARIABLE_13523 BOUND_VARIABLE_13524))))) (let ((_let_153 (forall ((BOUND_VARIABLE_13516 tptp.nat) (BOUND_VARIABLE_13517 tptp.nat)) (= (= BOUND_VARIABLE_13516 BOUND_VARIABLE_13517) (ll_10 BOUND_VARIABLE_13516 BOUND_VARIABLE_13517))))) (let ((_let_154 (forall ((BOUND_VARIABLE_13502 tptp.nat) (BOUND_VARIABLE_13503 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13502 BOUND_VARIABLE_13503))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13503) BOUND_VARIABLE_13502) _let_1) (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13502) BOUND_VARIABLE_13503) _let_1)) (ll_9 BOUND_VARIABLE_13502 BOUND_VARIABLE_13503)))))) (let ((_let_155 (forall ((BOUND_VARIABLE_13495 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13496 tptp.prefix1027212443list_a)) (= (= BOUND_VARIABLE_13495 BOUND_VARIABLE_13496) (ll_8 BOUND_VARIABLE_13495 BOUND_VARIABLE_13496))))) (let ((_let_156 (forall ((BOUND_VARIABLE_13484 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13485 tptp.prefix1027212443list_a)) (= (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13485) BOUND_VARIABLE_13484) (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13484) BOUND_VARIABLE_13485)) (ll_7 BOUND_VARIABLE_13484 BOUND_VARIABLE_13485))))) (let ((_let_157 (forall ((BOUND_VARIABLE_13474 tptp.nat) (BOUND_VARIABLE_13475 tptp.nat)) (= (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13474) BOUND_VARIABLE_13475) (= BOUND_VARIABLE_13474 BOUND_VARIABLE_13475)) (ll_6 BOUND_VARIABLE_13474 BOUND_VARIABLE_13475))))) (let ((_let_158 (forall ((BOUND_VARIABLE_13464 tptp.nat) (BOUND_VARIABLE_13465 tptp.nat)) (= (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13464) BOUND_VARIABLE_13465) (= BOUND_VARIABLE_13464 BOUND_VARIABLE_13465)) (ll_5 BOUND_VARIABLE_13464 BOUND_VARIABLE_13465))))) (let ((_let_159 (forall ((BOUND_VARIABLE_13452 tptp.prefix1027212443list_a) (BOUND_VARIABLE_13453 tptp.prefix1027212443list_a)) (let ((_let_1 (= BOUND_VARIABLE_13452 BOUND_VARIABLE_13453))) (= (or (and (@ (@ tptp.ord_le699472955list_a BOUND_VARIABLE_13452) BOUND_VARIABLE_13453) (not _let_1)) _let_1) (ll_4 BOUND_VARIABLE_13452 BOUND_VARIABLE_13453)))))) (let ((_let_160 (forall ((BOUND_VARIABLE_13440 tptp.nat) (BOUND_VARIABLE_13441 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13440 BOUND_VARIABLE_13441))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13440) BOUND_VARIABLE_13441) _let_1) (not _let_1)) (ll_3 BOUND_VARIABLE_13440 BOUND_VARIABLE_13441)))))) (let ((_let_161 (forall ((BOUND_VARIABLE_13428 tptp.nat) (BOUND_VARIABLE_13429 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_13428 BOUND_VARIABLE_13429))) (= (and (or (@ (@ tptp.ord_less_nat BOUND_VARIABLE_13428) BOUND_VARIABLE_13429) _let_1) (not _let_1)) (ll_2 BOUND_VARIABLE_13428 BOUND_VARIABLE_13429)))))) (let ((_let_162 (and _let_25 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127))) (let ((_let_163 (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_25)) (PREPROCESS :args ((and _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127)))) :args (_let_162)) (PREPROCESS :args ((= _let_162 (and _let_40 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92))))) (PREPROCESS :args ((and _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48)))) :args ((and _let_40 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48))) :args _let_46))) (let ((_let_164 (ho_39 _let_39 _let_26))) (let ((_let_165 (and _let_41 _let_43))) (let ((_let_166 (not _let_30))) (let ((_let_167 (and _let_166 _let_38))) (let ((_let_168 (or _let_167 _let_165 _let_164 _let_37))) (let ((_let_169 (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (ho_38 k_43 C2))) (or (and (not (ho_39 (ho_38 k_43 B) A)) (not (= B A))) (and (not (ho_39 _let_1 B)) (not (= B C2))) (ho_39 _let_1 A) (= A C2)))))) (let ((_let_170 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_33 :args ((forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C2))) (or (not (@ (@ tptp.ord_less_eq_nat B) A)) (not (@ _let_1 B)) (@ _let_1 A)))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (or (and (not (@ (@ tptp.ord_less_nat B) A)) (not (= B A))) (and (not (@ _let_1 B)) (not (= B C2))) (@ _let_1 A) (= A C2)))) _let_169))))))) (let ((_let_171 (not _let_167))) (let ((_let_172 (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 (not _let_31)))))) (let ((_let_173 (not _let_165))) (let ((_let_174 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_165 0)) :args ((or _let_41 _let_173))) _let_163 :args (_let_173 false _let_40)))) (let ((_let_175 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_164 _let_37 _let_165 _let_167 (not _let_168)))) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 (not _let_164))))) _let_174 (MACRO_RESOLUTION_TRUST _let_172 _let_35 (REORDERING (CNF_AND_POS :args (_let_167 1)) :args ((or _let_38 _let_171))) (REORDERING (CNF_AND_POS :args (_let_167 0)) :args ((or _let_166 _let_171))) :args (_let_171 false _let_31 true _let_28 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_170 :args (_let_27 _let_26 tptp.k QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_169)))) _let_170 :args (_let_168 false _let_169)) :args (_let_37 true _let_164 true _let_165 true _let_167 false _let_168)))) (let ((_let_176 (or))) (let ((_let_177 (REFL :args ((not _let_37))))) (let ((_let_178 (and _let_37 _let_43))) (let ((_let_179 (ASSUME :args (_let_43)))) (let ((_let_180 (ASSUME :args (_let_37)))) (let ((_let_181 (SYMM _let_180))) (let ((_let_182 (ho_39 _let_29 tptp.k))) 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tptp.ord_le699472955list_a Y5) X4)))) (= (lambda ((Y4 tptp.nat) (Z3 tptp.nat)) (= Y4 Z3)) (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4)))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a A) (@ F C2)))))) (forall ((A tptp.nat) (F (-> tptp.prefix1027212443list_a tptp.nat)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C2)))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a A) (@ F C2)))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C2)))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le699472955list_a (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le699472955list_a (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le699472955list_a (@ F A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C2))))) (forall ((A tptp.nat) (F (-> tptp.prefix1027212443list_a tptp.nat)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le699472955list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le699472955list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C2)))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))) (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z4) (@ _let_1 Z4))))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C2) (@ _let_1 C2))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X2 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X2) (@ P Y3))) (@ P X2))) (@ P A))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ _let_1 C2))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P3 X5))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P4 N3) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N3) (not (@ P4 M3)))))))) (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 ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))) (forall ((Y tptp.prefix1027212443list_a) (X tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a Y) X) (not (@ (@ tptp.ord_le887097159list_a X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (= tptp.ord_le699472955list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (or (@ (@ tptp.ord_le887097159list_a X4) Y5) (= X4 Y5)))) (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y5) (= X4 Y5)))) (= tptp.ord_le887097159list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (not (= X4 Y5))))) (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y5) (not (= X4 Y5))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_le887097159list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a A) (@ F C2)))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A) (@ F C2)))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_le887097159list_a (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le887097159list_a (@ F B)) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a (@ F A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.nat tptp.prefix1027212443list_a)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le887097159list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.nat) (F (-> tptp.prefix1027212443list_a tptp.nat)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.prefix1027212443list_a) (F (-> tptp.prefix1027212443list_a tptp.prefix1027212443list_a)) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (=> (forall ((X2 tptp.prefix1027212443list_a) (Y2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X2) Y2) (@ (@ tptp.ord_le699472955list_a (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X2)) (@ F Y2)))) (@ _let_1 (@ F C2))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.prefix1027212443list_a)) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_le699472955list_a (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_le887097159list_a (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_le887097159list_a (@ F A)) C2))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C2) (=> (forall ((X2 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y2) (@ (@ tptp.ord_less_nat (@ F X2)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A)) C2))))) _let_13 (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (not (= A B)) (@ (@ tptp.ord_le887097159list_a A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (not (@ (@ tptp.ord_le887097159list_a X) Y)) (= (@ (@ tptp.ord_le699472955list_a X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (= (not (@ (@ tptp.ord_le887097159list_a X) Y)) (= X Y)))) _let_12 (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le887097159list_a X) Y) (@ (@ tptp.ord_le699472955list_a X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a) (Z4 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (=> (@ (@ tptp.ord_le887097159list_a Y) Z4) (@ (@ tptp.ord_le887097159list_a X) Z4)))) (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z4) (@ (@ tptp.ord_less_nat X) Z4)))) (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a) (Z4 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le699472955list_a Y) Z4) (@ _let_1 Z4))))) (forall ((X tptp.nat) (Y tptp.nat) (Z4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z4) (@ _let_1 Z4))))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.prefix1027212443list_a) (Y tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a X) Y) (or (@ (@ tptp.ord_le887097159list_a X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))) (= tptp.ord_le887097159list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (not (@ (@ tptp.ord_le699472955list_a Y5) X4))))) _let_11 (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a A) B) (=> (@ (@ tptp.ord_le887097159list_a B) C2) (@ (@ tptp.ord_le887097159list_a A) C2)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C2) (@ (@ tptp.ord_less_nat A) C2)))) (forall ((A tptp.prefix1027212443list_a) (B tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le699472955list_a B) C2) (@ _let_1 C2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C2) (@ _let_1 C2))))) (= tptp.ord_le699472955list_a (lambda ((A2 tptp.prefix1027212443list_a) (B2 tptp.prefix1027212443list_a)) (or (@ (@ tptp.ord_le887097159list_a A2) B2) (= A2 B2)))) (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A2) B2) (= A2 B2)))) (= tptp.ord_le887097159list_a (lambda ((A2 tptp.prefix1027212443list_a) (B2 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a A2) B2) (not (= A2 B2))))) (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A2) B2) (not (= A2 B2))))) (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (let ((_let_1 (@ tptp.ord_le887097159list_a C2))) (=> (@ (@ tptp.ord_le699472955list_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.prefix1027212443list_a) (A tptp.prefix1027212443list_a) (C2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le887097159list_a B) A) (=> (@ (@ tptp.ord_le699472955list_a C2) B) (@ (@ tptp.ord_le887097159list_a C2) A)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C2) B) (@ (@ tptp.ord_less_nat C2) A)))) (@ _let_9 (@ (@ _let_10 _let_7) _let_1)) (forall ((Pi tptp.prefix1027212443list_a) (Pi2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.ord_le699472955list_a Pi) Pi2) (@ (@ tptp.ord_less_eq_nat (@ tptp.plen_P694648887list_a Pi)) (@ tptp.plen_P694648887list_a Pi2)))) (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))) (@ _let_9 (@ (@ _let_8 _let_7) _let_1)) (= tptp.ord_le887097159list_a (lambda ((X4 tptp.prefix1027212443list_a) (Y5 tptp.prefix1027212443list_a)) (and (@ (@ tptp.ord_le699472955list_a X4) Y5) (not (@ (@ tptp.ord_le699472955list_a Y5) X4))))) (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((P5 tptp.prefix1027212443list_a)) (exists ((X_1 tptp.trace_1367752404list_a)) (@ (@ tptp.prefix1041802747list_a P5) X_1))) (forall ((Pi tptp.prefix1027212443list_a) (Pi2 tptp.prefix1027212443list_a) (S tptp.trace_1367752404list_a)) (=> (@ (@ tptp.ord_le699472955list_a Pi) Pi2) (=> (@ (@ tptp.prefix1041802747list_a Pi2) S) (@ (@ tptp.prefix1041802747list_a Pi) S)))) (forall ((Pi tptp.prefix1027212443list_a) (Sigma tptp.trace_1367752404list_a) (Pi2 tptp.prefix1027212443list_a)) (=> (@ (@ tptp.prefix1041802747list_a Pi) Sigma) (=> (@ (@ tptp.prefix1041802747list_a Pi2) Sigma) (or (@ (@ tptp.ord_le699472955list_a Pi) Pi2) (@ (@ tptp.ord_le699472955list_a Pi2) Pi))))) (forall ((X91 tptp.formula_a) (X92 tptp.i) (X93 tptp.formula_a) (Y91 tptp.formula_a) (Y92 tptp.i) (Y93 tptp.formula_a)) (= (= (@ (@ (@ tptp.until_a X91) X92) X93) (@ (@ (@ tptp.until_a Y91) Y92) Y93)) (and (= X91 Y91) (= X92 Y92) (= X93 Y93)))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi)))))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi)))))) (@ (@ tptp.ord_less_eq_nat (@ _let_4 tptp.k)) _let_5) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ tptp.plen_P694648887list_a tptp.pi))))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_1) (@ tptp.plen_P694648887list_a tptp.pi)))))) (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ (@ tptp.plus_plus_nat (@ _let_1 tptp.ia)) tptp.b)) (@ (@ tptp.ord_less_nat K) (@ (@ (@ tptp.monito1457594016ress_a tptp.sigma) tptp.phi_2) (@ tptp.plen_P694648887list_a tptp.pi)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_6 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_6 tptp.j)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat)) (@ _let_4 tptp.ja)) (forall ((Sigma tptp.trace_1367752404list_a) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a Sigma))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 I)) (@ _let_1 J)) (@ (@ tptp.ord_less_nat I) J)))) (forall ((I tptp.nat) (X tptp.nat) (S tptp.trace_1367752404list_a)) (exists ((J3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) J3) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.tau_Pr257024512list_a S) J3))))) (forall ((I tptp.nat) (J tptp.nat) (S tptp.trace_1367752404list_a)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a S))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I)) (@ _let_1 J))))) (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))) (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N3 tptp.nat)) (exists ((K3 tptp.nat)) (= N3 (@ (@ tptp.plus_plus_nat M3) K3))))) (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N2) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((J tptp.nat) (Sigma tptp.trace_1367752404list_a) (Sigma2 tptp.trace_1367752404list_a) (Phi tptp.formula_a)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.tau_Pr257024512list_a Sigma) I2) (@ (@ tptp.tau_Pr257024512list_a Sigma2) I2)))) (= (@ (@ (@ tptp.monito1457594016ress_a Sigma) Phi) J) (@ (@ (@ tptp.monito1457594016ress_a Sigma2) Phi) J)))) (forall ((Sigma tptp.trace_1367752404list_a) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.tau_Pr257024512list_a Sigma))) (let ((_let_2 (@ _let_1 J))) (let ((_let_3 (@ _let_1 I))) (=> (@ (@ tptp.ord_less_eq_nat _let_3) _let_2) (=> (@ (@ tptp.ord_less_nat J) I) (= _let_3 _let_2))))))) (forall ((P5 tptp.prefix1027212443list_a) (S tptp.trace_1367752404list_a) (S2 tptp.trace_1367752404list_a) (I tptp.nat)) (let ((_let_1 (@ tptp.prefix1041802747list_a P5))) (=> (@ _let_1 S) (=> (@ _let_1 S2) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.plen_P694648887list_a P5)) (= (@ (@ tptp.tau_Pr257024512list_a S) I) (@ (@ tptp.tau_Pr257024512list_a S2) I))))))) (not (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.plen_P694648887list_a tptp.pi))) (let ((_let_2 (@ tptp.monito1457594016ress_a tptp.sigma2))) (let ((_let_3 (@ tptp.ord_less_eq_nat J3))) (let ((_let_4 (@ tptp.tau_Pr257024512list_a tptp.sigma2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_4 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_4 J3)) (=> (@ _let_3 (@ (@ _let_2 tptp.phi_1) _let_1)) (not (@ _let_3 (@ (@ _let_2 tptp.phi_2) _let_1))))))))))) (not (forall ((J3 tptp.nat)) (let ((_let_1 (@ tptp.plen_P694648887list_a tptp.pi))) (let ((_let_2 (@ tptp.monito1457594016ress_a tptp.sigma))) (let ((_let_3 (@ tptp.ord_less_eq_nat J3))) (let ((_let_4 (@ tptp.tau_Pr257024512list_a tptp.sigma))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_4 tptp.ia)) tptp.b)) tptp.one_one_nat)) (@ _let_4 J3)) (=> (@ _let_3 (@ (@ _let_2 tptp.phi_1) _let_1)) (not (@ _let_3 (@ (@ _let_2 tptp.phi_2) _let_1))))))))))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((A5 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A5 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A5) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))) (forall ((B5 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B5 (@ _let_2 B)) (= (@ _let_1 B5) (@ _let_2 (@ _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C2) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C2))))) (= tptp.plus_plus_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A2))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C2)) (= B C2)))) (forall ((B tptp.nat) (A tptp.nat) (C2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C2) A)) (= B C2))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C))))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))) (= tptp.ord_less_eq_nat (lambda ((A2 tptp.nat) (B2 tptp.nat)) (exists ((C3 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A2) C3))))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)))) (forall ((C2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C2))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.nat) (C2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) C2)) (@ (@ tptp.ord_less_nat A) B))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))) (forall ((A tptp.nat) (B tptp.nat) (C2 tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C2) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C2)) (@ (@ tptp.plus_plus_nat B) D2))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))) (= tptp.ord_less_nat (lambda ((A2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) __flatten_var_0))) _let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.90/1.13 )
% 0.90/1.13 % SZS output end Proof for ITP125^1
% 0.90/1.13 % cvc5---1.0.5 exiting
% 0.90/1.13 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------