TSTP Solution File: ITP081^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP081^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 03:18:03 EDT 2023
% Result : Theorem 0.72s 0.96s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.17 % Problem : ITP081^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n017.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 16:30:42 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.24/0.57 %----Proving TH0
% 0.24/0.58 %------------------------------------------------------------------------------
% 0.24/0.58 % File : ITP081^1 : TPTP v8.1.2. Released v7.5.0.
% 0.24/0.58 % Domain : Interactive Theorem Proving
% 0.24/0.58 % Problem : Sledgehammer Irreducible problem prob_472__6626992_1
% 0.24/0.58 % Version : Especial.
% 0.24/0.58 % English :
% 0.24/0.58
% 0.24/0.58 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.24/0.58 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.24/0.58 % Source : [Des21]
% 0.24/0.58 % Names : Irreducible/prob_472__6626992_1 [Des21]
% 0.24/0.58
% 0.24/0.58 % Status : Theorem
% 0.24/0.58 % Rating : 0.46 v8.1.0, 0.45 v7.5.0
% 0.24/0.58 % Syntax : Number of formulae : 419 ( 146 unt; 68 typ; 0 def)
% 0.24/0.58 % Number of atoms : 1059 ( 603 equ; 0 cnn)
% 0.24/0.58 % Maximal formula atoms : 14 ( 3 avg)
% 0.24/0.58 % Number of connectives : 4056 ( 203 ~; 21 |; 116 &;3214 @)
% 0.24/0.58 % ( 0 <=>; 502 =>; 0 <=; 0 <~>)
% 0.24/0.58 % Maximal formula depth : 26 ( 8 avg)
% 0.24/0.58 % Number of types : 13 ( 12 usr)
% 0.24/0.58 % Number of type conns : 242 ( 242 >; 0 *; 0 +; 0 <<)
% 0.24/0.58 % Number of symbols : 57 ( 56 usr; 17 con; 0-7 aty)
% 0.24/0.58 % Number of variables : 1257 ( 23 ^;1157 !; 77 ?;1257 :)
% 0.24/0.58 % SPC : TH0_THM_EQU_NAR
% 0.24/0.58
% 0.24/0.58 % Comments : This file was generated by Sledgehammer 2021-02-23 15:40:45.367
% 0.24/0.58 %------------------------------------------------------------------------------
% 0.24/0.58 % Could-be-implicit typings (12)
% 0.24/0.58 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 0.24/0.58 list_P561207620_edgeD: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 0.24/0.58 option_list_val: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 0.24/0.58 produc1432036078de_val: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 0.24/0.58 list_list_node: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__node_J_J,type,
% 0.24/0.58 set_list_node: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 0.24/0.58 list_node: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 0.24/0.58 list_val: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 0.24/0.58 set_node: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 0.24/0.58 set_val: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_tf__node,type,
% 0.24/0.58 node: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_tf__val,type,
% 0.24/0.58 val: $tType ).
% 0.24/0.58
% 0.24/0.58 thf(ty_n_tf__g,type,
% 0.24/0.58 g: $tType ).
% 0.24/0.58
% 0.24/0.58 % Explicit typings (56)
% 0.24/0.58 thf(sy_c_Finite__Set_Ofinite_001tf__node,type,
% 0.24/0.58 finite_finite_node: set_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Finite__Set_Ofinite_001tf__val,type,
% 0.24/0.58 finite_finite_val: set_val > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 0.24/0.58 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Graph__path_Ograph__path__base_Opath_001tf__g_001tf__node_001tf__edgeD,type,
% 0.24/0.58 graph_435229452_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > list_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 0.24/0.58 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Oappend_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 append_list_node: list_list_node > list_list_node > list_list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Oappend_001tf__node,type,
% 0.24/0.58 append_node: list_node > list_node > list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Oappend_001tf__val,type,
% 0.24/0.58 append_val: list_val > list_val > list_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Obutlast_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 butlast_list_node: list_list_node > list_list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Obutlast_001tf__node,type,
% 0.24/0.58 butlast_node: list_node > list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Obutlast_001tf__val,type,
% 0.24/0.58 butlast_val: list_val > list_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 cons_list_node: list_node > list_list_node > list_list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 0.24/0.58 cons_node: node > list_node > list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 0.24/0.58 cons_val: val > list_val > list_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 nil_list_node: list_list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 0.24/0.58 nil_node: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 0.24/0.58 nil_val: list_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 0.24/0.58 hd_node: list_node > node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 0.24/0.58 hd_val: list_val > val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Oset_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 set_list_node2: list_list_node > set_list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 0.24/0.58 set_node2: list_node > set_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 0.24/0.58 set_val2: list_val > set_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Otl_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 tl_list_node: list_list_node > list_list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 0.24/0.58 tl_node: list_node > list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 0.24/0.58 tl_val: list_val > list_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__node_J,type,
% 0.24/0.58 ord_less_eq_set_node: set_node > set_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__val_J,type,
% 0.24/0.58 ord_less_eq_set_val: set_val > set_val > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 0.24/0.58 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 0.24/0.58 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 0.24/0.58 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Set_OCollect_001tf__node,type,
% 0.24/0.58 collect_node: ( node > $o ) > set_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Set_OCollect_001tf__val,type,
% 0.24/0.58 collect_val: ( val > $o ) > set_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Sublist_Oprefix_001tf__node,type,
% 0.24/0.58 prefix_node: list_node > list_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 0.24/0.58 suffix_node: list_node > list_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_member_001t__List__Olist_Itf__node_J,type,
% 0.24/0.58 member_list_node: list_node > set_list_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_member_001tf__node,type,
% 0.24/0.58 member_node: node > set_node > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_c_member_001tf__val,type,
% 0.24/0.58 member_val: val > set_val > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v__092_060alpha_062n,type,
% 0.24/0.58 alpha_n: g > list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.24/0.58 phi_r: val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_defs,type,
% 0.24/0.58 defs: g > node > set_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_g,type,
% 0.24/0.58 g2: g ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_i____,type,
% 0.24/0.58 i: node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_inEdges_H,type,
% 0.24/0.58 inEdges: g > node > list_P561207620_edgeD ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_invar,type,
% 0.24/0.58 invar: g > $o ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_m,type,
% 0.24/0.58 m: node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_ms,type,
% 0.24/0.58 ms: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_ms_H____,type,
% 0.24/0.58 ms2: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_n,type,
% 0.24/0.58 n: node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_ns,type,
% 0.24/0.58 ns: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_phis,type,
% 0.24/0.58 phis: g > produc1432036078de_val > option_list_val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.24/0.58 pred_phi_r: node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_r,type,
% 0.24/0.58 r: val ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_ri____,type,
% 0.24/0.58 ri: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_rs_H____,type,
% 0.24/0.58 rs: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_rs____,type,
% 0.24/0.58 rs2: list_node ).
% 0.24/0.58
% 0.24/0.58 thf(sy_v_s,type,
% 0.24/0.58 s: val ).
% 0.24/0.58
% 0.24/0.58 % Relevant facts (350)
% 0.24/0.58 thf(fact_0_False,axiom,
% 0.24/0.58 r != phi_r ).
% 0.24/0.58
% 0.24/0.58 % False
% 0.24/0.58 thf(fact_1_ri__is__valid,axiom,
% 0.24/0.58 ( i
% 0.24/0.58 = ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ).
% 0.24/0.58
% 0.24/0.58 % ri_is_valid
% 0.24/0.58 thf(fact_2_old_Oinvar,axiom,
% 0.24/0.58 ! [G: g] : ( invar @ G ) ).
% 0.24/0.58
% 0.24/0.58 % old.invar
% 0.24/0.58 thf(fact_3_assms_I7_J,axiom,
% 0.24/0.58 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.24/0.58
% 0.24/0.58 % assms(7)
% 0.24/0.58 thf(fact_4_ri__props_I1_J,axiom,
% 0.24/0.58 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i ).
% 0.24/0.58
% 0.24/0.58 % ri_props(1)
% 0.24/0.58 thf(fact_5_old_Opath2__app,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_app
% 0.24/0.58 thf(fact_6__092_060open_062defNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060noteq_062_AdefNode_Ag_Ar_092_060close_062,axiom,
% 0.24/0.58 ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r )
% 0.24/0.58 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ) ).
% 0.24/0.58
% 0.24/0.58 % \<open>defNode g \<phi>\<^sub>r \<noteq> defNode g r\<close>
% 0.24/0.58 thf(fact_7_rs_H__props_I1_J,axiom,
% 0.24/0.58 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 0.24/0.58
% 0.24/0.58 % rs'_props(1)
% 0.24/0.58 thf(fact_8_assms_I10_J,axiom,
% 0.24/0.58 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.24/0.58
% 0.24/0.58 % assms(10)
% 0.24/0.58 thf(fact_9_rs__props_I1_J,axiom,
% 0.24/0.58 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.24/0.58
% 0.24/0.58 % rs_props(1)
% 0.24/0.58 thf(fact_10_ms_H__props_I1_J,axiom,
% 0.24/0.58 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms2 @ i ).
% 0.24/0.58
% 0.24/0.58 % ms'_props(1)
% 0.24/0.58 thf(fact_11__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062i_A_061_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_061_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062i_A_092_060noteq_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_059_Am_A_092_060noteq_062_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.24/0.58 ( ( i
% 0.24/0.58 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.24/0.58 => ( ( ( i
% 0.24/0.58 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.24/0.58 => ( m != i ) )
% 0.24/0.58 => ~ ( ( i
% 0.24/0.58 != ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) )
% 0.24/0.58 => ( m = i ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % \<open>\<And>thesis. \<lbrakk>i = defNode g \<phi>\<^sub>r \<Longrightarrow> thesis; \<lbrakk>i \<noteq> defNode g \<phi>\<^sub>r; m = i\<rbrakk> \<Longrightarrow> thesis; \<lbrakk>i \<noteq> defNode g \<phi>\<^sub>r; m \<noteq> i\<rbrakk> \<Longrightarrow> thesis\<rbrakk> \<Longrightarrow> thesis\<close>
% 0.24/0.58 thf(fact_12_old_Opath2__split_I2_J,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns2 ) @ M ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_split(2)
% 0.24/0.58 thf(fact_13_old_Opath2__not__Nil,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( Ns != nil_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_not_Nil
% 0.24/0.58 thf(fact_14_old_Opath2__not__Nil2,axiom,
% 0.24/0.58 ! [G: g,N: node,M: node] :
% 0.24/0.58 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_not_Nil2
% 0.24/0.58 thf(fact_15_rs_H__props_I3_J,axiom,
% 0.24/0.58 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.24/0.58
% 0.24/0.58 % rs'_props(3)
% 0.24/0.58 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_hd_in_\<alpha>n
% 0.24/0.58 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_hd_in_ns
% 0.24/0.58 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 0.24/0.58 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_in_\<alpha>n
% 0.24/0.58 thf(fact_19_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.24/0.58 ! [X: list_node,Xs: list_list_node,Ys: list_list_node,Y: list_node] :
% 0.24/0.58 ( ( member_list_node @ X @ ( set_list_node2 @ Xs ) )
% 0.24/0.58 => ( member_list_node @ X @ ( set_list_node2 @ ( tl_list_node @ ( append_list_node @ Ys @ ( cons_list_node @ Y @ Xs ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.elem_set_implies_elem_tl_app_cons
% 0.24/0.58 thf(fact_20_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.24/0.58 ! [X: val,Xs: list_val,Ys: list_val,Y: val] :
% 0.24/0.58 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.58 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y @ Xs ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.elem_set_implies_elem_tl_app_cons
% 0.24/0.58 thf(fact_21_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.24/0.58 ! [X: node,Xs: list_node,Ys: list_node,Y: node] :
% 0.24/0.58 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.58 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y @ Xs ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.elem_set_implies_elem_tl_app_cons
% 0.24/0.58 thf(fact_22_ri__props_I2_J,axiom,
% 0.24/0.58 member_node @ i @ ( set_node2 @ ms ) ).
% 0.24/0.58
% 0.24/0.58 % ri_props(2)
% 0.24/0.58 thf(fact_23_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_tl_in_\<alpha>n
% 0.24/0.58 thf(fact_24_old_Opath2__last__in__ns,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_last_in_ns
% 0.24/0.58 thf(fact_25_old_Opath2__split_I1_J,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,N2: node,Ns2: list_node,M: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns2 ) ) @ M )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_split(1)
% 0.24/0.58 thf(fact_26_rs__props_I3_J,axiom,
% 0.24/0.58 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % rs_props(3)
% 0.24/0.58 thf(fact_27_rs_H__loopfree,axiom,
% 0.24/0.58 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % rs'_loopfree
% 0.24/0.58 thf(fact_28_rs__def,axiom,
% 0.24/0.58 ( rs2
% 0.24/0.58 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % rs_def
% 0.24/0.58 thf(fact_29_ri__props_I4_J,axiom,
% 0.24/0.58 prefix_node @ ri @ rs2 ).
% 0.24/0.58
% 0.24/0.58 % ri_props(4)
% 0.24/0.58 thf(fact_30_old_Oempty__path2,axiom,
% 0.24/0.58 ! [N: node,G: g] :
% 0.24/0.58 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.58 => ( ( invar @ G )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.empty_path2
% 0.24/0.58 thf(fact_31_ms_H__props_I3_J,axiom,
% 0.24/0.58 ~ ( member_node @ i @ ( set_node2 @ ( butlast_node @ ms2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % ms'_props(3)
% 0.24/0.58 thf(fact_32_rs_H__props_I4_J,axiom,
% 0.24/0.58 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % rs'_props(4)
% 0.24/0.58 thf(fact_33_assms_I8_J,axiom,
% 0.24/0.58 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.24/0.58
% 0.24/0.58 % assms(8)
% 0.24/0.58 thf(fact_34_tl__append2,axiom,
% 0.24/0.58 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ( Xs != nil_list_node )
% 0.24/0.58 => ( ( tl_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.24/0.58 = ( append_list_node @ ( tl_list_node @ Xs ) @ Ys ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % tl_append2
% 0.24/0.58 thf(fact_35_tl__append2,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( Xs != nil_val )
% 0.24/0.58 => ( ( tl_val @ ( append_val @ Xs @ Ys ) )
% 0.24/0.58 = ( append_val @ ( tl_val @ Xs ) @ Ys ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % tl_append2
% 0.24/0.58 thf(fact_36_tl__append2,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( Xs != nil_node )
% 0.24/0.58 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 0.24/0.58 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % tl_append2
% 0.24/0.58 thf(fact_37_list__e__eq__lel_I2_J,axiom,
% 0.24/0.58 ! [L1: list_val,E: val,L2: list_val,E2: val] :
% 0.24/0.58 ( ( ( append_val @ L1 @ ( cons_val @ E @ L2 ) )
% 0.24/0.58 = ( cons_val @ E2 @ nil_val ) )
% 0.24/0.58 = ( ( L1 = nil_val )
% 0.24/0.58 & ( E = E2 )
% 0.24/0.58 & ( L2 = nil_val ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_e_eq_lel(2)
% 0.24/0.58 thf(fact_38_list__e__eq__lel_I2_J,axiom,
% 0.24/0.58 ! [L1: list_list_node,E: list_node,L2: list_list_node,E2: list_node] :
% 0.24/0.58 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) )
% 0.24/0.58 = ( cons_list_node @ E2 @ nil_list_node ) )
% 0.24/0.58 = ( ( L1 = nil_list_node )
% 0.24/0.58 & ( E = E2 )
% 0.24/0.58 & ( L2 = nil_list_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_e_eq_lel(2)
% 0.24/0.58 thf(fact_39_list__e__eq__lel_I2_J,axiom,
% 0.24/0.58 ! [L1: list_node,E: node,L2: list_node,E2: node] :
% 0.24/0.58 ( ( ( append_node @ L1 @ ( cons_node @ E @ L2 ) )
% 0.24/0.58 = ( cons_node @ E2 @ nil_node ) )
% 0.24/0.58 = ( ( L1 = nil_node )
% 0.24/0.58 & ( E = E2 )
% 0.24/0.58 & ( L2 = nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_e_eq_lel(2)
% 0.24/0.58 thf(fact_40_list__e__eq__lel_I1_J,axiom,
% 0.24/0.58 ! [E2: val,L1: list_val,E: val,L2: list_val] :
% 0.24/0.58 ( ( ( cons_val @ E2 @ nil_val )
% 0.24/0.58 = ( append_val @ L1 @ ( cons_val @ E @ L2 ) ) )
% 0.24/0.58 = ( ( L1 = nil_val )
% 0.24/0.58 & ( E = E2 )
% 0.24/0.58 & ( L2 = nil_val ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_e_eq_lel(1)
% 0.24/0.58 thf(fact_41_list__e__eq__lel_I1_J,axiom,
% 0.24/0.58 ! [E2: list_node,L1: list_list_node,E: list_node,L2: list_list_node] :
% 0.24/0.58 ( ( ( cons_list_node @ E2 @ nil_list_node )
% 0.24/0.58 = ( append_list_node @ L1 @ ( cons_list_node @ E @ L2 ) ) )
% 0.24/0.58 = ( ( L1 = nil_list_node )
% 0.24/0.58 & ( E = E2 )
% 0.24/0.58 & ( L2 = nil_list_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_e_eq_lel(1)
% 0.24/0.58 thf(fact_42_list__e__eq__lel_I1_J,axiom,
% 0.24/0.58 ! [E2: node,L1: list_node,E: node,L2: list_node] :
% 0.24/0.58 ( ( ( cons_node @ E2 @ nil_node )
% 0.24/0.58 = ( append_node @ L1 @ ( cons_node @ E @ L2 ) ) )
% 0.24/0.58 = ( ( L1 = nil_node )
% 0.24/0.58 & ( E = E2 )
% 0.24/0.58 & ( L2 = nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_e_eq_lel(1)
% 0.24/0.58 thf(fact_43_list__se__match_I4_J,axiom,
% 0.24/0.58 ! [L2: list_val,A: val,L1: list_val] :
% 0.24/0.58 ( ( L2 != nil_val )
% 0.24/0.58 => ( ( ( cons_val @ A @ nil_val )
% 0.24/0.58 = ( append_val @ L1 @ L2 ) )
% 0.24/0.58 = ( ( L1 = nil_val )
% 0.24/0.58 & ( L2
% 0.24/0.58 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(4)
% 0.24/0.58 thf(fact_44_list__se__match_I4_J,axiom,
% 0.24/0.58 ! [L2: list_list_node,A: list_node,L1: list_list_node] :
% 0.24/0.58 ( ( L2 != nil_list_node )
% 0.24/0.58 => ( ( ( cons_list_node @ A @ nil_list_node )
% 0.24/0.58 = ( append_list_node @ L1 @ L2 ) )
% 0.24/0.58 = ( ( L1 = nil_list_node )
% 0.24/0.58 & ( L2
% 0.24/0.58 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(4)
% 0.24/0.58 thf(fact_45_list__se__match_I4_J,axiom,
% 0.24/0.58 ! [L2: list_node,A: node,L1: list_node] :
% 0.24/0.58 ( ( L2 != nil_node )
% 0.24/0.58 => ( ( ( cons_node @ A @ nil_node )
% 0.24/0.58 = ( append_node @ L1 @ L2 ) )
% 0.24/0.58 = ( ( L1 = nil_node )
% 0.24/0.58 & ( L2
% 0.24/0.58 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(4)
% 0.24/0.58 thf(fact_46_list__se__match_I3_J,axiom,
% 0.24/0.58 ! [L1: list_val,A: val,L2: list_val] :
% 0.24/0.58 ( ( L1 != nil_val )
% 0.24/0.58 => ( ( ( cons_val @ A @ nil_val )
% 0.24/0.58 = ( append_val @ L1 @ L2 ) )
% 0.24/0.58 = ( ( L1
% 0.24/0.58 = ( cons_val @ A @ nil_val ) )
% 0.24/0.58 & ( L2 = nil_val ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(3)
% 0.24/0.58 thf(fact_47_list__se__match_I3_J,axiom,
% 0.24/0.58 ! [L1: list_list_node,A: list_node,L2: list_list_node] :
% 0.24/0.58 ( ( L1 != nil_list_node )
% 0.24/0.58 => ( ( ( cons_list_node @ A @ nil_list_node )
% 0.24/0.58 = ( append_list_node @ L1 @ L2 ) )
% 0.24/0.58 = ( ( L1
% 0.24/0.58 = ( cons_list_node @ A @ nil_list_node ) )
% 0.24/0.58 & ( L2 = nil_list_node ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(3)
% 0.24/0.58 thf(fact_48_list__se__match_I3_J,axiom,
% 0.24/0.58 ! [L1: list_node,A: node,L2: list_node] :
% 0.24/0.58 ( ( L1 != nil_node )
% 0.24/0.58 => ( ( ( cons_node @ A @ nil_node )
% 0.24/0.58 = ( append_node @ L1 @ L2 ) )
% 0.24/0.58 = ( ( L1
% 0.24/0.58 = ( cons_node @ A @ nil_node ) )
% 0.24/0.58 & ( L2 = nil_node ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(3)
% 0.24/0.58 thf(fact_49_list__se__match_I2_J,axiom,
% 0.24/0.58 ! [L2: list_val,L1: list_val,A: val] :
% 0.24/0.58 ( ( L2 != nil_val )
% 0.24/0.58 => ( ( ( append_val @ L1 @ L2 )
% 0.24/0.58 = ( cons_val @ A @ nil_val ) )
% 0.24/0.58 = ( ( L1 = nil_val )
% 0.24/0.58 & ( L2
% 0.24/0.58 = ( cons_val @ A @ nil_val ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(2)
% 0.24/0.58 thf(fact_50_list__se__match_I2_J,axiom,
% 0.24/0.58 ! [L2: list_list_node,L1: list_list_node,A: list_node] :
% 0.24/0.58 ( ( L2 != nil_list_node )
% 0.24/0.58 => ( ( ( append_list_node @ L1 @ L2 )
% 0.24/0.58 = ( cons_list_node @ A @ nil_list_node ) )
% 0.24/0.58 = ( ( L1 = nil_list_node )
% 0.24/0.58 & ( L2
% 0.24/0.58 = ( cons_list_node @ A @ nil_list_node ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(2)
% 0.24/0.58 thf(fact_51_list__se__match_I2_J,axiom,
% 0.24/0.58 ! [L2: list_node,L1: list_node,A: node] :
% 0.24/0.58 ( ( L2 != nil_node )
% 0.24/0.58 => ( ( ( append_node @ L1 @ L2 )
% 0.24/0.58 = ( cons_node @ A @ nil_node ) )
% 0.24/0.58 = ( ( L1 = nil_node )
% 0.24/0.58 & ( L2
% 0.24/0.58 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(2)
% 0.24/0.58 thf(fact_52_list__se__match_I1_J,axiom,
% 0.24/0.58 ! [L1: list_val,L2: list_val,A: val] :
% 0.24/0.58 ( ( L1 != nil_val )
% 0.24/0.58 => ( ( ( append_val @ L1 @ L2 )
% 0.24/0.58 = ( cons_val @ A @ nil_val ) )
% 0.24/0.58 = ( ( L1
% 0.24/0.58 = ( cons_val @ A @ nil_val ) )
% 0.24/0.58 & ( L2 = nil_val ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(1)
% 0.24/0.58 thf(fact_53_list__se__match_I1_J,axiom,
% 0.24/0.58 ! [L1: list_list_node,L2: list_list_node,A: list_node] :
% 0.24/0.58 ( ( L1 != nil_list_node )
% 0.24/0.58 => ( ( ( append_list_node @ L1 @ L2 )
% 0.24/0.58 = ( cons_list_node @ A @ nil_list_node ) )
% 0.24/0.58 = ( ( L1
% 0.24/0.58 = ( cons_list_node @ A @ nil_list_node ) )
% 0.24/0.58 & ( L2 = nil_list_node ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(1)
% 0.24/0.58 thf(fact_54_list__se__match_I1_J,axiom,
% 0.24/0.58 ! [L1: list_node,L2: list_node,A: node] :
% 0.24/0.58 ( ( L1 != nil_node )
% 0.24/0.58 => ( ( ( append_node @ L1 @ L2 )
% 0.24/0.58 = ( cons_node @ A @ nil_node ) )
% 0.24/0.58 = ( ( L1
% 0.24/0.58 = ( cons_node @ A @ nil_node ) )
% 0.24/0.58 & ( L2 = nil_node ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_se_match(1)
% 0.24/0.58 thf(fact_55_list__ee__eq__leel_I2_J,axiom,
% 0.24/0.58 ! [L1: list_val,E1: val,E22: val,L2: list_val,E12: val,E23: val] :
% 0.24/0.58 ( ( ( append_val @ L1 @ ( cons_val @ E1 @ ( cons_val @ E22 @ L2 ) ) )
% 0.24/0.58 = ( cons_val @ E12 @ ( cons_val @ E23 @ nil_val ) ) )
% 0.24/0.58 = ( ( L1 = nil_val )
% 0.24/0.58 & ( E12 = E1 )
% 0.24/0.58 & ( E23 = E22 )
% 0.24/0.58 & ( L2 = nil_val ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_ee_eq_leel(2)
% 0.24/0.58 thf(fact_56_list__ee__eq__leel_I2_J,axiom,
% 0.24/0.58 ! [L1: list_list_node,E1: list_node,E22: list_node,L2: list_list_node,E12: list_node,E23: list_node] :
% 0.24/0.58 ( ( ( append_list_node @ L1 @ ( cons_list_node @ E1 @ ( cons_list_node @ E22 @ L2 ) ) )
% 0.24/0.58 = ( cons_list_node @ E12 @ ( cons_list_node @ E23 @ nil_list_node ) ) )
% 0.24/0.58 = ( ( L1 = nil_list_node )
% 0.24/0.58 & ( E12 = E1 )
% 0.24/0.58 & ( E23 = E22 )
% 0.24/0.58 & ( L2 = nil_list_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_ee_eq_leel(2)
% 0.24/0.58 thf(fact_57_list__ee__eq__leel_I2_J,axiom,
% 0.24/0.58 ! [L1: list_node,E1: node,E22: node,L2: list_node,E12: node,E23: node] :
% 0.24/0.58 ( ( ( append_node @ L1 @ ( cons_node @ E1 @ ( cons_node @ E22 @ L2 ) ) )
% 0.24/0.58 = ( cons_node @ E12 @ ( cons_node @ E23 @ nil_node ) ) )
% 0.24/0.58 = ( ( L1 = nil_node )
% 0.24/0.58 & ( E12 = E1 )
% 0.24/0.58 & ( E23 = E22 )
% 0.24/0.58 & ( L2 = nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_ee_eq_leel(2)
% 0.24/0.58 thf(fact_58_list__ee__eq__leel_I1_J,axiom,
% 0.24/0.58 ! [E12: val,E23: val,L1: list_val,E1: val,E22: val,L2: list_val] :
% 0.24/0.58 ( ( ( cons_val @ E12 @ ( cons_val @ E23 @ nil_val ) )
% 0.24/0.58 = ( append_val @ L1 @ ( cons_val @ E1 @ ( cons_val @ E22 @ L2 ) ) ) )
% 0.24/0.58 = ( ( L1 = nil_val )
% 0.24/0.58 & ( E12 = E1 )
% 0.24/0.58 & ( E23 = E22 )
% 0.24/0.58 & ( L2 = nil_val ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_ee_eq_leel(1)
% 0.24/0.58 thf(fact_59_list__ee__eq__leel_I1_J,axiom,
% 0.24/0.58 ! [E12: list_node,E23: list_node,L1: list_list_node,E1: list_node,E22: list_node,L2: list_list_node] :
% 0.24/0.58 ( ( ( cons_list_node @ E12 @ ( cons_list_node @ E23 @ nil_list_node ) )
% 0.24/0.58 = ( append_list_node @ L1 @ ( cons_list_node @ E1 @ ( cons_list_node @ E22 @ L2 ) ) ) )
% 0.24/0.58 = ( ( L1 = nil_list_node )
% 0.24/0.58 & ( E12 = E1 )
% 0.24/0.58 & ( E23 = E22 )
% 0.24/0.58 & ( L2 = nil_list_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_ee_eq_leel(1)
% 0.24/0.58 thf(fact_60_list__ee__eq__leel_I1_J,axiom,
% 0.24/0.58 ! [E12: node,E23: node,L1: list_node,E1: node,E22: node,L2: list_node] :
% 0.24/0.58 ( ( ( cons_node @ E12 @ ( cons_node @ E23 @ nil_node ) )
% 0.24/0.58 = ( append_node @ L1 @ ( cons_node @ E1 @ ( cons_node @ E22 @ L2 ) ) ) )
% 0.24/0.58 = ( ( L1 = nil_node )
% 0.24/0.58 & ( E12 = E1 )
% 0.24/0.58 & ( E23 = E22 )
% 0.24/0.58 & ( L2 = nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_ee_eq_leel(1)
% 0.24/0.58 thf(fact_61_ms_H__props_I2_J,axiom,
% 0.24/0.58 prefix_node @ ms2 @ ms ).
% 0.24/0.58
% 0.24/0.58 % ms'_props(2)
% 0.24/0.58 thf(fact_62_ri__props_I3_J,axiom,
% 0.24/0.58 ! [X2: node] :
% 0.24/0.58 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ ri ) ) )
% 0.24/0.58 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % ri_props(3)
% 0.24/0.58 thf(fact_63_list_Oinject,axiom,
% 0.24/0.58 ! [X21: val,X22: list_val,Y21: val,Y22: list_val] :
% 0.24/0.58 ( ( ( cons_val @ X21 @ X22 )
% 0.24/0.58 = ( cons_val @ Y21 @ Y22 ) )
% 0.24/0.58 = ( ( X21 = Y21 )
% 0.24/0.58 & ( X22 = Y22 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list.inject
% 0.24/0.58 thf(fact_64_list_Oinject,axiom,
% 0.24/0.58 ! [X21: list_node,X22: list_list_node,Y21: list_node,Y22: list_list_node] :
% 0.24/0.58 ( ( ( cons_list_node @ X21 @ X22 )
% 0.24/0.58 = ( cons_list_node @ Y21 @ Y22 ) )
% 0.24/0.58 = ( ( X21 = Y21 )
% 0.24/0.58 & ( X22 = Y22 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list.inject
% 0.24/0.58 thf(fact_65_list_Oinject,axiom,
% 0.24/0.58 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 0.24/0.58 ( ( ( cons_node @ X21 @ X22 )
% 0.24/0.58 = ( cons_node @ Y21 @ Y22 ) )
% 0.24/0.58 = ( ( X21 = Y21 )
% 0.24/0.58 & ( X22 = Y22 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list.inject
% 0.24/0.58 thf(fact_66_append_Oassoc,axiom,
% 0.24/0.58 ! [A: list_val,B: list_val,C: list_val] :
% 0.24/0.58 ( ( append_val @ ( append_val @ A @ B ) @ C )
% 0.24/0.58 = ( append_val @ A @ ( append_val @ B @ C ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append.assoc
% 0.24/0.58 thf(fact_67_append_Oassoc,axiom,
% 0.24/0.58 ! [A: list_node,B: list_node,C: list_node] :
% 0.24/0.58 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 0.24/0.58 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append.assoc
% 0.24/0.58 thf(fact_68_mem__Collect__eq,axiom,
% 0.24/0.58 ! [A: val,P: val > $o] :
% 0.24/0.58 ( ( member_val @ A @ ( collect_val @ P ) )
% 0.24/0.58 = ( P @ A ) ) ).
% 0.24/0.58
% 0.24/0.58 % mem_Collect_eq
% 0.24/0.58 thf(fact_69_mem__Collect__eq,axiom,
% 0.24/0.58 ! [A: node,P: node > $o] :
% 0.24/0.58 ( ( member_node @ A @ ( collect_node @ P ) )
% 0.24/0.58 = ( P @ A ) ) ).
% 0.24/0.58
% 0.24/0.58 % mem_Collect_eq
% 0.24/0.58 thf(fact_70_Collect__mem__eq,axiom,
% 0.24/0.58 ! [A2: set_val] :
% 0.24/0.58 ( ( collect_val
% 0.24/0.58 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 0.24/0.58 = A2 ) ).
% 0.24/0.58
% 0.24/0.58 % Collect_mem_eq
% 0.24/0.58 thf(fact_71_Collect__mem__eq,axiom,
% 0.24/0.58 ! [A2: set_node] :
% 0.24/0.58 ( ( collect_node
% 0.24/0.58 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 0.24/0.58 = A2 ) ).
% 0.24/0.58
% 0.24/0.58 % Collect_mem_eq
% 0.24/0.58 thf(fact_72_Collect__cong,axiom,
% 0.24/0.58 ! [P: node > $o,Q: node > $o] :
% 0.24/0.58 ( ! [X4: node] :
% 0.24/0.58 ( ( P @ X4 )
% 0.24/0.58 = ( Q @ X4 ) )
% 0.24/0.58 => ( ( collect_node @ P )
% 0.24/0.58 = ( collect_node @ Q ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % Collect_cong
% 0.24/0.58 thf(fact_73_Collect__cong,axiom,
% 0.24/0.58 ! [P: val > $o,Q: val > $o] :
% 0.24/0.58 ( ! [X4: val] :
% 0.24/0.58 ( ( P @ X4 )
% 0.24/0.58 = ( Q @ X4 ) )
% 0.24/0.58 => ( ( collect_val @ P )
% 0.24/0.58 = ( collect_val @ Q ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % Collect_cong
% 0.24/0.58 thf(fact_74_append__assoc,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 0.24/0.58 ( ( append_val @ ( append_val @ Xs @ Ys ) @ Zs )
% 0.24/0.58 = ( append_val @ Xs @ ( append_val @ Ys @ Zs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_assoc
% 0.24/0.58 thf(fact_75_append__assoc,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.58 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 0.24/0.58 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_assoc
% 0.24/0.58 thf(fact_76_append__same__eq,axiom,
% 0.24/0.58 ! [Ys: list_val,Xs: list_val,Zs: list_val] :
% 0.24/0.58 ( ( ( append_val @ Ys @ Xs )
% 0.24/0.58 = ( append_val @ Zs @ Xs ) )
% 0.24/0.58 = ( Ys = Zs ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_same_eq
% 0.24/0.58 thf(fact_77_append__same__eq,axiom,
% 0.24/0.58 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.24/0.58 ( ( ( append_node @ Ys @ Xs )
% 0.24/0.58 = ( append_node @ Zs @ Xs ) )
% 0.24/0.58 = ( Ys = Zs ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_same_eq
% 0.24/0.58 thf(fact_78_same__append__eq,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val,Zs: list_val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ Ys )
% 0.24/0.58 = ( append_val @ Xs @ Zs ) )
% 0.24/0.58 = ( Ys = Zs ) ) ).
% 0.24/0.58
% 0.24/0.58 % same_append_eq
% 0.24/0.58 thf(fact_79_same__append__eq,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ Ys )
% 0.24/0.58 = ( append_node @ Xs @ Zs ) )
% 0.24/0.58 = ( Ys = Zs ) ) ).
% 0.24/0.58
% 0.24/0.58 % same_append_eq
% 0.24/0.58 thf(fact_80_old_Opredecessor__is__node,axiom,
% 0.24/0.58 ! [N: node,G: g,N2: node] :
% 0.24/0.58 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.24/0.58 => ( ( invar @ G )
% 0.24/0.58 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.predecessor_is_node
% 0.24/0.58 thf(fact_81_old_Osuccessor__is__node,axiom,
% 0.24/0.58 ! [N: node,G: g,N2: node] :
% 0.24/0.58 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.24/0.58 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.58 => ( ( invar @ G )
% 0.24/0.58 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.successor_is_node
% 0.24/0.58 thf(fact_82_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.24/0.58 ! [G: g,N: node] :
% 0.24/0.58 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 0.24/0.58 != nil_node )
% 0.24/0.58 => ( ( invar @ G )
% 0.24/0.58 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.successor_in_\<alpha>n
% 0.24/0.58 thf(fact_83_old_Opath2__app_H,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ ( butlast_node @ Ns ) @ Ms ) @ L ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_app'
% 0.24/0.58 thf(fact_84_append__Nil2,axiom,
% 0.24/0.58 ! [Xs: list_list_node] :
% 0.24/0.58 ( ( append_list_node @ Xs @ nil_list_node )
% 0.24/0.58 = Xs ) ).
% 0.24/0.58
% 0.24/0.58 % append_Nil2
% 0.24/0.58 thf(fact_85_append__Nil2,axiom,
% 0.24/0.58 ! [Xs: list_val] :
% 0.24/0.58 ( ( append_val @ Xs @ nil_val )
% 0.24/0.58 = Xs ) ).
% 0.24/0.58
% 0.24/0.58 % append_Nil2
% 0.24/0.58 thf(fact_86_append__Nil2,axiom,
% 0.24/0.58 ! [Xs: list_node] :
% 0.24/0.58 ( ( append_node @ Xs @ nil_node )
% 0.24/0.58 = Xs ) ).
% 0.24/0.58
% 0.24/0.58 % append_Nil2
% 0.24/0.58 thf(fact_87_append__self__conv,axiom,
% 0.24/0.58 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ( ( append_list_node @ Xs @ Ys )
% 0.24/0.58 = Xs )
% 0.24/0.58 = ( Ys = nil_list_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_self_conv
% 0.24/0.58 thf(fact_88_append__self__conv,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ Ys )
% 0.24/0.58 = Xs )
% 0.24/0.58 = ( Ys = nil_val ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_self_conv
% 0.24/0.58 thf(fact_89_append__self__conv,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ Ys )
% 0.24/0.58 = Xs )
% 0.24/0.58 = ( Ys = nil_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_self_conv
% 0.24/0.58 thf(fact_90_self__append__conv,axiom,
% 0.24/0.58 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ( Xs
% 0.24/0.58 = ( append_list_node @ Xs @ Ys ) )
% 0.24/0.58 = ( Ys = nil_list_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % self_append_conv
% 0.24/0.58 thf(fact_91_self__append__conv,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( Xs
% 0.24/0.58 = ( append_val @ Xs @ Ys ) )
% 0.24/0.58 = ( Ys = nil_val ) ) ).
% 0.24/0.58
% 0.24/0.58 % self_append_conv
% 0.24/0.58 thf(fact_92_self__append__conv,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( Xs
% 0.24/0.58 = ( append_node @ Xs @ Ys ) )
% 0.24/0.58 = ( Ys = nil_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % self_append_conv
% 0.24/0.58 thf(fact_93_append__self__conv2,axiom,
% 0.24/0.58 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ( ( append_list_node @ Xs @ Ys )
% 0.24/0.58 = Ys )
% 0.24/0.58 = ( Xs = nil_list_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_self_conv2
% 0.24/0.58 thf(fact_94_append__self__conv2,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ Ys )
% 0.24/0.58 = Ys )
% 0.24/0.58 = ( Xs = nil_val ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_self_conv2
% 0.24/0.58 thf(fact_95_append__self__conv2,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ Ys )
% 0.24/0.58 = Ys )
% 0.24/0.58 = ( Xs = nil_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_self_conv2
% 0.24/0.58 thf(fact_96_self__append__conv2,axiom,
% 0.24/0.58 ! [Ys: list_list_node,Xs: list_list_node] :
% 0.24/0.58 ( ( Ys
% 0.24/0.58 = ( append_list_node @ Xs @ Ys ) )
% 0.24/0.58 = ( Xs = nil_list_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % self_append_conv2
% 0.24/0.58 thf(fact_97_self__append__conv2,axiom,
% 0.24/0.58 ! [Ys: list_val,Xs: list_val] :
% 0.24/0.58 ( ( Ys
% 0.24/0.58 = ( append_val @ Xs @ Ys ) )
% 0.24/0.58 = ( Xs = nil_val ) ) ).
% 0.24/0.58
% 0.24/0.58 % self_append_conv2
% 0.24/0.58 thf(fact_98_self__append__conv2,axiom,
% 0.24/0.58 ! [Ys: list_node,Xs: list_node] :
% 0.24/0.58 ( ( Ys
% 0.24/0.58 = ( append_node @ Xs @ Ys ) )
% 0.24/0.58 = ( Xs = nil_node ) ) ).
% 0.24/0.58
% 0.24/0.58 % self_append_conv2
% 0.24/0.58 thf(fact_99_Nil__is__append__conv,axiom,
% 0.24/0.58 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ( nil_list_node
% 0.24/0.58 = ( append_list_node @ Xs @ Ys ) )
% 0.24/0.58 = ( ( Xs = nil_list_node )
% 0.24/0.58 & ( Ys = nil_list_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % Nil_is_append_conv
% 0.24/0.58 thf(fact_100_Nil__is__append__conv,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( nil_val
% 0.24/0.58 = ( append_val @ Xs @ Ys ) )
% 0.24/0.58 = ( ( Xs = nil_val )
% 0.24/0.58 & ( Ys = nil_val ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % Nil_is_append_conv
% 0.24/0.58 thf(fact_101_Nil__is__append__conv,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( nil_node
% 0.24/0.58 = ( append_node @ Xs @ Ys ) )
% 0.24/0.58 = ( ( Xs = nil_node )
% 0.24/0.58 & ( Ys = nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % Nil_is_append_conv
% 0.24/0.58 thf(fact_102_append__is__Nil__conv,axiom,
% 0.24/0.58 ! [Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ( ( append_list_node @ Xs @ Ys )
% 0.24/0.58 = nil_list_node )
% 0.24/0.58 = ( ( Xs = nil_list_node )
% 0.24/0.58 & ( Ys = nil_list_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_is_Nil_conv
% 0.24/0.58 thf(fact_103_append__is__Nil__conv,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ Ys )
% 0.24/0.58 = nil_val )
% 0.24/0.58 = ( ( Xs = nil_val )
% 0.24/0.58 & ( Ys = nil_val ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_is_Nil_conv
% 0.24/0.58 thf(fact_104_append__is__Nil__conv,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ Ys )
% 0.24/0.58 = nil_node )
% 0.24/0.58 = ( ( Xs = nil_node )
% 0.24/0.58 & ( Ys = nil_node ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_is_Nil_conv
% 0.24/0.58 thf(fact_105_empty__append__eq__id,axiom,
% 0.24/0.58 ( ( append_list_node @ nil_list_node )
% 0.24/0.58 = ( ^ [X3: list_list_node] : X3 ) ) ).
% 0.24/0.58
% 0.24/0.58 % empty_append_eq_id
% 0.24/0.58 thf(fact_106_empty__append__eq__id,axiom,
% 0.24/0.58 ( ( append_val @ nil_val )
% 0.24/0.58 = ( ^ [X3: list_val] : X3 ) ) ).
% 0.24/0.58
% 0.24/0.58 % empty_append_eq_id
% 0.24/0.58 thf(fact_107_empty__append__eq__id,axiom,
% 0.24/0.58 ( ( append_node @ nil_node )
% 0.24/0.58 = ( ^ [X3: list_node] : X3 ) ) ).
% 0.24/0.58
% 0.24/0.58 % empty_append_eq_id
% 0.24/0.58 thf(fact_108_append_Oright__neutral,axiom,
% 0.24/0.58 ! [A: list_list_node] :
% 0.24/0.58 ( ( append_list_node @ A @ nil_list_node )
% 0.24/0.58 = A ) ).
% 0.24/0.58
% 0.24/0.58 % append.right_neutral
% 0.24/0.58 thf(fact_109_append_Oright__neutral,axiom,
% 0.24/0.58 ! [A: list_val] :
% 0.24/0.58 ( ( append_val @ A @ nil_val )
% 0.24/0.58 = A ) ).
% 0.24/0.58
% 0.24/0.58 % append.right_neutral
% 0.24/0.58 thf(fact_110_append_Oright__neutral,axiom,
% 0.24/0.58 ! [A: list_node] :
% 0.24/0.58 ( ( append_node @ A @ nil_node )
% 0.24/0.58 = A ) ).
% 0.24/0.58
% 0.24/0.58 % append.right_neutral
% 0.24/0.58 thf(fact_111_old_Opath2__split__ex_H,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.24/0.58 => ~ ! [Ns_1: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 0.24/0.58 => ! [Ns_2: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 0.24/0.58 => ( Ns
% 0.24/0.58 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_split_ex'
% 0.24/0.58 thf(fact_112_old_Opath2__prefix__ex,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( member_node @ M2 @ ( set_node2 @ Ns ) )
% 0.24/0.58 => ~ ! [Ns3: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M2 )
% 0.24/0.58 => ( ( prefix_node @ Ns3 @ Ns )
% 0.24/0.58 => ( member_node @ M2 @ ( set_node2 @ ( butlast_node @ Ns3 ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_prefix_ex
% 0.24/0.58 thf(fact_113_old_Opath2__split__first__prop,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ? [X2: node] :
% 0.24/0.58 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.24/0.58 & ( P @ X2 ) )
% 0.24/0.58 => ~ ! [M3: node,Ns3: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ M3 )
% 0.24/0.58 => ( ( P @ M3 )
% 0.24/0.58 => ( ! [X2: node] :
% 0.24/0.58 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ns3 ) ) )
% 0.24/0.58 => ~ ( P @ X2 ) )
% 0.24/0.58 => ~ ( prefix_node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_split_first_prop
% 0.24/0.58 thf(fact_114_old_Opath2__induct,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( ( invar @ G )
% 0.24/0.58 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 0.24/0.58 => ( ! [Ns4: list_node,N3: node,N4: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns4 @ M )
% 0.24/0.58 => ( ( P @ N4 @ Ns4 @ M )
% 0.24/0.58 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N4 ) ) )
% 0.24/0.58 => ( P @ N3 @ ( cons_node @ N3 @ Ns4 ) @ M ) ) ) )
% 0.24/0.58 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_induct
% 0.24/0.58 thf(fact_115_old_Opath2__split__ex,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.24/0.58 => ~ ! [Ns_1: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns_1 @ X )
% 0.24/0.58 => ! [Ns_2: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_2 @ M )
% 0.24/0.58 => ( ( Ns
% 0.24/0.58 = ( append_node @ Ns_1 @ ( tl_node @ Ns_2 ) ) )
% 0.24/0.58 => ( Ns
% 0.24/0.58 != ( append_node @ ( butlast_node @ Ns_1 ) @ Ns_2 ) ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_split_ex
% 0.24/0.58 thf(fact_116_old_Opath2__prefix,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,Ns2: list_node,M2: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( prefix_node @ ( append_node @ Ns2 @ ( cons_node @ M2 @ nil_node ) ) @ Ns )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns2 @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_prefix
% 0.24/0.58 thf(fact_117_old_Opath2__rev__induct,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.58 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 0.24/0.58 => ( ! [Ns4: list_node,M3: node,M4: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns4 @ M3 )
% 0.24/0.58 => ( ( P @ N @ Ns4 @ M3 )
% 0.24/0.58 => ( ( member_node @ M3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M4 ) ) )
% 0.24/0.58 => ( P @ N @ ( append_node @ Ns4 @ ( cons_node @ M4 @ nil_node ) ) @ M4 ) ) ) )
% 0.24/0.58 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_rev_induct
% 0.24/0.58 thf(fact_118_old_Opath2__snoc,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M2 ) ) )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.path2_snoc
% 0.24/0.58 thf(fact_119_append1__eq__conv,axiom,
% 0.24/0.58 ! [Xs: list_val,X: val,Ys: list_val,Y: val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ ( cons_val @ X @ nil_val ) )
% 0.24/0.58 = ( append_val @ Ys @ ( cons_val @ Y @ nil_val ) ) )
% 0.24/0.58 = ( ( Xs = Ys )
% 0.24/0.58 & ( X = Y ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append1_eq_conv
% 0.24/0.58 thf(fact_120_append1__eq__conv,axiom,
% 0.24/0.58 ! [Xs: list_list_node,X: list_node,Ys: list_list_node,Y: list_node] :
% 0.24/0.58 ( ( ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) )
% 0.24/0.58 = ( append_list_node @ Ys @ ( cons_list_node @ Y @ nil_list_node ) ) )
% 0.24/0.58 = ( ( Xs = Ys )
% 0.24/0.58 & ( X = Y ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append1_eq_conv
% 0.24/0.58 thf(fact_121_append1__eq__conv,axiom,
% 0.24/0.58 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 0.24/0.58 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.24/0.58 = ( ( Xs = Ys )
% 0.24/0.58 & ( X = Y ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append1_eq_conv
% 0.24/0.58 thf(fact_122_butlast__snoc,axiom,
% 0.24/0.58 ! [Xs: list_val,X: val] :
% 0.24/0.58 ( ( butlast_val @ ( append_val @ Xs @ ( cons_val @ X @ nil_val ) ) )
% 0.24/0.58 = Xs ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_snoc
% 0.24/0.58 thf(fact_123_butlast__snoc,axiom,
% 0.24/0.58 ! [Xs: list_list_node,X: list_node] :
% 0.24/0.58 ( ( butlast_list_node @ ( append_list_node @ Xs @ ( cons_list_node @ X @ nil_list_node ) ) )
% 0.24/0.58 = Xs ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_snoc
% 0.24/0.58 thf(fact_124_butlast__snoc,axiom,
% 0.24/0.58 ! [Xs: list_node,X: node] :
% 0.24/0.58 ( ( butlast_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) )
% 0.24/0.58 = Xs ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_snoc
% 0.24/0.58 thf(fact_125__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ms_H_O_A_092_060lbrakk_062g_A_092_060turnstile_062_Am_Nms_H_092_060rightarrow_062i_059_Aprefix_Ams_H_Ams_059_Ai_A_092_060notin_062_Aset_A_Ibutlast_Ams_H_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.24/0.58 ~ ! [Ms2: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ Ms2 @ i )
% 0.24/0.58 => ( ( prefix_node @ Ms2 @ ms )
% 0.24/0.58 => ( member_node @ i @ ( set_node2 @ ( butlast_node @ Ms2 ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % \<open>\<And>thesis. (\<And>ms'. \<lbrakk>g \<turnstile> m-ms'\<rightarrow>i; prefix ms' ms; i \<notin> set (butlast ms')\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.24/0.58 thf(fact_126__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062i_Ari_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nri_092_060rightarrow_062i_059_Ai_A_092_060in_062_Aset_Ams_059_A_092_060forall_062n_092_060in_062set_A_Ibutlast_Ari_J_O_An_A_092_060notin_062_Aset_Ams_059_Aprefix_Ari_Ars_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.24/0.58 ~ ! [I: node,Ri: list_node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Ri @ I )
% 0.24/0.58 => ( ( member_node @ I @ ( set_node2 @ ms ) )
% 0.24/0.58 => ( ! [X2: node] :
% 0.24/0.58 ( ( member_node @ X2 @ ( set_node2 @ ( butlast_node @ Ri ) ) )
% 0.24/0.58 => ~ ( member_node @ X2 @ ( set_node2 @ ms ) ) )
% 0.24/0.58 => ~ ( prefix_node @ Ri @ rs2 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % \<open>\<And>thesis. (\<And>i ri. \<lbrakk>g \<turnstile> defNode g r-ri\<rightarrow>i; i \<in> set ms; \<forall>n\<in>set (butlast ri). n \<notin> set ms; prefix ri rs\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.24/0.58 thf(fact_127_old_OCons__path2,axiom,
% 0.24/0.58 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 0.24/0.58 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.58 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.24/0.58 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % old.Cons_path2
% 0.24/0.58 thf(fact_128_butlast_Osimps_I1_J,axiom,
% 0.24/0.58 ( ( butlast_list_node @ nil_list_node )
% 0.24/0.58 = nil_list_node ) ).
% 0.24/0.58
% 0.24/0.58 % butlast.simps(1)
% 0.24/0.58 thf(fact_129_butlast_Osimps_I1_J,axiom,
% 0.24/0.58 ( ( butlast_val @ nil_val )
% 0.24/0.58 = nil_val ) ).
% 0.24/0.58
% 0.24/0.58 % butlast.simps(1)
% 0.24/0.58 thf(fact_130_butlast_Osimps_I1_J,axiom,
% 0.24/0.58 ( ( butlast_node @ nil_node )
% 0.24/0.58 = nil_node ) ).
% 0.24/0.58
% 0.24/0.58 % butlast.simps(1)
% 0.24/0.58 thf(fact_131_in__set__butlastD,axiom,
% 0.24/0.58 ! [X: val,Xs: list_val] :
% 0.24/0.58 ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 0.24/0.58 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % in_set_butlastD
% 0.24/0.58 thf(fact_132_in__set__butlastD,axiom,
% 0.24/0.58 ! [X: node,Xs: list_node] :
% 0.24/0.58 ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 0.24/0.58 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % in_set_butlastD
% 0.24/0.58 thf(fact_133_butlast__tl,axiom,
% 0.24/0.58 ! [Xs: list_val] :
% 0.24/0.58 ( ( butlast_val @ ( tl_val @ Xs ) )
% 0.24/0.58 = ( tl_val @ ( butlast_val @ Xs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_tl
% 0.24/0.58 thf(fact_134_butlast__tl,axiom,
% 0.24/0.58 ! [Xs: list_node] :
% 0.24/0.58 ( ( butlast_node @ ( tl_node @ Xs ) )
% 0.24/0.58 = ( tl_node @ ( butlast_node @ Xs ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_tl
% 0.24/0.58 thf(fact_135_butlast_Osimps_I2_J,axiom,
% 0.24/0.58 ! [Xs: list_val,X: val] :
% 0.24/0.58 ( ( ( Xs = nil_val )
% 0.24/0.58 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 0.24/0.58 = nil_val ) )
% 0.24/0.58 & ( ( Xs != nil_val )
% 0.24/0.58 => ( ( butlast_val @ ( cons_val @ X @ Xs ) )
% 0.24/0.58 = ( cons_val @ X @ ( butlast_val @ Xs ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast.simps(2)
% 0.24/0.58 thf(fact_136_butlast_Osimps_I2_J,axiom,
% 0.24/0.58 ! [Xs: list_list_node,X: list_node] :
% 0.24/0.58 ( ( ( Xs = nil_list_node )
% 0.24/0.58 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 0.24/0.58 = nil_list_node ) )
% 0.24/0.58 & ( ( Xs != nil_list_node )
% 0.24/0.58 => ( ( butlast_list_node @ ( cons_list_node @ X @ Xs ) )
% 0.24/0.58 = ( cons_list_node @ X @ ( butlast_list_node @ Xs ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast.simps(2)
% 0.24/0.58 thf(fact_137_butlast_Osimps_I2_J,axiom,
% 0.24/0.58 ! [Xs: list_node,X: node] :
% 0.24/0.58 ( ( ( Xs = nil_node )
% 0.24/0.58 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 0.24/0.58 = nil_node ) )
% 0.24/0.58 & ( ( Xs != nil_node )
% 0.24/0.58 => ( ( butlast_node @ ( cons_node @ X @ Xs ) )
% 0.24/0.58 = ( cons_node @ X @ ( butlast_node @ Xs ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast.simps(2)
% 0.24/0.58 thf(fact_138_butlast__append,axiom,
% 0.24/0.58 ! [Ys: list_list_node,Xs: list_list_node] :
% 0.24/0.58 ( ( ( Ys = nil_list_node )
% 0.24/0.58 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.24/0.58 = ( butlast_list_node @ Xs ) ) )
% 0.24/0.58 & ( ( Ys != nil_list_node )
% 0.24/0.58 => ( ( butlast_list_node @ ( append_list_node @ Xs @ Ys ) )
% 0.24/0.58 = ( append_list_node @ Xs @ ( butlast_list_node @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_append
% 0.24/0.58 thf(fact_139_butlast__append,axiom,
% 0.24/0.58 ! [Ys: list_val,Xs: list_val] :
% 0.24/0.58 ( ( ( Ys = nil_val )
% 0.24/0.58 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 0.24/0.58 = ( butlast_val @ Xs ) ) )
% 0.24/0.58 & ( ( Ys != nil_val )
% 0.24/0.58 => ( ( butlast_val @ ( append_val @ Xs @ Ys ) )
% 0.24/0.58 = ( append_val @ Xs @ ( butlast_val @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_append
% 0.24/0.58 thf(fact_140_butlast__append,axiom,
% 0.24/0.58 ! [Ys: list_node,Xs: list_node] :
% 0.24/0.58 ( ( ( Ys = nil_node )
% 0.24/0.58 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 0.24/0.58 = ( butlast_node @ Xs ) ) )
% 0.24/0.58 & ( ( Ys != nil_node )
% 0.24/0.58 => ( ( butlast_node @ ( append_node @ Xs @ Ys ) )
% 0.24/0.58 = ( append_node @ Xs @ ( butlast_node @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_append
% 0.24/0.58 thf(fact_141_in__set__butlast__appendI,axiom,
% 0.24/0.58 ! [X: val,Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ( ( member_val @ X @ ( set_val2 @ ( butlast_val @ Xs ) ) )
% 0.24/0.58 | ( member_val @ X @ ( set_val2 @ ( butlast_val @ Ys ) ) ) )
% 0.24/0.58 => ( member_val @ X @ ( set_val2 @ ( butlast_val @ ( append_val @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % in_set_butlast_appendI
% 0.24/0.58 thf(fact_142_in__set__butlast__appendI,axiom,
% 0.24/0.58 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ( ( member_node @ X @ ( set_node2 @ ( butlast_node @ Xs ) ) )
% 0.24/0.58 | ( member_node @ X @ ( set_node2 @ ( butlast_node @ Ys ) ) ) )
% 0.24/0.58 => ( member_node @ X @ ( set_node2 @ ( butlast_node @ ( append_node @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % in_set_butlast_appendI
% 0.24/0.58 thf(fact_143_butlast__eq__cons__conv,axiom,
% 0.24/0.58 ! [L: list_val,X: val,Xs: list_val] :
% 0.24/0.58 ( ( ( butlast_val @ L )
% 0.24/0.58 = ( cons_val @ X @ Xs ) )
% 0.24/0.58 = ( ? [Xl: val] :
% 0.24/0.58 ( L
% 0.24/0.58 = ( cons_val @ X @ ( append_val @ Xs @ ( cons_val @ Xl @ nil_val ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_eq_cons_conv
% 0.24/0.58 thf(fact_144_butlast__eq__cons__conv,axiom,
% 0.24/0.58 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 0.24/0.58 ( ( ( butlast_list_node @ L )
% 0.24/0.58 = ( cons_list_node @ X @ Xs ) )
% 0.24/0.58 = ( ? [Xl: list_node] :
% 0.24/0.58 ( L
% 0.24/0.58 = ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl @ nil_list_node ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_eq_cons_conv
% 0.24/0.58 thf(fact_145_butlast__eq__cons__conv,axiom,
% 0.24/0.58 ! [L: list_node,X: node,Xs: list_node] :
% 0.24/0.58 ( ( ( butlast_node @ L )
% 0.24/0.58 = ( cons_node @ X @ Xs ) )
% 0.24/0.58 = ( ? [Xl: node] :
% 0.24/0.58 ( L
% 0.24/0.58 = ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl @ nil_node ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_eq_cons_conv
% 0.24/0.58 thf(fact_146_butlast__eq__consE,axiom,
% 0.24/0.58 ! [L: list_val,X: val,Xs: list_val] :
% 0.24/0.58 ( ( ( butlast_val @ L )
% 0.24/0.58 = ( cons_val @ X @ Xs ) )
% 0.24/0.58 => ~ ! [Xl2: val] :
% 0.24/0.58 ( L
% 0.24/0.58 != ( cons_val @ X @ ( append_val @ Xs @ ( cons_val @ Xl2 @ nil_val ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_eq_consE
% 0.24/0.58 thf(fact_147_butlast__eq__consE,axiom,
% 0.24/0.58 ! [L: list_list_node,X: list_node,Xs: list_list_node] :
% 0.24/0.58 ( ( ( butlast_list_node @ L )
% 0.24/0.58 = ( cons_list_node @ X @ Xs ) )
% 0.24/0.58 => ~ ! [Xl2: list_node] :
% 0.24/0.58 ( L
% 0.24/0.58 != ( cons_list_node @ X @ ( append_list_node @ Xs @ ( cons_list_node @ Xl2 @ nil_list_node ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_eq_consE
% 0.24/0.58 thf(fact_148_butlast__eq__consE,axiom,
% 0.24/0.58 ! [L: list_node,X: node,Xs: list_node] :
% 0.24/0.58 ( ( ( butlast_node @ L )
% 0.24/0.58 = ( cons_node @ X @ Xs ) )
% 0.24/0.58 => ~ ! [Xl2: node] :
% 0.24/0.58 ( L
% 0.24/0.58 != ( cons_node @ X @ ( append_node @ Xs @ ( cons_node @ Xl2 @ nil_node ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % butlast_eq_consE
% 0.24/0.58 thf(fact_149_list__tail__coinc,axiom,
% 0.24/0.58 ! [N1: val,R1: list_val,N22: val,R2: list_val] :
% 0.24/0.58 ( ( ( cons_val @ N1 @ R1 )
% 0.24/0.58 = ( cons_val @ N22 @ R2 ) )
% 0.24/0.58 => ( ( N1 = N22 )
% 0.24/0.58 & ( R1 = R2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_tail_coinc
% 0.24/0.58 thf(fact_150_list__tail__coinc,axiom,
% 0.24/0.58 ! [N1: list_node,R1: list_list_node,N22: list_node,R2: list_list_node] :
% 0.24/0.58 ( ( ( cons_list_node @ N1 @ R1 )
% 0.24/0.58 = ( cons_list_node @ N22 @ R2 ) )
% 0.24/0.58 => ( ( N1 = N22 )
% 0.24/0.58 & ( R1 = R2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_tail_coinc
% 0.24/0.58 thf(fact_151_list__tail__coinc,axiom,
% 0.24/0.58 ! [N1: node,R1: list_node,N22: node,R2: list_node] :
% 0.24/0.58 ( ( ( cons_node @ N1 @ R1 )
% 0.24/0.58 = ( cons_node @ N22 @ R2 ) )
% 0.24/0.58 => ( ( N1 = N22 )
% 0.24/0.58 & ( R1 = R2 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_tail_coinc
% 0.24/0.58 thf(fact_152_not__Cons__self2,axiom,
% 0.24/0.58 ! [X: val,Xs: list_val] :
% 0.24/0.58 ( ( cons_val @ X @ Xs )
% 0.24/0.58 != Xs ) ).
% 0.24/0.58
% 0.24/0.58 % not_Cons_self2
% 0.24/0.58 thf(fact_153_not__Cons__self2,axiom,
% 0.24/0.58 ! [X: list_node,Xs: list_list_node] :
% 0.24/0.58 ( ( cons_list_node @ X @ Xs )
% 0.24/0.58 != Xs ) ).
% 0.24/0.58
% 0.24/0.58 % not_Cons_self2
% 0.24/0.58 thf(fact_154_not__Cons__self2,axiom,
% 0.24/0.58 ! [X: node,Xs: list_node] :
% 0.24/0.58 ( ( cons_node @ X @ Xs )
% 0.24/0.58 != Xs ) ).
% 0.24/0.58
% 0.24/0.58 % not_Cons_self2
% 0.24/0.58 thf(fact_155_append__eq__appendI,axiom,
% 0.24/0.58 ! [Xs: list_val,Xs1: list_val,Zs: list_val,Ys: list_val,Us: list_val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ Xs1 )
% 0.24/0.58 = Zs )
% 0.24/0.58 => ( ( Ys
% 0.24/0.58 = ( append_val @ Xs1 @ Us ) )
% 0.24/0.58 => ( ( append_val @ Xs @ Ys )
% 0.24/0.58 = ( append_val @ Zs @ Us ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_eq_appendI
% 0.24/0.58 thf(fact_156_append__eq__appendI,axiom,
% 0.24/0.58 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us: list_node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ Xs1 )
% 0.24/0.58 = Zs )
% 0.24/0.58 => ( ( Ys
% 0.24/0.58 = ( append_node @ Xs1 @ Us ) )
% 0.24/0.58 => ( ( append_node @ Xs @ Ys )
% 0.24/0.58 = ( append_node @ Zs @ Us ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_eq_appendI
% 0.24/0.58 thf(fact_157_append__eq__append__conv2,axiom,
% 0.24/0.58 ! [Xs: list_val,Ys: list_val,Zs: list_val,Ts: list_val] :
% 0.24/0.58 ( ( ( append_val @ Xs @ Ys )
% 0.24/0.58 = ( append_val @ Zs @ Ts ) )
% 0.24/0.58 = ( ? [Us2: list_val] :
% 0.24/0.58 ( ( ( Xs
% 0.24/0.58 = ( append_val @ Zs @ Us2 ) )
% 0.24/0.58 & ( ( append_val @ Us2 @ Ys )
% 0.24/0.58 = Ts ) )
% 0.24/0.58 | ( ( ( append_val @ Xs @ Us2 )
% 0.24/0.58 = Zs )
% 0.24/0.58 & ( Ys
% 0.24/0.58 = ( append_val @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_eq_append_conv2
% 0.24/0.58 thf(fact_158_append__eq__append__conv2,axiom,
% 0.24/0.58 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 0.24/0.58 ( ( ( append_node @ Xs @ Ys )
% 0.24/0.58 = ( append_node @ Zs @ Ts ) )
% 0.24/0.58 = ( ? [Us2: list_node] :
% 0.24/0.58 ( ( ( Xs
% 0.24/0.58 = ( append_node @ Zs @ Us2 ) )
% 0.24/0.58 & ( ( append_node @ Us2 @ Ys )
% 0.24/0.58 = Ts ) )
% 0.24/0.58 | ( ( ( append_node @ Xs @ Us2 )
% 0.24/0.58 = Zs )
% 0.24/0.58 & ( Ys
% 0.24/0.58 = ( append_node @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % append_eq_append_conv2
% 0.24/0.58 thf(fact_159_strict__sorted_Oinduct,axiom,
% 0.24/0.58 ! [P: list_val > $o,A0: list_val] :
% 0.24/0.58 ( ( P @ nil_val )
% 0.24/0.58 => ( ! [X4: val,Ys2: list_val] :
% 0.24/0.58 ( ( P @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_val @ X4 @ Ys2 ) ) )
% 0.24/0.58 => ( P @ A0 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % strict_sorted.induct
% 0.24/0.58 thf(fact_160_strict__sorted_Oinduct,axiom,
% 0.24/0.58 ! [P: list_node > $o,A0: list_node] :
% 0.24/0.58 ( ( P @ nil_node )
% 0.24/0.58 => ( ! [X4: node,Ys2: list_node] :
% 0.24/0.58 ( ( P @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Ys2 ) ) )
% 0.24/0.58 => ( P @ A0 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % strict_sorted.induct
% 0.24/0.58 thf(fact_161_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_node > list_val > $o,R: node > val > $o,Xs: list_node,Ys: list_val] :
% 0.24/0.58 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_val )
% 0.24/0.58 => ( ! [X_1: list_val] : ( P @ nil_node @ X_1 )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node,Y2: val,Ys2: list_val] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node,Y2: val,Ys2: list_val] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_162_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_val > list_val > $o,R: val > val > $o,Xs: list_val,Ys: list_val] :
% 0.24/0.58 ( ! [Xs2: list_val] : ( P @ Xs2 @ nil_val )
% 0.24/0.58 => ( ! [X_1: list_val] : ( P @ nil_val @ X_1 )
% 0.24/0.58 => ( ! [X4: val,Xs2: list_val,Y2: val,Ys2: list_val] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: val,Xs2: list_val,Y2: val,Ys2: list_val] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_val @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_163_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_list_node > list_val > $o,R: list_node > val > $o,Xs: list_list_node,Ys: list_val] :
% 0.24/0.58 ( ! [Xs2: list_list_node] : ( P @ Xs2 @ nil_val )
% 0.24/0.58 => ( ! [X_1: list_val] : ( P @ nil_list_node @ X_1 )
% 0.24/0.58 => ( ! [X4: list_node,Xs2: list_list_node,Y2: val,Ys2: list_val] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_val @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: list_node,Xs2: list_list_node,Y2: val,Ys2: list_val] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_list_node @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_val @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_164_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_node > list_list_node > $o,R: node > list_node > $o,Xs: list_node,Ys: list_list_node] :
% 0.24/0.58 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_list_node )
% 0.24/0.58 => ( ! [X_1: list_list_node] : ( P @ nil_node @ X_1 )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node,Y2: list_node,Ys2: list_list_node] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node,Y2: list_node,Ys2: list_list_node] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_165_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_val > list_list_node > $o,R: val > list_node > $o,Xs: list_val,Ys: list_list_node] :
% 0.24/0.58 ( ! [Xs2: list_val] : ( P @ Xs2 @ nil_list_node )
% 0.24/0.58 => ( ! [X_1: list_list_node] : ( P @ nil_val @ X_1 )
% 0.24/0.58 => ( ! [X4: val,Xs2: list_val,Y2: list_node,Ys2: list_list_node] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: val,Xs2: list_val,Y2: list_node,Ys2: list_list_node] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_val @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_val @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_166_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_list_node > list_list_node > $o,R: list_node > list_node > $o,Xs: list_list_node,Ys: list_list_node] :
% 0.24/0.58 ( ! [Xs2: list_list_node] : ( P @ Xs2 @ nil_list_node )
% 0.24/0.58 => ( ! [X_1: list_list_node] : ( P @ nil_list_node @ X_1 )
% 0.24/0.58 => ( ! [X4: list_node,Xs2: list_list_node,Y2: list_node,Ys2: list_list_node] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_list_node @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: list_node,Xs2: list_list_node,Y2: list_node,Ys2: list_list_node] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_list_node @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_list_node @ X4 @ Xs2 ) @ ( cons_list_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_167_mergesort__by__rel__merge__induct,axiom,
% 0.24/0.58 ! [P: list_node > list_node > $o,R: node > node > $o,Xs: list_node,Ys: list_node] :
% 0.24/0.58 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.24/0.58 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.58 ( ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.58 ( ~ ( R @ X4 @ Y2 )
% 0.24/0.58 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge_induct
% 0.24/0.58 thf(fact_168_mergesort__by__rel__merge_Oinduct,axiom,
% 0.24/0.58 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.24/0.58 ( ! [R3: node > node > $o,X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.58 ( ( ( R3 @ X4 @ Y2 )
% 0.24/0.58 => ( P @ R3 @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) ) )
% 0.24/0.58 => ( ( ~ ( R3 @ X4 @ Y2 )
% 0.24/0.58 => ( P @ R3 @ ( cons_node @ X4 @ Xs2 ) @ Ys2 ) )
% 0.24/0.58 => ( P @ R3 @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.58 => ( ! [R3: node > node > $o,Xs2: list_node] : ( P @ R3 @ Xs2 @ nil_node )
% 0.24/0.58 => ( ! [R3: node > node > $o,V: node,Va: list_node] : ( P @ R3 @ nil_node @ ( cons_node @ V @ Va ) )
% 0.24/0.58 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % mergesort_by_rel_merge.induct
% 0.24/0.58 thf(fact_169_map__tailrec__rev_Oinduct,axiom,
% 0.24/0.58 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 0.24/0.58 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 0.24/0.58 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 0.24/0.58 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 0.24/0.58 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 0.24/0.58 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % map_tailrec_rev.induct
% 0.24/0.58 thf(fact_170_list__nonempty__induct,axiom,
% 0.24/0.58 ! [Xs: list_node,P: list_node > $o] :
% 0.24/0.58 ( ( Xs != nil_node )
% 0.24/0.58 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.24/0.58 => ( ! [X4: node,Xs2: list_node] :
% 0.24/0.58 ( ( Xs2 != nil_node )
% 0.24/0.58 => ( ( P @ Xs2 )
% 0.24/0.58 => ( P @ ( cons_node @ X4 @ Xs2 ) ) ) )
% 0.24/0.58 => ( P @ Xs ) ) ) ) ).
% 0.24/0.58
% 0.24/0.58 % list_nonempty_induct
% 0.24/0.58 thf(fact_171_list__all__zip_Oinduct,axiom,
% 0.24/0.59 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.24/0.59 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 0.24/0.59 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 0.24/0.59 ( ( P @ P2 @ As @ Bs )
% 0.24/0.59 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 0.24/0.59 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V @ Va ) @ nil_node )
% 0.24/0.59 => ( ! [P2: node > node > $o,V: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V @ Va ) )
% 0.24/0.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_all_zip.induct
% 0.24/0.59 thf(fact_172_successively_Oinduct,axiom,
% 0.24/0.59 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.24/0.59 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.24/0.59 => ( ! [P2: node > node > $o,X4: node] : ( P @ P2 @ ( cons_node @ X4 @ nil_node ) )
% 0.24/0.59 => ( ! [P2: node > node > $o,X4: node,Y2: node,Xs2: list_node] :
% 0.24/0.59 ( ( P @ P2 @ ( cons_node @ Y2 @ Xs2 ) )
% 0.24/0.59 => ( P @ P2 @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) )
% 0.24/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % successively.induct
% 0.24/0.59 thf(fact_173_list__induct__first2,axiom,
% 0.24/0.59 ! [P: list_node > $o,Xs: list_node] :
% 0.24/0.59 ( ( P @ nil_node )
% 0.24/0.59 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.24/0.59 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 0.24/0.59 ( ( P @ Xs2 )
% 0.24/0.59 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 0.24/0.59 => ( P @ Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_induct_first2
% 0.24/0.59 thf(fact_174_remdups__adj_Oinduct,axiom,
% 0.24/0.59 ! [P: list_node > $o,A0: list_node] :
% 0.24/0.59 ( ( P @ nil_node )
% 0.24/0.59 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.24/0.59 => ( ! [X4: node,Y2: node,Xs2: list_node] :
% 0.24/0.59 ( ( ( X4 = Y2 )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 0.24/0.59 => ( ( ( X4 != Y2 )
% 0.24/0.59 => ( P @ ( cons_node @ Y2 @ Xs2 ) ) )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) ) )
% 0.24/0.59 => ( P @ A0 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % remdups_adj.induct
% 0.24/0.59 thf(fact_175_sorted__wrt_Oinduct,axiom,
% 0.24/0.59 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.24/0.59 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.24/0.59 => ( ! [P2: node > node > $o,X4: node,Ys2: list_node] :
% 0.24/0.59 ( ( P @ P2 @ Ys2 )
% 0.24/0.59 => ( P @ P2 @ ( cons_node @ X4 @ Ys2 ) ) )
% 0.24/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % sorted_wrt.induct
% 0.24/0.59 thf(fact_176_remdups__adj_Ocases,axiom,
% 0.24/0.59 ! [X: list_node] :
% 0.24/0.59 ( ( X != nil_node )
% 0.24/0.59 => ( ! [X4: node] :
% 0.24/0.59 ( X
% 0.24/0.59 != ( cons_node @ X4 @ nil_node ) )
% 0.24/0.59 => ~ ! [X4: node,Y2: node,Xs2: list_node] :
% 0.24/0.59 ( X
% 0.24/0.59 != ( cons_node @ X4 @ ( cons_node @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % remdups_adj.cases
% 0.24/0.59 thf(fact_177_list__2pre__induct,axiom,
% 0.24/0.59 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 0.24/0.59 ( ( P @ nil_node @ nil_node )
% 0.24/0.59 => ( ! [E3: node,W12: list_node,W22: list_node] :
% 0.24/0.59 ( ( P @ W12 @ W22 )
% 0.24/0.59 => ( P @ ( cons_node @ E3 @ W12 ) @ W22 ) )
% 0.24/0.59 => ( ! [E3: node,W13: list_node,W23: list_node] :
% 0.24/0.59 ( ( P @ W13 @ W23 )
% 0.24/0.59 => ( P @ W13 @ ( cons_node @ E3 @ W23 ) ) )
% 0.24/0.59 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_2pre_induct
% 0.24/0.59 thf(fact_178_transpose_Ocases,axiom,
% 0.24/0.59 ! [X: list_list_node] :
% 0.24/0.59 ( ( X != nil_list_node )
% 0.24/0.59 => ( ! [Xss: list_list_node] :
% 0.24/0.59 ( X
% 0.24/0.59 != ( cons_list_node @ nil_node @ Xss ) )
% 0.24/0.59 => ~ ! [X4: node,Xs2: list_node,Xss: list_list_node] :
% 0.24/0.59 ( X
% 0.24/0.59 != ( cons_list_node @ ( cons_node @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % transpose.cases
% 0.24/0.59 thf(fact_179_shuffles_Oinduct,axiom,
% 0.24/0.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.24/0.59 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.24/0.59 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( P @ Xs2 @ ( cons_node @ Y2 @ Ys2 ) )
% 0.24/0.59 => ( ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) ) )
% 0.24/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % shuffles.induct
% 0.24/0.59 thf(fact_180_min__list_Oinduct,axiom,
% 0.24/0.59 ! [P: list_node > $o,A0: list_node] :
% 0.24/0.59 ( ! [X4: node,Xs2: list_node] :
% 0.24/0.59 ( ! [X212: node,X222: list_node] :
% 0.24/0.59 ( ( Xs2
% 0.24/0.59 = ( cons_node @ X212 @ X222 ) )
% 0.24/0.59 => ( P @ Xs2 ) )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ Xs2 ) ) )
% 0.24/0.59 => ( ( P @ nil_node )
% 0.24/0.59 => ( P @ A0 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % min_list.induct
% 0.24/0.59 thf(fact_181_min__list_Ocases,axiom,
% 0.24/0.59 ! [X: list_node] :
% 0.24/0.59 ( ! [X4: node,Xs2: list_node] :
% 0.24/0.59 ( X
% 0.24/0.59 != ( cons_node @ X4 @ Xs2 ) )
% 0.24/0.59 => ( X = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % min_list.cases
% 0.24/0.59 thf(fact_182_induct__list012,axiom,
% 0.24/0.59 ! [P: list_node > $o,Xs: list_node] :
% 0.24/0.59 ( ( P @ nil_node )
% 0.24/0.59 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.24/0.59 => ( ! [X4: node,Y2: node,Zs2: list_node] :
% 0.24/0.59 ( ( P @ Zs2 )
% 0.24/0.59 => ( ( P @ ( cons_node @ Y2 @ Zs2 ) )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ ( cons_node @ Y2 @ Zs2 ) ) ) ) )
% 0.24/0.59 => ( P @ Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % induct_list012
% 0.24/0.59 thf(fact_183_splice_Oinduct,axiom,
% 0.24/0.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.24/0.59 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Ys2: list_node] :
% 0.24/0.59 ( ( P @ Ys2 @ Xs2 )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ Xs2 ) @ Ys2 ) )
% 0.24/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % splice.induct
% 0.24/0.59 thf(fact_184_list__induct2_H,axiom,
% 0.24/0.59 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( P @ nil_node @ nil_node )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node] : ( P @ ( cons_node @ X4 @ Xs2 ) @ nil_node )
% 0.24/0.59 => ( ! [Y2: node,Ys2: list_node] : ( P @ nil_node @ ( cons_node @ Y2 @ Ys2 ) )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ Xs2 ) @ ( cons_node @ Y2 @ Ys2 ) ) )
% 0.24/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_induct2'
% 0.24/0.59 thf(fact_185_neq__Nil__conv,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 = ( ? [Y3: node,Ys3: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( cons_node @ Y3 @ Ys3 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % neq_Nil_conv
% 0.24/0.59 thf(fact_186_list_Oinducts,axiom,
% 0.24/0.59 ! [P: list_node > $o,List: list_node] :
% 0.24/0.59 ( ( P @ nil_node )
% 0.24/0.59 => ( ! [X1: node,X23: list_node] :
% 0.24/0.59 ( ( P @ X23 )
% 0.24/0.59 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 0.24/0.59 => ( P @ List ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.inducts
% 0.24/0.59 thf(fact_187_list_Oexhaust,axiom,
% 0.24/0.59 ! [Y: list_node] :
% 0.24/0.59 ( ( Y != nil_node )
% 0.24/0.59 => ~ ! [X213: node,X223: list_node] :
% 0.24/0.59 ( Y
% 0.24/0.59 != ( cons_node @ X213 @ X223 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.exhaust
% 0.24/0.59 thf(fact_188_revg_Oinduct,axiom,
% 0.24/0.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.24/0.59 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.24/0.59 => ( ! [A3: node,As: list_node,B2: list_node] :
% 0.24/0.59 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 0.24/0.59 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 0.24/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % revg.induct
% 0.24/0.59 thf(fact_189_list_OdiscI,axiom,
% 0.24/0.59 ! [List: list_node,X21: node,X22: list_node] :
% 0.24/0.59 ( ( List
% 0.24/0.59 = ( cons_node @ X21 @ X22 ) )
% 0.24/0.59 => ( List != nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.discI
% 0.24/0.59 thf(fact_190_neq__NilE,axiom,
% 0.24/0.59 ! [L: list_node] :
% 0.24/0.59 ( ( L != nil_node )
% 0.24/0.59 => ~ ! [X4: node,Xs2: list_node] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( cons_node @ X4 @ Xs2 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % neq_NilE
% 0.24/0.59 thf(fact_191_list_Odistinct_I1_J,axiom,
% 0.24/0.59 ! [X21: node,X22: list_node] :
% 0.24/0.59 ( nil_node
% 0.24/0.59 != ( cons_node @ X21 @ X22 ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.distinct(1)
% 0.24/0.59 thf(fact_192_list_Oset__cases,axiom,
% 0.24/0.59 ! [E2: val,A: list_val] :
% 0.24/0.59 ( ( member_val @ E2 @ ( set_val2 @ A ) )
% 0.24/0.59 => ( ! [Z2: list_val] :
% 0.24/0.59 ( A
% 0.24/0.59 != ( cons_val @ E2 @ Z2 ) )
% 0.24/0.59 => ~ ! [Z1: val,Z2: list_val] :
% 0.24/0.59 ( ( A
% 0.24/0.59 = ( cons_val @ Z1 @ Z2 ) )
% 0.24/0.59 => ~ ( member_val @ E2 @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_cases
% 0.24/0.59 thf(fact_193_list_Oset__cases,axiom,
% 0.24/0.59 ! [E2: node,A: list_node] :
% 0.24/0.59 ( ( member_node @ E2 @ ( set_node2 @ A ) )
% 0.24/0.59 => ( ! [Z2: list_node] :
% 0.24/0.59 ( A
% 0.24/0.59 != ( cons_node @ E2 @ Z2 ) )
% 0.24/0.59 => ~ ! [Z1: node,Z2: list_node] :
% 0.24/0.59 ( ( A
% 0.24/0.59 = ( cons_node @ Z1 @ Z2 ) )
% 0.24/0.59 => ~ ( member_node @ E2 @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_cases
% 0.24/0.59 thf(fact_194_set__ConsD,axiom,
% 0.24/0.59 ! [Y: val,X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ Y @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 0.24/0.59 => ( ( Y = X )
% 0.24/0.59 | ( member_val @ Y @ ( set_val2 @ Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % set_ConsD
% 0.24/0.59 thf(fact_195_set__ConsD,axiom,
% 0.24/0.59 ! [Y: node,X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ Y @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 0.24/0.59 => ( ( Y = X )
% 0.24/0.59 | ( member_node @ Y @ ( set_node2 @ Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % set_ConsD
% 0.24/0.59 thf(fact_196_list_Oset__intros_I1_J,axiom,
% 0.24/0.59 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_intros(1)
% 0.24/0.59 thf(fact_197_list_Oset__intros_I1_J,axiom,
% 0.24/0.59 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_intros(1)
% 0.24/0.59 thf(fact_198_list_Oset__intros_I2_J,axiom,
% 0.24/0.59 ! [Y: val,X22: list_val,X21: val] :
% 0.24/0.59 ( ( member_val @ Y @ ( set_val2 @ X22 ) )
% 0.24/0.59 => ( member_val @ Y @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_intros(2)
% 0.24/0.59 thf(fact_199_list_Oset__intros_I2_J,axiom,
% 0.24/0.59 ! [Y: node,X22: list_node,X21: node] :
% 0.24/0.59 ( ( member_node @ Y @ ( set_node2 @ X22 ) )
% 0.24/0.59 => ( member_node @ Y @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_intros(2)
% 0.24/0.59 thf(fact_200_Cons__eq__appendI,axiom,
% 0.24/0.59 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.24/0.59 ( ( ( cons_node @ X @ Xs1 )
% 0.24/0.59 = Ys )
% 0.24/0.59 => ( ( Xs
% 0.24/0.59 = ( append_node @ Xs1 @ Zs ) )
% 0.24/0.59 => ( ( cons_node @ X @ Xs )
% 0.24/0.59 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % Cons_eq_appendI
% 0.24/0.59 thf(fact_201_append__Cons,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.24/0.59 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % append_Cons
% 0.24/0.59 thf(fact_202_list__match__lel__lel,axiom,
% 0.24/0.59 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 0.24/0.59 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 0.24/0.59 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 0.24/0.59 => ( ! [C21: list_node] :
% 0.24/0.59 ( ( C1
% 0.24/0.59 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 0.24/0.59 => ( C22
% 0.24/0.59 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 0.24/0.59 => ( ( ( C12 = C1 )
% 0.24/0.59 => ( ( Qs2 = Qs )
% 0.24/0.59 => ( C22 != C2 ) ) )
% 0.24/0.59 => ~ ! [C212: list_node] :
% 0.24/0.59 ( ( C12
% 0.24/0.59 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 0.24/0.59 => ( C2
% 0.24/0.59 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_match_lel_lel
% 0.24/0.59 thf(fact_203_eq__Nil__appendI,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( Xs = Ys )
% 0.24/0.59 => ( Xs
% 0.24/0.59 = ( append_node @ nil_node @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % eq_Nil_appendI
% 0.24/0.59 thf(fact_204_append__Nil,axiom,
% 0.24/0.59 ! [Ys: list_node] :
% 0.24/0.59 ( ( append_node @ nil_node @ Ys )
% 0.24/0.59 = Ys ) ).
% 0.24/0.59
% 0.24/0.59 % append_Nil
% 0.24/0.59 thf(fact_205_append_Oleft__neutral,axiom,
% 0.24/0.59 ! [A: list_node] :
% 0.24/0.59 ( ( append_node @ nil_node @ A )
% 0.24/0.59 = A ) ).
% 0.24/0.59
% 0.24/0.59 % append.left_neutral
% 0.24/0.59 thf(fact_206_list_Osel_I3_J,axiom,
% 0.24/0.59 ! [X21: node,X22: list_node] :
% 0.24/0.59 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 0.24/0.59 = X22 ) ).
% 0.24/0.59
% 0.24/0.59 % list.sel(3)
% 0.24/0.59 thf(fact_207_list_Osel_I2_J,axiom,
% 0.24/0.59 ( ( tl_node @ nil_node )
% 0.24/0.59 = nil_node ) ).
% 0.24/0.59
% 0.24/0.59 % list.sel(2)
% 0.24/0.59 thf(fact_208_list__append__eq__Cons__cases,axiom,
% 0.24/0.59 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.24/0.59 ( ( ( append_node @ Ys @ Zs )
% 0.24/0.59 = ( cons_node @ X @ Xs ) )
% 0.24/0.59 => ( ( ( Ys = nil_node )
% 0.24/0.59 => ( Zs
% 0.24/0.59 != ( cons_node @ X @ Xs ) ) )
% 0.24/0.59 => ~ ! [Ys4: list_node] :
% 0.24/0.59 ( ( Ys
% 0.24/0.59 = ( cons_node @ X @ Ys4 ) )
% 0.24/0.59 => ( ( append_node @ Ys4 @ Zs )
% 0.24/0.59 != Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_append_eq_Cons_cases
% 0.24/0.59 thf(fact_209_list__Cons__eq__append__cases,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.59 ( ( ( cons_node @ X @ Xs )
% 0.24/0.59 = ( append_node @ Ys @ Zs ) )
% 0.24/0.59 => ( ( ( Ys = nil_node )
% 0.24/0.59 => ( Zs
% 0.24/0.59 != ( cons_node @ X @ Xs ) ) )
% 0.24/0.59 => ~ ! [Ys4: list_node] :
% 0.24/0.59 ( ( Ys
% 0.24/0.59 = ( cons_node @ X @ Ys4 ) )
% 0.24/0.59 => ( ( append_node @ Ys4 @ Zs )
% 0.24/0.59 != Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list_Cons_eq_append_cases
% 0.24/0.59 thf(fact_210_rev__nonempty__induct2_H,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ( ( Ys != nil_node )
% 0.24/0.59 => ( ! [X4: node,Y2: node] : ( P @ ( cons_node @ X4 @ nil_node ) @ ( cons_node @ Y2 @ nil_node ) )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node] :
% 0.24/0.59 ( ( Xs2 != nil_node )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( cons_node @ Y2 @ nil_node ) ) )
% 0.24/0.59 => ( ! [X4: node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( Ys2 != nil_node )
% 0.24/0.59 => ( P @ ( cons_node @ X4 @ nil_node ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.24/0.59 => ( ( Xs2 != nil_node )
% 0.24/0.59 => ( ( Ys2 != nil_node )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ) )
% 0.24/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % rev_nonempty_induct2'
% 0.24/0.59 thf(fact_211_rev__nonempty__induct,axiom,
% 0.24/0.59 ! [Xs: list_node,P: list_node > $o] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ( ! [X4: node] : ( P @ ( cons_node @ X4 @ nil_node ) )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node] :
% 0.24/0.59 ( ( Xs2 != nil_node )
% 0.24/0.59 => ( ( P @ Xs2 )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) ) )
% 0.24/0.59 => ( P @ Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % rev_nonempty_induct
% 0.24/0.59 thf(fact_212_append__eq__Cons__conv,axiom,
% 0.24/0.59 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.24/0.59 ( ( ( append_node @ Ys @ Zs )
% 0.24/0.59 = ( cons_node @ X @ Xs ) )
% 0.24/0.59 = ( ( ( Ys = nil_node )
% 0.24/0.59 & ( Zs
% 0.24/0.59 = ( cons_node @ X @ Xs ) ) )
% 0.24/0.59 | ? [Ys5: list_node] :
% 0.24/0.59 ( ( Ys
% 0.24/0.59 = ( cons_node @ X @ Ys5 ) )
% 0.24/0.59 & ( ( append_node @ Ys5 @ Zs )
% 0.24/0.59 = Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % append_eq_Cons_conv
% 0.24/0.59 thf(fact_213_Cons__eq__append__conv,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.59 ( ( ( cons_node @ X @ Xs )
% 0.24/0.59 = ( append_node @ Ys @ Zs ) )
% 0.24/0.59 = ( ( ( Ys = nil_node )
% 0.24/0.59 & ( ( cons_node @ X @ Xs )
% 0.24/0.59 = Zs ) )
% 0.24/0.59 | ? [Ys5: list_node] :
% 0.24/0.59 ( ( ( cons_node @ X @ Ys5 )
% 0.24/0.59 = Ys )
% 0.24/0.59 & ( Xs
% 0.24/0.59 = ( append_node @ Ys5 @ Zs ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % Cons_eq_append_conv
% 0.24/0.59 thf(fact_214_neq__Nil__rev__conv,axiom,
% 0.24/0.59 ! [L: list_node] :
% 0.24/0.59 ( ( L != nil_node )
% 0.24/0.59 = ( ? [Xs3: list_node,X3: node] :
% 0.24/0.59 ( L
% 0.24/0.59 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % neq_Nil_rev_conv
% 0.24/0.59 thf(fact_215_rev__induct2_H,axiom,
% 0.24/0.59 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( P @ nil_node @ nil_node )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 0.24/0.59 => ( ! [Y2: node,Ys2: list_node] : ( P @ nil_node @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 0.24/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % rev_induct2'
% 0.24/0.59 thf(fact_216_neq__Nil__revE,axiom,
% 0.24/0.59 ! [L: list_node] :
% 0.24/0.59 ( ( L != nil_node )
% 0.24/0.59 => ~ ! [Ll: list_node,E3: node] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_node @ Ll @ ( cons_node @ E3 @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % neq_Nil_revE
% 0.24/0.59 thf(fact_217_rev__exhaust,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ~ ! [Ys2: list_node,Y2: node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 != ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % rev_exhaust
% 0.24/0.59 thf(fact_218_rev__induct,axiom,
% 0.24/0.59 ! [P: list_node > $o,Xs: list_node] :
% 0.24/0.59 ( ( P @ nil_node )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node] :
% 0.24/0.59 ( ( P @ Xs2 )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) ) )
% 0.24/0.59 => ( P @ Xs ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % rev_induct
% 0.24/0.59 thf(fact_219_split__list__first__prop__iff,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ( ? [X3: node] :
% 0.24/0.59 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X3 ) ) )
% 0.24/0.59 = ( ? [Ys3: list_node,X3: node] :
% 0.24/0.59 ( ? [Zs3: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys3 @ ( cons_node @ X3 @ Zs3 ) ) )
% 0.24/0.59 & ( P @ X3 )
% 0.24/0.59 & ! [Y3: node] :
% 0.24/0.59 ( ( member_node @ Y3 @ ( set_node2 @ Ys3 ) )
% 0.24/0.59 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_first_prop_iff
% 0.24/0.59 thf(fact_220_split__list__last__prop__iff,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ( ? [X3: node] :
% 0.24/0.59 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X3 ) ) )
% 0.24/0.59 = ( ? [Ys3: list_node,X3: node,Zs3: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys3 @ ( cons_node @ X3 @ Zs3 ) ) )
% 0.24/0.59 & ( P @ X3 )
% 0.24/0.59 & ! [Y3: node] :
% 0.24/0.59 ( ( member_node @ Y3 @ ( set_node2 @ Zs3 ) )
% 0.24/0.59 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_last_prop_iff
% 0.24/0.59 thf(fact_221_in__set__conv__decomp__first,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 = ( ? [Ys3: list_val,Zs3: list_val] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 0.24/0.59 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_conv_decomp_first
% 0.24/0.59 thf(fact_222_in__set__conv__decomp__first,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 = ( ? [Ys3: list_node,Zs3: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 0.24/0.59 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_conv_decomp_first
% 0.24/0.59 thf(fact_223_in__set__conv__decomp__last,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 = ( ? [Ys3: list_val,Zs3: list_val] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 0.24/0.59 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_conv_decomp_last
% 0.24/0.59 thf(fact_224_in__set__conv__decomp__last,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 = ( ? [Ys3: list_node,Zs3: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 0.24/0.59 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_conv_decomp_last
% 0.24/0.59 thf(fact_225_split__list__first__propE,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ~ ! [Ys2: list_node,X4: node] :
% 0.24/0.59 ( ? [Zs2: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.24/0.59 => ( ( P @ X4 )
% 0.24/0.59 => ~ ! [Xa: node] :
% 0.24/0.59 ( ( member_node @ Xa @ ( set_node2 @ Ys2 ) )
% 0.24/0.59 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_first_propE
% 0.24/0.59 thf(fact_226_split__list__last__propE,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ~ ! [Ys2: list_node,X4: node,Zs2: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.24/0.59 => ( ( P @ X4 )
% 0.24/0.59 => ~ ! [Xa: node] :
% 0.24/0.59 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 0.24/0.59 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_last_propE
% 0.24/0.59 thf(fact_227_split__list__first__prop,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ? [Ys2: list_node,X4: node] :
% 0.24/0.59 ( ? [Zs2: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.24/0.59 & ( P @ X4 )
% 0.24/0.59 & ! [Xa: node] :
% 0.24/0.59 ( ( member_node @ Xa @ ( set_node2 @ Ys2 ) )
% 0.24/0.59 => ~ ( P @ Xa ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_first_prop
% 0.24/0.59 thf(fact_228_split__list__last__prop,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ? [Ys2: list_node,X4: node,Zs2: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.24/0.59 & ( P @ X4 )
% 0.24/0.59 & ! [Xa: node] :
% 0.24/0.59 ( ( member_node @ Xa @ ( set_node2 @ Zs2 ) )
% 0.24/0.59 => ~ ( P @ Xa ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_last_prop
% 0.24/0.59 thf(fact_229_in__set__list__format,axiom,
% 0.24/0.59 ! [E2: val,L: list_val] :
% 0.24/0.59 ( ( member_val @ E2 @ ( set_val2 @ L ) )
% 0.24/0.59 => ~ ! [L12: list_val,L22: list_val] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_val @ L12 @ ( cons_val @ E2 @ L22 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_list_format
% 0.24/0.59 thf(fact_230_in__set__list__format,axiom,
% 0.24/0.59 ! [E2: node,L: list_node] :
% 0.24/0.59 ( ( member_node @ E2 @ ( set_node2 @ L ) )
% 0.24/0.59 => ~ ! [L12: list_node,L22: list_node] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_node @ L12 @ ( cons_node @ E2 @ L22 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_list_format
% 0.24/0.59 thf(fact_231_in__set__conv__decomp,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 = ( ? [Ys3: list_val,Zs3: list_val] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_conv_decomp
% 0.24/0.59 thf(fact_232_in__set__conv__decomp,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 = ( ? [Ys3: list_node,Zs3: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_set_conv_decomp
% 0.24/0.59 thf(fact_233_append__Cons__eq__iff,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 0.24/0.59 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 0.24/0.59 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 0.24/0.59 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 0.24/0.59 = ( ( Xs = Xs4 )
% 0.24/0.59 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % append_Cons_eq_iff
% 0.24/0.59 thf(fact_234_append__Cons__eq__iff,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 0.24/0.59 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 0.24/0.59 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 0.24/0.59 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 0.24/0.59 = ( ( Xs = Xs4 )
% 0.24/0.59 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % append_Cons_eq_iff
% 0.24/0.59 thf(fact_235_split__list__propE,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ~ ! [Ys2: list_node,X4: node] :
% 0.24/0.59 ( ? [Zs2: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.24/0.59 => ~ ( P @ X4 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_propE
% 0.24/0.59 thf(fact_236_split__list__first,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 => ? [Ys2: list_val,Zs2: list_val] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 0.24/0.59 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_first
% 0.24/0.59 thf(fact_237_split__list__first,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 => ? [Ys2: list_node,Zs2: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 0.24/0.59 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_first
% 0.24/0.59 thf(fact_238_xy__in__set__cases,axiom,
% 0.24/0.59 ! [X: val,L: list_val,Y: val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ L ) )
% 0.24/0.59 => ( ( member_val @ Y @ ( set_val2 @ L ) )
% 0.24/0.59 => ( ( ( X = Y )
% 0.24/0.59 => ! [L12: list_val,L22: list_val] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_val @ L12 @ ( cons_val @ Y @ L22 ) ) ) )
% 0.24/0.59 => ( ( ( X != Y )
% 0.24/0.59 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y @ L3 ) ) ) ) ) )
% 0.24/0.59 => ~ ( ( X != Y )
% 0.24/0.59 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_val @ L12 @ ( cons_val @ Y @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % xy_in_set_cases
% 0.24/0.59 thf(fact_239_xy__in__set__cases,axiom,
% 0.24/0.59 ! [X: node,L: list_node,Y: node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ L ) )
% 0.24/0.59 => ( ( member_node @ Y @ ( set_node2 @ L ) )
% 0.24/0.59 => ( ( ( X = Y )
% 0.24/0.59 => ! [L12: list_node,L22: list_node] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_node @ L12 @ ( cons_node @ Y @ L22 ) ) ) )
% 0.24/0.59 => ( ( ( X != Y )
% 0.24/0.59 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y @ L3 ) ) ) ) ) )
% 0.24/0.59 => ~ ( ( X != Y )
% 0.24/0.59 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.24/0.59 ( L
% 0.24/0.59 != ( append_node @ L12 @ ( cons_node @ Y @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % xy_in_set_cases
% 0.24/0.59 thf(fact_240_split__list__prop,axiom,
% 0.24/0.59 ! [Xs: list_node,P: node > $o] :
% 0.24/0.59 ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Xs ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ? [Ys2: list_node,X4: node] :
% 0.24/0.59 ( ? [Zs2: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X4 @ Zs2 ) ) )
% 0.24/0.59 & ( P @ X4 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_prop
% 0.24/0.59 thf(fact_241_split__list__last,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 => ? [Ys2: list_val,Zs2: list_val] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 0.24/0.59 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_last
% 0.24/0.59 thf(fact_242_split__list__last,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 => ? [Ys2: list_node,Zs2: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 0.24/0.59 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list_last
% 0.24/0.59 thf(fact_243_split__list,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.59 => ? [Ys2: list_val,Zs2: list_val] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list
% 0.24/0.59 thf(fact_244_split__list,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node] :
% 0.24/0.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.59 => ? [Ys2: list_node,Zs2: list_node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % split_list
% 0.24/0.59 thf(fact_245_tl__obtain__elem,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ( ( ( tl_node @ Xs )
% 0.24/0.59 = nil_node )
% 0.24/0.59 => ~ ! [E3: node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 != ( cons_node @ E3 @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % tl_obtain_elem
% 0.24/0.59 thf(fact_246_tl__Nil,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( ( tl_node @ Xs )
% 0.24/0.59 = nil_node )
% 0.24/0.59 = ( ( Xs = nil_node )
% 0.24/0.59 | ? [X3: node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % tl_Nil
% 0.24/0.59 thf(fact_247_Nil__tl,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( nil_node
% 0.24/0.59 = ( tl_node @ Xs ) )
% 0.24/0.59 = ( ( Xs = nil_node )
% 0.24/0.59 | ? [X3: node] :
% 0.24/0.59 ( Xs
% 0.24/0.59 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % Nil_tl
% 0.24/0.59 thf(fact_248_list_Oset__sel_I2_J,axiom,
% 0.24/0.59 ! [A: list_val,X: val] :
% 0.24/0.59 ( ( A != nil_val )
% 0.24/0.59 => ( ( member_val @ X @ ( set_val2 @ ( tl_val @ A ) ) )
% 0.24/0.59 => ( member_val @ X @ ( set_val2 @ A ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_sel(2)
% 0.24/0.59 thf(fact_249_list_Oset__sel_I2_J,axiom,
% 0.24/0.59 ! [A: list_node,X: node] :
% 0.24/0.59 ( ( A != nil_node )
% 0.24/0.59 => ( ( member_node @ X @ ( set_node2 @ ( tl_node @ A ) ) )
% 0.24/0.59 => ( member_node @ X @ ( set_node2 @ A ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_sel(2)
% 0.24/0.59 thf(fact_250_prefix__snoc,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.24/0.59 ( ( prefix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.24/0.59 = ( ( Xs
% 0.24/0.59 = ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.24/0.59 | ( prefix_node @ Xs @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % prefix_snoc
% 0.24/0.59 thf(fact_251_old_Opath2__split__first__last,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node,M: node,X: node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.59 => ( ( member_node @ X @ ( set_node2 @ Ns ) )
% 0.24/0.59 => ~ ! [Ns_1: list_node,Ns_3: list_node,Ns_2: list_node] :
% 0.24/0.59 ( ( Ns
% 0.24/0.59 = ( append_node @ Ns_1 @ ( append_node @ Ns_3 @ Ns_2 ) ) )
% 0.24/0.59 => ( ( prefix_node @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ Ns )
% 0.24/0.59 => ( ( suffix_node @ ( cons_node @ X @ Ns_2 ) @ Ns )
% 0.24/0.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns_1 @ ( cons_node @ X @ nil_node ) ) @ X )
% 0.24/0.59 => ( ~ ( member_node @ X @ ( set_node2 @ Ns_1 ) )
% 0.24/0.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ Ns_3 @ X )
% 0.24/0.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ X @ ( cons_node @ X @ Ns_2 ) @ M )
% 0.24/0.59 => ( member_node @ X @ ( set_node2 @ Ns_2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path2_split_first_last
% 0.24/0.59 thf(fact_252_same__prefix__nil,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ Xs )
% 0.24/0.59 = ( Ys = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % same_prefix_nil
% 0.24/0.59 thf(fact_253_old_Opath2__simple__loop,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node,N2: node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ N )
% 0.24/0.59 => ( ( member_node @ N2 @ ( set_node2 @ Ns ) )
% 0.24/0.59 => ~ ! [Ns3: list_node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns3 @ N )
% 0.24/0.59 => ( ( member_node @ N2 @ ( set_node2 @ Ns3 ) )
% 0.24/0.59 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ ( butlast_node @ Ns3 ) ) ) )
% 0.24/0.59 => ~ ( ord_less_eq_set_node @ ( set_node2 @ Ns3 ) @ ( set_node2 @ Ns ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path2_simple_loop
% 0.24/0.59 thf(fact_254_old_Opath2__cases,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.59 => ( ( ( Ns
% 0.24/0.59 = ( cons_node @ N @ nil_node ) )
% 0.24/0.59 => ( M != N ) )
% 0.24/0.59 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 0.24/0.59 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path2_cases
% 0.24/0.59 thf(fact_255_old_Opath__snoc,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node,N: node,M: node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ nil_node ) ) )
% 0.24/0.59 => ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ N @ ( cons_node @ M @ nil_node ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_snoc
% 0.24/0.59 thf(fact_256_phiUses__finite,axiom,
% 0.24/0.59 ! [N: node,G: g] :
% 0.24/0.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.59 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % phiUses_finite
% 0.24/0.59 thf(fact_257_old_Opath2__split__last__prop,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.59 => ( ? [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.24/0.59 & ( P @ X2 ) )
% 0.24/0.59 => ~ ! [N3: node,Ns3: list_node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns3 @ M )
% 0.24/0.59 => ( ( P @ N3 )
% 0.24/0.59 => ( ! [X2: node] :
% 0.24/0.59 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns3 ) ) )
% 0.24/0.59 => ~ ( P @ X2 ) )
% 0.24/0.59 => ~ ( suffix_node @ Ns3 @ Ns ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path2_split_last_prop
% 0.24/0.59 thf(fact_258_defs__finite,axiom,
% 0.24/0.59 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 0.24/0.59
% 0.24/0.59 % defs_finite
% 0.24/0.59 thf(fact_259_prefix__order_Oorder__refl,axiom,
% 0.24/0.59 ! [X: list_node] : ( prefix_node @ X @ X ) ).
% 0.24/0.59
% 0.24/0.59 % prefix_order.order_refl
% 0.24/0.59 thf(fact_260_prefix__order_Odual__order_Orefl,axiom,
% 0.24/0.59 ! [A: list_node] : ( prefix_node @ A @ A ) ).
% 0.24/0.59
% 0.24/0.59 % prefix_order.dual_order.refl
% 0.24/0.59 thf(fact_261_suffix__order_Oorder__refl,axiom,
% 0.24/0.59 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.order_refl
% 0.24/0.59 thf(fact_262_suffix__order_Odual__order_Orefl,axiom,
% 0.24/0.59 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.dual_order.refl
% 0.24/0.59 thf(fact_263_old_Opath__not__Nil,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.24/0.59 => ( Ns != nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_not_Nil
% 0.24/0.59 thf(fact_264_old_Opath2__hd,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.59 => ( N
% 0.24/0.59 = ( hd_node @ Ns ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path2_hd
% 0.24/0.59 thf(fact_265_old_Opath2__forget__hd,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.24/0.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.24/0.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path2_forget_hd
% 0.24/0.59 thf(fact_266_old_Opath__hd,axiom,
% 0.24/0.59 ! [G: g,N: node,Ns: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ Ns ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_hd
% 0.24/0.59 thf(fact_267_old_Opath__split_I2_J,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ M @ Ns2 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_split(2)
% 0.24/0.59 thf(fact_268_List_Ofinite__set,axiom,
% 0.24/0.59 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 0.24/0.59
% 0.24/0.59 % List.finite_set
% 0.24/0.59 thf(fact_269_List_Ofinite__set,axiom,
% 0.24/0.59 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 0.24/0.59
% 0.24/0.59 % List.finite_set
% 0.24/0.59 thf(fact_270_Cons__prefix__Cons,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 0.24/0.59 ( ( prefix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 0.24/0.59 = ( ( X = Y )
% 0.24/0.59 & ( prefix_node @ Xs @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % Cons_prefix_Cons
% 0.24/0.59 thf(fact_271_prefix__code_I1_J,axiom,
% 0.24/0.59 ! [Xs: list_node] : ( prefix_node @ nil_node @ Xs ) ).
% 0.24/0.59
% 0.24/0.59 % prefix_code(1)
% 0.24/0.59 thf(fact_272_prefix__Nil,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( prefix_node @ Xs @ nil_node )
% 0.24/0.59 = ( Xs = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % prefix_Nil
% 0.24/0.59 thf(fact_273_prefix__bot_Obot_Oextremum__unique,axiom,
% 0.24/0.59 ! [A: list_node] :
% 0.24/0.59 ( ( prefix_node @ A @ nil_node )
% 0.24/0.59 = ( A = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % prefix_bot.bot.extremum_unique
% 0.24/0.59 thf(fact_274_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.24/0.59 ! [A: list_node] :
% 0.24/0.59 ( ( suffix_node @ A @ nil_node )
% 0.24/0.59 = ( A = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_bot.bot.extremum_unique
% 0.24/0.59 thf(fact_275_suffix__Nil,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ nil_node )
% 0.24/0.59 = ( Xs = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_Nil
% 0.24/0.59 thf(fact_276_same__prefix__prefix,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.59 ( ( prefix_node @ ( append_node @ Xs @ Ys ) @ ( append_node @ Xs @ Zs ) )
% 0.24/0.59 = ( prefix_node @ Ys @ Zs ) ) ).
% 0.24/0.59
% 0.24/0.59 % same_prefix_prefix
% 0.24/0.59 thf(fact_277_same__suffix__suffix,axiom,
% 0.24/0.59 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.24/0.59 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 0.24/0.59 = ( suffix_node @ Ys @ Zs ) ) ).
% 0.24/0.59
% 0.24/0.59 % same_suffix_suffix
% 0.24/0.59 thf(fact_278_old_Oempty__path,axiom,
% 0.24/0.59 ! [N: node,G: g] :
% 0.24/0.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.59 => ( ( invar @ G )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.empty_path
% 0.24/0.59 thf(fact_279_old_Opath__split_I1_J,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node,M: node,Ns2: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ Ns2 ) ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( append_node @ Ns @ ( cons_node @ M @ nil_node ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_split(1)
% 0.24/0.59 thf(fact_280_old_OCons__path,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node,N2: node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.24/0.59 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns ) ) ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.Cons_path
% 0.24/0.59 thf(fact_281_old_Opath_Osimps,axiom,
% 0.24/0.59 ! [G: g,A: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 0.24/0.59 = ( ? [N5: node] :
% 0.24/0.59 ( ( A
% 0.24/0.59 = ( cons_node @ N5 @ nil_node ) )
% 0.24/0.59 & ( member_node @ N5 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.59 & ( invar @ G ) )
% 0.24/0.59 | ? [Ns5: list_node,N6: node] :
% 0.24/0.59 ( ( A
% 0.24/0.59 = ( cons_node @ N6 @ Ns5 ) )
% 0.24/0.59 & ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns5 )
% 0.24/0.59 & ( member_node @ N6 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns5 ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path.simps
% 0.24/0.59 thf(fact_282_old_Opath_Oinducts,axiom,
% 0.24/0.59 ! [G: g,X: list_node,P: list_node > $o] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ X )
% 0.24/0.59 => ( ! [N4: node] :
% 0.24/0.59 ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.59 => ( ( invar @ G )
% 0.24/0.59 => ( P @ ( cons_node @ N4 @ nil_node ) ) ) )
% 0.24/0.59 => ( ! [Ns4: list_node,N3: node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns4 )
% 0.24/0.59 => ( ( P @ Ns4 )
% 0.24/0.59 => ( ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns4 ) ) ) )
% 0.24/0.59 => ( P @ ( cons_node @ N3 @ Ns4 ) ) ) ) )
% 0.24/0.59 => ( P @ X ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path.inducts
% 0.24/0.59 thf(fact_283_old_Opath_Ocases,axiom,
% 0.24/0.59 ! [G: g,A: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ A )
% 0.24/0.59 => ( ! [N4: node] :
% 0.24/0.59 ( ( A
% 0.24/0.59 = ( cons_node @ N4 @ nil_node ) )
% 0.24/0.59 => ( ( member_node @ N4 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.24/0.59 => ~ ( invar @ G ) ) )
% 0.24/0.59 => ~ ! [Ns4: list_node,N3: node] :
% 0.24/0.59 ( ( A
% 0.24/0.59 = ( cons_node @ N3 @ Ns4 ) )
% 0.24/0.59 => ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns4 )
% 0.24/0.59 => ~ ( member_node @ N3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ Ns4 ) ) ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path.cases
% 0.24/0.59 thf(fact_284_same__suffix__nil,axiom,
% 0.24/0.59 ! [Ys: list_node,Xs: list_node] :
% 0.24/0.59 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 0.24/0.59 = ( Ys = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % same_suffix_nil
% 0.24/0.59 thf(fact_285_hd__append2,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.24/0.59 = ( hd_node @ Xs ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % hd_append2
% 0.24/0.59 thf(fact_286_suffix__snoc,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.24/0.59 = ( ( Xs = nil_node )
% 0.24/0.59 | ? [Zs3: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Zs3 @ ( cons_node @ Y @ nil_node ) ) )
% 0.24/0.59 & ( suffix_node @ Zs3 @ Ys ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_snoc
% 0.24/0.59 thf(fact_287_snoc__suffix__snoc,axiom,
% 0.24/0.59 ! [Xs: list_node,X: node,Ys: list_node,Y: node] :
% 0.24/0.59 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y @ nil_node ) ) )
% 0.24/0.59 = ( ( X = Y )
% 0.24/0.59 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % snoc_suffix_snoc
% 0.24/0.59 thf(fact_288_hd__Cons__tl,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 0.24/0.59 = Xs ) ) ).
% 0.24/0.59
% 0.24/0.59 % hd_Cons_tl
% 0.24/0.59 thf(fact_289_list_Ocollapse,axiom,
% 0.24/0.59 ! [List: list_node] :
% 0.24/0.59 ( ( List != nil_node )
% 0.24/0.59 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 0.24/0.59 = List ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.collapse
% 0.24/0.59 thf(fact_290_in__hd__or__tl__conv,axiom,
% 0.24/0.59 ! [L: list_val,X: val] :
% 0.24/0.59 ( ( L != nil_val )
% 0.24/0.59 => ( ( ( X
% 0.24/0.59 = ( hd_val @ L ) )
% 0.24/0.59 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 0.24/0.59 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_hd_or_tl_conv
% 0.24/0.59 thf(fact_291_in__hd__or__tl__conv,axiom,
% 0.24/0.59 ! [L: list_node,X: node] :
% 0.24/0.59 ( ( L != nil_node )
% 0.24/0.59 => ( ( ( X
% 0.24/0.59 = ( hd_node @ L ) )
% 0.24/0.59 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 0.24/0.59 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % in_hd_or_tl_conv
% 0.24/0.59 thf(fact_292_old_Opath__invar,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.24/0.59 => ( invar @ G ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_invar
% 0.24/0.59 thf(fact_293_old_Opath__in___092_060alpha_062n,axiom,
% 0.24/0.59 ! [G: g,Ns: list_node,N: node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ Ns )
% 0.24/0.59 => ( ( member_node @ N @ ( set_node2 @ Ns ) )
% 0.24/0.59 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_in_\<alpha>n
% 0.24/0.59 thf(fact_294_old_Opath__by__tail,axiom,
% 0.24/0.59 ! [G: g,N: node,N2: node,Ns: list_node,Ms: list_node] :
% 0.24/0.59 ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ns ) ) )
% 0.24/0.59 => ( ( ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ns ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N2 @ Ms ) ) )
% 0.24/0.59 => ( graph_435229452_edgeD @ alpha_n @ invar @ inEdges @ G @ ( cons_node @ N @ ( cons_node @ N2 @ Ms ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % old.path_by_tail
% 0.24/0.59 thf(fact_295_set__mono__suffix,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ Ys )
% 0.24/0.59 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % set_mono_suffix
% 0.24/0.59 thf(fact_296_subset__Collect__conv,axiom,
% 0.24/0.59 ! [S: set_node,P: node > $o] :
% 0.24/0.59 ( ( ord_less_eq_set_node @ S @ ( collect_node @ P ) )
% 0.24/0.59 = ( ! [X3: node] :
% 0.24/0.59 ( ( member_node @ X3 @ S )
% 0.24/0.59 => ( P @ X3 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % subset_Collect_conv
% 0.24/0.59 thf(fact_297_ord__eq__le__eq__trans,axiom,
% 0.24/0.59 ! [A: set_node,B: set_node,C: set_node,D: set_node] :
% 0.24/0.59 ( ( A = B )
% 0.24/0.59 => ( ( ord_less_eq_set_node @ B @ C )
% 0.24/0.59 => ( ( C = D )
% 0.24/0.59 => ( ord_less_eq_set_node @ A @ D ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % ord_eq_le_eq_trans
% 0.24/0.59 thf(fact_298_suffix__ConsD2,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Y: node,Ys: list_node] :
% 0.24/0.59 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y @ Ys ) )
% 0.24/0.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_ConsD2
% 0.24/0.59 thf(fact_299_suffix__ConsI,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,Y: node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ Ys )
% 0.24/0.59 => ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_ConsI
% 0.24/0.59 thf(fact_300_suffix__ConsD,axiom,
% 0.24/0.59 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.24/0.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_ConsD
% 0.24/0.59 thf(fact_301_suffix__Cons,axiom,
% 0.24/0.59 ! [Xs: list_node,Y: node,Ys: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ ( cons_node @ Y @ Ys ) )
% 0.24/0.59 = ( ( Xs
% 0.24/0.59 = ( cons_node @ Y @ Ys ) )
% 0.24/0.59 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_Cons
% 0.24/0.59 thf(fact_302_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.24/0.59 ! [A: list_node] :
% 0.24/0.59 ( ( suffix_node @ A @ nil_node )
% 0.24/0.59 => ( A = nil_node ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_bot.bot.extremum_uniqueI
% 0.24/0.59 thf(fact_303_suffix__bot_Obot_Oextremum,axiom,
% 0.24/0.59 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_bot.bot.extremum
% 0.24/0.59 thf(fact_304_Nil__suffix,axiom,
% 0.24/0.59 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 0.24/0.59
% 0.24/0.59 % Nil_suffix
% 0.24/0.59 thf(fact_305_suffixE,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ Ys )
% 0.24/0.59 => ~ ! [Zs2: list_node] :
% 0.24/0.59 ( Ys
% 0.24/0.59 != ( append_node @ Zs2 @ Xs ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffixE
% 0.24/0.59 thf(fact_306_suffixI,axiom,
% 0.24/0.59 ! [Ys: list_node,Zs: list_node,Xs: list_node] :
% 0.24/0.59 ( ( Ys
% 0.24/0.59 = ( append_node @ Zs @ Xs ) )
% 0.24/0.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffixI
% 0.24/0.59 thf(fact_307_Sublist_Osuffix__def,axiom,
% 0.24/0.59 ( suffix_node
% 0.24/0.59 = ( ^ [Xs3: list_node,Ys3: list_node] :
% 0.24/0.59 ? [Zs3: list_node] :
% 0.24/0.59 ( Ys3
% 0.24/0.59 = ( append_node @ Zs3 @ Xs3 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % Sublist.suffix_def
% 0.24/0.59 thf(fact_308_suffix__append,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ ( append_node @ Ys @ Zs ) )
% 0.24/0.59 = ( ( suffix_node @ Xs @ Zs )
% 0.24/0.59 | ? [Xs5: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Xs5 @ Zs ) )
% 0.24/0.59 & ( suffix_node @ Xs5 @ Ys ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_append
% 0.24/0.59 thf(fact_309_suffix__appendD,axiom,
% 0.24/0.59 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 0.24/0.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_appendD
% 0.24/0.59 thf(fact_310_suffix__appendI,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs @ Ys )
% 0.24/0.59 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_appendI
% 0.24/0.59 thf(fact_311_suffix__tl,axiom,
% 0.24/0.59 ! [Xs: list_node] : ( suffix_node @ ( tl_node @ Xs ) @ Xs ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_tl
% 0.24/0.59 thf(fact_312_suffix__same__cases,axiom,
% 0.24/0.59 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 0.24/0.59 ( ( suffix_node @ Xs_1 @ Ys )
% 0.24/0.59 => ( ( suffix_node @ Xs_2 @ Ys )
% 0.24/0.59 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 0.24/0.59 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_same_cases
% 0.24/0.59 thf(fact_313_suffix__order_Oeq__iff,axiom,
% 0.24/0.59 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.24/0.59 = ( ^ [X3: list_node,Y3: list_node] :
% 0.24/0.59 ( ( suffix_node @ X3 @ Y3 )
% 0.24/0.59 & ( suffix_node @ Y3 @ X3 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.eq_iff
% 0.24/0.59 thf(fact_314_suffix__order_Oantisym,axiom,
% 0.24/0.59 ! [X: list_node,Y: list_node] :
% 0.24/0.59 ( ( suffix_node @ X @ Y )
% 0.24/0.59 => ( ( suffix_node @ Y @ X )
% 0.24/0.59 => ( X = Y ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.antisym
% 0.24/0.59 thf(fact_315_suffix__order_Oeq__refl,axiom,
% 0.24/0.59 ! [X: list_node,Y: list_node] :
% 0.24/0.59 ( ( X = Y )
% 0.24/0.59 => ( suffix_node @ X @ Y ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.eq_refl
% 0.24/0.59 thf(fact_316_suffix__order_Oorder_Otrans,axiom,
% 0.24/0.59 ! [A: list_node,B: list_node,C: list_node] :
% 0.24/0.59 ( ( suffix_node @ A @ B )
% 0.24/0.59 => ( ( suffix_node @ B @ C )
% 0.24/0.59 => ( suffix_node @ A @ C ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.order.trans
% 0.24/0.59 thf(fact_317_suffix__order_Oorder__trans,axiom,
% 0.24/0.59 ! [X: list_node,Y: list_node,Z3: list_node] :
% 0.24/0.59 ( ( suffix_node @ X @ Y )
% 0.24/0.59 => ( ( suffix_node @ Y @ Z3 )
% 0.24/0.59 => ( suffix_node @ X @ Z3 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.order_trans
% 0.24/0.59 thf(fact_318_suffix__order_Oantisym__conv,axiom,
% 0.24/0.59 ! [Y: list_node,X: list_node] :
% 0.24/0.59 ( ( suffix_node @ Y @ X )
% 0.24/0.59 => ( ( suffix_node @ X @ Y )
% 0.24/0.59 = ( X = Y ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.antisym_conv
% 0.24/0.59 thf(fact_319_suffix__order_Oorder_Oeq__iff,axiom,
% 0.24/0.59 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.24/0.59 = ( ^ [A4: list_node,B3: list_node] :
% 0.24/0.59 ( ( suffix_node @ A4 @ B3 )
% 0.24/0.59 & ( suffix_node @ B3 @ A4 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.order.eq_iff
% 0.24/0.59 thf(fact_320_suffix__order_Oorder_Oantisym,axiom,
% 0.24/0.59 ! [A: list_node,B: list_node] :
% 0.24/0.59 ( ( suffix_node @ A @ B )
% 0.24/0.59 => ( ( suffix_node @ B @ A )
% 0.24/0.59 => ( A = B ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.order.antisym
% 0.24/0.59 thf(fact_321_suffix__order_Oord__eq__le__trans,axiom,
% 0.24/0.59 ! [A: list_node,B: list_node,C: list_node] :
% 0.24/0.59 ( ( A = B )
% 0.24/0.59 => ( ( suffix_node @ B @ C )
% 0.24/0.59 => ( suffix_node @ A @ C ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.ord_eq_le_trans
% 0.24/0.59 thf(fact_322_suffix__order_Oord__le__eq__trans,axiom,
% 0.24/0.59 ! [A: list_node,B: list_node,C: list_node] :
% 0.24/0.59 ( ( suffix_node @ A @ B )
% 0.24/0.59 => ( ( B = C )
% 0.24/0.59 => ( suffix_node @ A @ C ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.ord_le_eq_trans
% 0.24/0.59 thf(fact_323_suffix__order_Odual__order_Otrans,axiom,
% 0.24/0.59 ! [B: list_node,A: list_node,C: list_node] :
% 0.24/0.59 ( ( suffix_node @ B @ A )
% 0.24/0.59 => ( ( suffix_node @ C @ B )
% 0.24/0.59 => ( suffix_node @ C @ A ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.dual_order.trans
% 0.24/0.59 thf(fact_324_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.24/0.59 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.24/0.59 = ( ^ [A4: list_node,B3: list_node] :
% 0.24/0.59 ( ( suffix_node @ B3 @ A4 )
% 0.24/0.59 & ( suffix_node @ A4 @ B3 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.dual_order.eq_iff
% 0.24/0.59 thf(fact_325_suffix__order_Odual__order_Oantisym,axiom,
% 0.24/0.59 ! [B: list_node,A: list_node] :
% 0.24/0.59 ( ( suffix_node @ B @ A )
% 0.24/0.59 => ( ( suffix_node @ A @ B )
% 0.24/0.59 => ( A = B ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % suffix_order.dual_order.antisym
% 0.24/0.59 thf(fact_326_list_Osel_I1_J,axiom,
% 0.24/0.59 ! [X21: node,X22: list_node] :
% 0.24/0.59 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 0.24/0.59 = X21 ) ).
% 0.24/0.59
% 0.24/0.59 % list.sel(1)
% 0.24/0.59 thf(fact_327_finite__list,axiom,
% 0.24/0.59 ! [A2: set_node] :
% 0.24/0.59 ( ( finite_finite_node @ A2 )
% 0.24/0.59 => ? [Xs2: list_node] :
% 0.24/0.59 ( ( set_node2 @ Xs2 )
% 0.24/0.59 = A2 ) ) ).
% 0.24/0.59
% 0.24/0.59 % finite_list
% 0.24/0.59 thf(fact_328_finite__list,axiom,
% 0.24/0.59 ! [A2: set_val] :
% 0.24/0.59 ( ( finite_finite_val @ A2 )
% 0.24/0.59 => ? [Xs2: list_val] :
% 0.24/0.59 ( ( set_val2 @ Xs2 )
% 0.24/0.59 = A2 ) ) ).
% 0.24/0.59
% 0.24/0.59 % finite_list
% 0.24/0.59 thf(fact_329_subset__code_I1_J,axiom,
% 0.24/0.59 ! [Xs: list_val,B4: set_val] :
% 0.24/0.59 ( ( ord_less_eq_set_val @ ( set_val2 @ Xs ) @ B4 )
% 0.24/0.59 = ( ! [X3: val] :
% 0.24/0.59 ( ( member_val @ X3 @ ( set_val2 @ Xs ) )
% 0.24/0.59 => ( member_val @ X3 @ B4 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % subset_code(1)
% 0.24/0.59 thf(fact_330_subset__code_I1_J,axiom,
% 0.24/0.59 ! [Xs: list_node,B4: set_node] :
% 0.24/0.59 ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ B4 )
% 0.24/0.59 = ( ! [X3: node] :
% 0.24/0.59 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.24/0.59 => ( member_node @ X3 @ B4 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % subset_code(1)
% 0.24/0.59 thf(fact_331_set__mono__prefix,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( prefix_node @ Xs @ Ys )
% 0.24/0.59 => ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ Ys ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % set_mono_prefix
% 0.24/0.59 thf(fact_332_list_Oset__sel_I1_J,axiom,
% 0.24/0.59 ! [A: list_val] :
% 0.24/0.59 ( ( A != nil_val )
% 0.24/0.59 => ( member_val @ ( hd_val @ A ) @ ( set_val2 @ A ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_sel(1)
% 0.24/0.59 thf(fact_333_list_Oset__sel_I1_J,axiom,
% 0.24/0.59 ! [A: list_node] :
% 0.24/0.59 ( ( A != nil_node )
% 0.24/0.59 => ( member_node @ ( hd_node @ A ) @ ( set_node2 @ A ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.set_sel(1)
% 0.24/0.59 thf(fact_334_hd__in__set,axiom,
% 0.24/0.59 ! [Xs: list_val] :
% 0.24/0.59 ( ( Xs != nil_val )
% 0.24/0.59 => ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ Xs ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % hd_in_set
% 0.24/0.59 thf(fact_335_hd__in__set,axiom,
% 0.24/0.59 ! [Xs: list_node] :
% 0.24/0.59 ( ( Xs != nil_node )
% 0.24/0.59 => ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ Xs ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % hd_in_set
% 0.24/0.59 thf(fact_336_hd__append,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ( ( ( Xs = nil_node )
% 0.24/0.59 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.24/0.59 = ( hd_node @ Ys ) ) )
% 0.24/0.59 & ( ( Xs != nil_node )
% 0.24/0.59 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.24/0.59 = ( hd_node @ Xs ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % hd_append
% 0.24/0.59 thf(fact_337_longest__common__prefix,axiom,
% 0.24/0.59 ! [Xs: list_node,Ys: list_node] :
% 0.24/0.59 ? [Ps: list_node,Xs6: list_node,Ys4: list_node] :
% 0.24/0.59 ( ( Xs
% 0.24/0.59 = ( append_node @ Ps @ Xs6 ) )
% 0.24/0.59 & ( Ys
% 0.24/0.59 = ( append_node @ Ps @ Ys4 ) )
% 0.24/0.59 & ( ( Xs6 = nil_node )
% 0.24/0.59 | ( Ys4 = nil_node )
% 0.24/0.59 | ( ( hd_node @ Xs6 )
% 0.24/0.59 != ( hd_node @ Ys4 ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % longest_common_prefix
% 0.24/0.59 thf(fact_338_not__suffix__cases,axiom,
% 0.24/0.59 ! [Ps2: list_node,Ls: list_node] :
% 0.24/0.59 ( ~ ( suffix_node @ Ps2 @ Ls )
% 0.24/0.59 => ( ( ( Ps2 != nil_node )
% 0.24/0.59 => ( Ls != nil_node ) )
% 0.24/0.59 => ( ! [A3: node,As: list_node] :
% 0.24/0.59 ( ( Ps2
% 0.24/0.59 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.24/0.59 => ! [X4: node,Xs2: list_node] :
% 0.24/0.59 ( ( Ls
% 0.24/0.59 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 0.24/0.59 => ( ( X4 = A3 )
% 0.24/0.59 => ( suffix_node @ As @ Xs2 ) ) ) )
% 0.24/0.59 => ~ ! [A3: node] :
% 0.24/0.59 ( ? [As: list_node] :
% 0.24/0.59 ( Ps2
% 0.24/0.59 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.24/0.59 => ! [X4: node] :
% 0.24/0.59 ( ? [Xs2: list_node] :
% 0.24/0.59 ( Ls
% 0.24/0.59 = ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) )
% 0.24/0.59 => ( X4 = A3 ) ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % not_suffix_cases
% 0.24/0.59 thf(fact_339_not__suffix__induct,axiom,
% 0.24/0.59 ! [Ps2: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 0.24/0.59 ( ~ ( suffix_node @ Ps2 @ Ls )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ nil_node )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( X4 != Y2 )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) )
% 0.24/0.59 => ( ! [X4: node,Xs2: list_node,Y2: node,Ys2: list_node] :
% 0.24/0.59 ( ( X4 = Y2 )
% 0.24/0.59 => ( ~ ( suffix_node @ Xs2 @ Ys2 )
% 0.24/0.59 => ( ( P @ Xs2 @ Ys2 )
% 0.24/0.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X4 @ nil_node ) ) @ ( append_node @ Ys2 @ ( cons_node @ Y2 @ nil_node ) ) ) ) ) )
% 0.24/0.59 => ( P @ Ps2 @ Ls ) ) ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % not_suffix_induct
% 0.24/0.59 thf(fact_340_list_Oexpand,axiom,
% 0.24/0.59 ! [List: list_node,List2: list_node] :
% 0.24/0.59 ( ( ( List = nil_node )
% 0.24/0.59 = ( List2 = nil_node ) )
% 0.24/0.59 => ( ( ( List != nil_node )
% 0.24/0.59 => ( ( List2 != nil_node )
% 0.24/0.59 => ( ( ( hd_node @ List )
% 0.24/0.59 = ( hd_node @ List2 ) )
% 0.24/0.59 & ( ( tl_node @ List )
% 0.24/0.59 = ( tl_node @ List2 ) ) ) ) )
% 0.24/0.59 => ( List = List2 ) ) ) ).
% 0.24/0.59
% 0.24/0.59 % list.expand
% 0.24/0.59 thf(fact_341_not__hd__in__tl,axiom,
% 0.24/0.59 ! [X: val,Xs: list_val] :
% 0.24/0.68 ( ( X
% 0.24/0.68 != ( hd_val @ Xs ) )
% 0.24/0.68 => ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.24/0.68 => ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % not_hd_in_tl
% 0.24/0.68 thf(fact_342_not__hd__in__tl,axiom,
% 0.24/0.68 ! [X: node,Xs: list_node] :
% 0.24/0.68 ( ( X
% 0.24/0.68 != ( hd_node @ Xs ) )
% 0.24/0.68 => ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.24/0.68 => ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % not_hd_in_tl
% 0.24/0.68 thf(fact_343_set__subset__Cons,axiom,
% 0.24/0.68 ! [Xs: list_node,X: node] : ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ ( set_node2 @ ( cons_node @ X @ Xs ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % set_subset_Cons
% 0.24/0.68 thf(fact_344_list_Oexhaust__sel,axiom,
% 0.24/0.68 ! [List: list_node] :
% 0.24/0.68 ( ( List != nil_node )
% 0.24/0.68 => ( List
% 0.24/0.68 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % list.exhaust_sel
% 0.24/0.68 thf(fact_345_tl__subset,axiom,
% 0.24/0.68 ! [Xs: list_node,A2: set_node] :
% 0.24/0.68 ( ( Xs != nil_node )
% 0.24/0.68 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 0.24/0.68 => ( ord_less_eq_set_node @ ( set_node2 @ ( tl_node @ Xs ) ) @ A2 ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % tl_subset
% 0.24/0.68 thf(fact_346_butlast__subset,axiom,
% 0.24/0.68 ! [Xs: list_node,A2: set_node] :
% 0.24/0.68 ( ( Xs != nil_node )
% 0.24/0.68 => ( ( ord_less_eq_set_node @ ( set_node2 @ Xs ) @ A2 )
% 0.24/0.68 => ( ord_less_eq_set_node @ ( set_node2 @ ( butlast_node @ Xs ) ) @ A2 ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % butlast_subset
% 0.24/0.68 thf(fact_347_prefix__same__cases,axiom,
% 0.24/0.68 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 0.24/0.68 ( ( prefix_node @ Xs_1 @ Ys )
% 0.24/0.68 => ( ( prefix_node @ Xs_2 @ Ys )
% 0.24/0.68 => ( ( prefix_node @ Xs_1 @ Xs_2 )
% 0.24/0.68 | ( prefix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % prefix_same_cases
% 0.24/0.68 thf(fact_348_prefix__order_Oeq__iff,axiom,
% 0.24/0.68 ( ( ^ [Y4: list_node,Z: list_node] : ( Y4 = Z ) )
% 0.24/0.68 = ( ^ [X3: list_node,Y3: list_node] :
% 0.24/0.68 ( ( prefix_node @ X3 @ Y3 )
% 0.24/0.68 & ( prefix_node @ Y3 @ X3 ) ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % prefix_order.eq_iff
% 0.24/0.68 thf(fact_349_prefix__order_Oantisym,axiom,
% 0.24/0.68 ! [X: list_node,Y: list_node] :
% 0.24/0.68 ( ( prefix_node @ X @ Y )
% 0.24/0.68 => ( ( prefix_node @ Y @ X )
% 0.24/0.68 => ( X = Y ) ) ) ).
% 0.24/0.68
% 0.24/0.68 % prefix_order.antisym
% 0.24/0.68
% 0.24/0.68 % Conjectures (1)
% 0.24/0.68 thf(conj_0,conjecture,
% 0.24/0.68 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ).
% 0.24/0.68
% 0.24/0.68 %------------------------------------------------------------------------------
% 0.24/0.68 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qnavuydIOC/cvc5---1.0.5_28241.p...
% 0.24/0.68 (declare-sort $$unsorted 0)
% 0.24/0.68 (declare-sort tptp.list_P561207620_edgeD 0)
% 0.24/0.68 (declare-sort tptp.option_list_val 0)
% 0.24/0.68 (declare-sort tptp.produc1432036078de_val 0)
% 0.24/0.68 (declare-sort tptp.list_list_node 0)
% 0.24/0.68 (declare-sort tptp.set_list_node 0)
% 0.24/0.68 (declare-sort tptp.list_node 0)
% 0.24/0.68 (declare-sort tptp.list_val 0)
% 0.24/0.68 (declare-sort tptp.set_node 0)
% 0.24/0.68 (declare-sort tptp.set_val 0)
% 0.24/0.68 (declare-sort tptp.node 0)
% 0.24/0.68 (declare-sort tptp.val 0)
% 0.24/0.68 (declare-sort tptp.g 0)
% 0.24/0.68 (declare-fun tptp.finite_finite_node (tptp.set_node) Bool)
% 0.24/0.68 (declare-fun tptp.finite_finite_val (tptp.set_val) Bool)
% 0.24/0.68 (declare-fun tptp.graph_1012773594_edgeD ((-> tptp.g tptp.list_node) (-> tptp.g Bool) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) tptp.g tptp.node tptp.list_node tptp.node) Bool)
% 0.24/0.68 (declare-fun tptp.graph_435229452_edgeD ((-> tptp.g tptp.list_node) (-> tptp.g Bool) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) tptp.g tptp.list_node) Bool)
% 0.24/0.68 (declare-fun tptp.graph_272749361_edgeD ((-> tptp.g tptp.node tptp.list_P561207620_edgeD) tptp.g tptp.node) tptp.list_node)
% 0.24/0.68 (declare-fun tptp.append_list_node (tptp.list_list_node tptp.list_list_node) tptp.list_list_node)
% 0.24/0.68 (declare-fun tptp.append_node (tptp.list_node tptp.list_node) tptp.list_node)
% 0.24/0.68 (declare-fun tptp.append_val (tptp.list_val tptp.list_val) tptp.list_val)
% 0.24/0.68 (declare-fun tptp.butlast_list_node (tptp.list_list_node) tptp.list_list_node)
% 0.24/0.68 (declare-fun tptp.butlast_node (tptp.list_node) tptp.list_node)
% 0.24/0.68 (declare-fun tptp.butlast_val (tptp.list_val) tptp.list_val)
% 0.24/0.68 (declare-fun tptp.cons_list_node (tptp.list_node tptp.list_list_node) tptp.list_list_node)
% 0.24/0.68 (declare-fun tptp.cons_node (tptp.node tptp.list_node) tptp.list_node)
% 0.24/0.68 (declare-fun tptp.cons_val (tptp.val tptp.list_val) tptp.list_val)
% 0.24/0.68 (declare-fun tptp.nil_list_node () tptp.list_list_node)
% 0.24/0.68 (declare-fun tptp.nil_node () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.nil_val () tptp.list_val)
% 0.24/0.68 (declare-fun tptp.hd_node (tptp.list_node) tptp.node)
% 0.24/0.68 (declare-fun tptp.hd_val (tptp.list_val) tptp.val)
% 0.24/0.68 (declare-fun tptp.set_list_node2 (tptp.list_list_node) tptp.set_list_node)
% 0.24/0.68 (declare-fun tptp.set_node2 (tptp.list_node) tptp.set_node)
% 0.24/0.68 (declare-fun tptp.set_val2 (tptp.list_val) tptp.set_val)
% 0.24/0.68 (declare-fun tptp.tl_list_node (tptp.list_list_node) tptp.list_list_node)
% 0.24/0.68 (declare-fun tptp.tl_node (tptp.list_node) tptp.list_node)
% 0.24/0.68 (declare-fun tptp.tl_val (tptp.list_val) tptp.list_val)
% 0.24/0.68 (declare-fun tptp.ord_less_eq_set_node (tptp.set_node tptp.set_node) Bool)
% 0.24/0.68 (declare-fun tptp.ord_less_eq_set_val (tptp.set_val tptp.set_val) Bool)
% 0.24/0.68 (declare-fun tptp.sSA_CF848637139eD_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.list_P561207620_edgeD) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.node) tptp.set_val)
% 0.24/0.68 (declare-fun tptp.sSA_CF551432799de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val) tptp.node)
% 0.24/0.68 (declare-fun tptp.sSA_CF1252180629de_val ((-> tptp.g tptp.list_node) (-> tptp.g tptp.node tptp.set_val) (-> tptp.g tptp.produc1432036078de_val tptp.option_list_val) tptp.g tptp.val tptp.val) Bool)
% 0.24/0.68 (declare-fun tptp.collect_node ((-> tptp.node Bool)) tptp.set_node)
% 0.24/0.68 (declare-fun tptp.collect_val ((-> tptp.val Bool)) tptp.set_val)
% 0.24/0.68 (declare-fun tptp.prefix_node (tptp.list_node tptp.list_node) Bool)
% 0.24/0.68 (declare-fun tptp.suffix_node (tptp.list_node tptp.list_node) Bool)
% 0.24/0.68 (declare-fun tptp.member_list_node (tptp.list_node tptp.set_list_node) Bool)
% 0.24/0.68 (declare-fun tptp.member_node (tptp.node tptp.set_node) Bool)
% 0.24/0.68 (declare-fun tptp.member_val (tptp.val tptp.set_val) Bool)
% 0.24/0.68 (declare-fun tptp.alpha_n (tptp.g) tptp.list_node)
% 0.24/0.68 (declare-fun tptp.phi_r () tptp.val)
% 0.24/0.68 (declare-fun tptp.defs (tptp.g tptp.node) tptp.set_val)
% 0.24/0.68 (declare-fun tptp.g2 () tptp.g)
% 0.24/0.68 (declare-fun tptp.i () tptp.node)
% 0.24/0.68 (declare-fun tptp.inEdges (tptp.g tptp.node) tptp.list_P561207620_edgeD)
% 0.24/0.68 (declare-fun tptp.invar (tptp.g) Bool)
% 0.24/0.68 (declare-fun tptp.m () tptp.node)
% 0.24/0.68 (declare-fun tptp.ms () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.ms2 () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.n () tptp.node)
% 0.24/0.68 (declare-fun tptp.ns () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.phis (tptp.g tptp.produc1432036078de_val) tptp.option_list_val)
% 0.24/0.68 (declare-fun tptp.pred_phi_r () tptp.node)
% 0.24/0.68 (declare-fun tptp.r () tptp.val)
% 0.24/0.68 (declare-fun tptp.ri () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.rs () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.rs2 () tptp.list_node)
% 0.24/0.68 (declare-fun tptp.s () tptp.val)
% 0.24/0.68 (assert (not (= tptp.r tptp.phi_r)))
% 0.24/0.68 (assert (= tptp.i (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r)))
% 0.24/0.68 (assert (forall ((G tptp.g)) (@ tptp.invar G)))
% 0.24/0.68 (assert (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) tptp.n) tptp.ns) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)))
% 0.24/0.68 (assert (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)) tptp.ri) tptp.i))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ms tptp.list_node) (L tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_2 (@ _let_1 N))) (=> (@ (@ _let_2 Ns) M) (=> (@ (@ (@ _let_1 M) Ms) L) (@ (@ _let_2 (@ (@ tptp.append_node Ns) (@ tptp.tl_node Ms))) L)))))))
% 0.24/0.68 (assert (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2))) (not (= (@ _let_1 tptp.phi_r) (@ _let_1 tptp.r)))))
% 0.24/0.68 (assert (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)) tptp.rs) tptp.pred_phi_r))
% 0.24/0.68 (assert (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r) tptp.r))
% 0.24/0.68 (assert (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2))) (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) (@ _let_1 tptp.r)) tptp.rs2) (@ _let_1 tptp.phi_r))))
% 0.24/0.68 (assert (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) tptp.m) tptp.ms2) tptp.i))
% 0.24/0.68 (assert (let ((_let_1 (= tptp.m tptp.i))) (let ((_let_2 (not (= tptp.i (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r))))) (=> _let_2 (=> (=> _let_2 (not _let_1)) (not (=> _let_2 _let_1)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (N2 tptp.node) (Ns2 tptp.list_node) (M tptp.node)) (let ((_let_1 (@ (@ tptp.cons_node N2) Ns2))) (let ((_let_2 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_2 N) (@ (@ tptp.append_node Ns) _let_1)) M) (@ (@ (@ _let_2 N2) _let_1) M))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (not (= Ns tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (M tptp.node)) (not (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) tptp.nil_node) M))))
% 0.24/0.68 (assert (@ (@ tptp.member_val tptp.r) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) tptp.g2) tptp.pred_phi_r)))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node N) (@ tptp.set_node2 Ns)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (L tptp.node)) (let ((_let_1 (@ tptp.member_node L))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ _let_1 (@ tptp.set_node2 Ns)) (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))))))))
% 0.24/0.68 (assert (forall ((X tptp.list_node) (Xs tptp.list_list_node) (Ys tptp.list_list_node) (Y tptp.list_node)) (let ((_let_1 (@ tptp.member_list_node X))) (=> (@ _let_1 (@ tptp.set_list_node2 Xs)) (@ _let_1 (@ tptp.set_list_node2 (@ tptp.tl_list_node (@ (@ tptp.append_list_node Ys) (@ (@ tptp.cons_list_node Y) Xs)))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val) (Ys tptp.list_val) (Y tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val (@ (@ tptp.append_val Ys) (@ (@ tptp.cons_val Y) Xs)))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) Xs)))))))))
% 0.24/0.68 (assert (@ (@ tptp.member_node tptp.i) (@ tptp.set_node2 tptp.ms)))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ tptp.alpha_n G))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node M) (@ tptp.set_node2 Ns)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (N2 tptp.node) (Ns2 tptp.list_node) (M tptp.node)) (let ((_let_1 (@ tptp.cons_node N2))) (let ((_let_2 (@ tptp.append_node Ns))) (let ((_let_3 (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N))) (=> (@ (@ _let_3 (@ _let_2 (@ _let_1 Ns2))) M) (@ (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_node))) N2)))))))
% 0.24/0.68 (assert (not (@ (@ tptp.member_node (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)) (@ tptp.set_node2 (@ tptp.tl_node tptp.rs2)))))
% 0.24/0.68 (assert (not (@ (@ tptp.member_node (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)) (@ tptp.set_node2 (@ tptp.tl_node tptp.rs)))))
% 0.24/0.68 (assert (= tptp.rs2 (@ (@ tptp.append_node tptp.rs) (@ (@ tptp.cons_node (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r)) tptp.nil_node))))
% 0.24/0.68 (assert (@ (@ tptp.prefix_node tptp.ri) tptp.rs2))
% 0.24/0.68 (assert (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ tptp.invar G) (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) (@ (@ tptp.cons_node N) tptp.nil_node)) N)))))
% 0.24/0.68 (assert (not (@ (@ tptp.member_node tptp.i) (@ tptp.set_node2 (@ tptp.butlast_node tptp.ms2)))))
% 0.24/0.68 (assert (@ (@ tptp.member_node tptp.pred_phi_r) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) tptp.g2) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r)))))
% 0.24/0.68 (assert (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) tptp.m) tptp.ms) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.s)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (=> (not (= Xs tptp.nil_list_node)) (= (@ tptp.tl_list_node (@ (@ tptp.append_list_node Xs) Ys)) (@ (@ tptp.append_list_node (@ tptp.tl_list_node Xs)) Ys)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (=> (not (= Xs tptp.nil_val)) (= (@ tptp.tl_val (@ (@ tptp.append_val Xs) Ys)) (@ (@ tptp.append_val (@ tptp.tl_val Xs)) Ys)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (= (@ tptp.tl_node (@ (@ tptp.append_node Xs) Ys)) (@ (@ tptp.append_node (@ tptp.tl_node Xs)) Ys)))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_val) (E tptp.val) (L2 tptp.list_val) (E2 tptp.val)) (= (= (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E) L2)) (@ (@ tptp.cons_val E2) tptp.nil_val)) (and (= L1 tptp.nil_val) (= E E2) (= L2 tptp.nil_val)))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_list_node) (E tptp.list_node) (L2 tptp.list_list_node) (E2 tptp.list_node)) (= (= (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E) L2)) (@ (@ tptp.cons_list_node E2) tptp.nil_list_node)) (and (= L1 tptp.nil_list_node) (= E E2) (= L2 tptp.nil_list_node)))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_node) (E tptp.node) (L2 tptp.list_node) (E2 tptp.node)) (= (= (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E) L2)) (@ (@ tptp.cons_node E2) tptp.nil_node)) (and (= L1 tptp.nil_node) (= E E2) (= L2 tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((E2 tptp.val) (L1 tptp.list_val) (E tptp.val) (L2 tptp.list_val)) (= (= (@ (@ tptp.cons_val E2) tptp.nil_val) (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E) L2))) (and (= L1 tptp.nil_val) (= E E2) (= L2 tptp.nil_val)))))
% 0.24/0.68 (assert (forall ((E2 tptp.list_node) (L1 tptp.list_list_node) (E tptp.list_node) (L2 tptp.list_list_node)) (= (= (@ (@ tptp.cons_list_node E2) tptp.nil_list_node) (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E) L2))) (and (= L1 tptp.nil_list_node) (= E E2) (= L2 tptp.nil_list_node)))))
% 0.24/0.68 (assert (forall ((E2 tptp.node) (L1 tptp.list_node) (E tptp.node) (L2 tptp.list_node)) (= (= (@ (@ tptp.cons_node E2) tptp.nil_node) (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E) L2))) (and (= L1 tptp.nil_node) (= E E2) (= L2 tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((L2 tptp.list_val) (A tptp.val) (L1 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L2 tptp.nil_val)) (= (= _let_1 (@ (@ tptp.append_val L1) L2)) (and (= L1 tptp.nil_val) (= L2 _let_1)))))))
% 0.24/0.68 (assert (forall ((L2 tptp.list_list_node) (A tptp.list_node) (L1 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L2 tptp.nil_list_node)) (= (= _let_1 (@ (@ tptp.append_list_node L1) L2)) (and (= L1 tptp.nil_list_node) (= L2 _let_1)))))))
% 0.24/0.68 (assert (forall ((L2 tptp.list_node) (A tptp.node) (L1 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L2 tptp.nil_node)) (= (= _let_1 (@ (@ tptp.append_node L1) L2)) (and (= L1 tptp.nil_node) (= L2 _let_1)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_val) (A tptp.val) (L2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L1 tptp.nil_val)) (= (= _let_1 (@ (@ tptp.append_val L1) L2)) (and (= L1 _let_1) (= L2 tptp.nil_val)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_list_node) (A tptp.list_node) (L2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L1 tptp.nil_list_node)) (= (= _let_1 (@ (@ tptp.append_list_node L1) L2)) (and (= L1 _let_1) (= L2 tptp.nil_list_node)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_node) (A tptp.node) (L2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L1 tptp.nil_node)) (= (= _let_1 (@ (@ tptp.append_node L1) L2)) (and (= L1 _let_1) (= L2 tptp.nil_node)))))))
% 0.24/0.68 (assert (forall ((L2 tptp.list_val) (L1 tptp.list_val) (A tptp.val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L2 tptp.nil_val)) (= (= (@ (@ tptp.append_val L1) L2) _let_1) (and (= L1 tptp.nil_val) (= L2 _let_1)))))))
% 0.24/0.68 (assert (forall ((L2 tptp.list_list_node) (L1 tptp.list_list_node) (A tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L2 tptp.nil_list_node)) (= (= (@ (@ tptp.append_list_node L1) L2) _let_1) (and (= L1 tptp.nil_list_node) (= L2 _let_1)))))))
% 0.24/0.68 (assert (forall ((L2 tptp.list_node) (L1 tptp.list_node) (A tptp.node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L2 tptp.nil_node)) (= (= (@ (@ tptp.append_node L1) L2) _let_1) (and (= L1 tptp.nil_node) (= L2 _let_1)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_val) (L2 tptp.list_val) (A tptp.val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L1 tptp.nil_val)) (= (= (@ (@ tptp.append_val L1) L2) _let_1) (and (= L1 _let_1) (= L2 tptp.nil_val)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_list_node) (L2 tptp.list_list_node) (A tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L1 tptp.nil_list_node)) (= (= (@ (@ tptp.append_list_node L1) L2) _let_1) (and (= L1 _let_1) (= L2 tptp.nil_list_node)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_node) (L2 tptp.list_node) (A tptp.node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L1 tptp.nil_node)) (= (= (@ (@ tptp.append_node L1) L2) _let_1) (and (= L1 _let_1) (= L2 tptp.nil_node)))))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_val) (E1 tptp.val) (E22 tptp.val) (L2 tptp.list_val) (E12 tptp.val) (E23 tptp.val)) (= (= (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E1) (@ (@ tptp.cons_val E22) L2))) (@ (@ tptp.cons_val E12) (@ (@ tptp.cons_val E23) tptp.nil_val))) (and (= L1 tptp.nil_val) (= E12 E1) (= E23 E22) (= L2 tptp.nil_val)))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_list_node) (E1 tptp.list_node) (E22 tptp.list_node) (L2 tptp.list_list_node) (E12 tptp.list_node) (E23 tptp.list_node)) (= (= (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E1) (@ (@ tptp.cons_list_node E22) L2))) (@ (@ tptp.cons_list_node E12) (@ (@ tptp.cons_list_node E23) tptp.nil_list_node))) (and (= L1 tptp.nil_list_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_list_node)))))
% 0.24/0.68 (assert (forall ((L1 tptp.list_node) (E1 tptp.node) (E22 tptp.node) (L2 tptp.list_node) (E12 tptp.node) (E23 tptp.node)) (= (= (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E1) (@ (@ tptp.cons_node E22) L2))) (@ (@ tptp.cons_node E12) (@ (@ tptp.cons_node E23) tptp.nil_node))) (and (= L1 tptp.nil_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((E12 tptp.val) (E23 tptp.val) (L1 tptp.list_val) (E1 tptp.val) (E22 tptp.val) (L2 tptp.list_val)) (= (= (@ (@ tptp.cons_val E12) (@ (@ tptp.cons_val E23) tptp.nil_val)) (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E1) (@ (@ tptp.cons_val E22) L2)))) (and (= L1 tptp.nil_val) (= E12 E1) (= E23 E22) (= L2 tptp.nil_val)))))
% 0.24/0.68 (assert (forall ((E12 tptp.list_node) (E23 tptp.list_node) (L1 tptp.list_list_node) (E1 tptp.list_node) (E22 tptp.list_node) (L2 tptp.list_list_node)) (= (= (@ (@ tptp.cons_list_node E12) (@ (@ tptp.cons_list_node E23) tptp.nil_list_node)) (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E1) (@ (@ tptp.cons_list_node E22) L2)))) (and (= L1 tptp.nil_list_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_list_node)))))
% 0.24/0.68 (assert (forall ((E12 tptp.node) (E23 tptp.node) (L1 tptp.list_node) (E1 tptp.node) (E22 tptp.node) (L2 tptp.list_node)) (= (= (@ (@ tptp.cons_node E12) (@ (@ tptp.cons_node E23) tptp.nil_node)) (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E1) (@ (@ tptp.cons_node E22) L2)))) (and (= L1 tptp.nil_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_node)))))
% 0.24/0.68 (assert (@ (@ tptp.prefix_node tptp.ms2) tptp.ms))
% 0.24/0.68 (assert (forall ((X2 tptp.node)) (let ((_let_1 (@ tptp.member_node X2))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node tptp.ri))) (not (@ _let_1 (@ tptp.set_node2 tptp.ms)))))))
% 0.24/0.68 (assert (forall ((X21 tptp.val) (X22 tptp.list_val) (Y21 tptp.val) (Y22 tptp.list_val)) (= (= (@ (@ tptp.cons_val X21) X22) (@ (@ tptp.cons_val Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.24/0.68 (assert (forall ((X21 tptp.list_node) (X22 tptp.list_list_node) (Y21 tptp.list_node) (Y22 tptp.list_list_node)) (= (= (@ (@ tptp.cons_list_node X21) X22) (@ (@ tptp.cons_list_node Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.24/0.68 (assert (forall ((X21 tptp.node) (X22 tptp.list_node) (Y21 tptp.node) (Y22 tptp.list_node)) (= (= (@ (@ tptp.cons_node X21) X22) (@ (@ tptp.cons_node Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.24/0.68 (assert (forall ((A tptp.list_val) (B tptp.list_val) (C tptp.list_val)) (let ((_let_1 (@ tptp.append_val A))) (= (@ (@ tptp.append_val (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_val B) C))))))
% 0.24/0.68 (assert (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.append_node A))) (= (@ (@ tptp.append_node (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_node B) C))))))
% 0.24/0.68 (assert (forall ((A tptp.val) (P (-> tptp.val Bool))) (= (@ (@ tptp.member_val A) (@ tptp.collect_val P)) (@ P A))))
% 0.24/0.68 (assert (forall ((A tptp.node) (P (-> tptp.node Bool))) (= (@ (@ tptp.member_node A) (@ tptp.collect_node P)) (@ P A))))
% 0.24/0.68 (assert (forall ((A2 tptp.set_val)) (= (@ tptp.collect_val (lambda ((X3 tptp.val)) (@ (@ tptp.member_val X3) A2))) A2)))
% 0.24/0.68 (assert (forall ((A2 tptp.set_node)) (= (@ tptp.collect_node (lambda ((X3 tptp.node)) (@ (@ tptp.member_node X3) A2))) A2)))
% 0.24/0.68 (assert (forall ((P (-> tptp.node Bool)) (Q (-> tptp.node Bool))) (=> (forall ((X4 tptp.node)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_node P) (@ tptp.collect_node Q)))))
% 0.24/0.68 (assert (forall ((P (-> tptp.val Bool)) (Q (-> tptp.val Bool))) (=> (forall ((X4 tptp.val)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_val P) (@ tptp.collect_val Q)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val) (Zs tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (= (@ (@ tptp.append_val (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_val Ys) Zs))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (= (@ (@ tptp.append_node (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_node Ys) Zs))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_val) (Xs tptp.list_val) (Zs tptp.list_val)) (= (= (@ (@ tptp.append_val Ys) Xs) (@ (@ tptp.append_val Zs) Xs)) (= Ys Zs))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Xs tptp.list_node) (Zs tptp.list_node)) (= (= (@ (@ tptp.append_node Ys) Xs) (@ (@ tptp.append_node Zs) Xs)) (= Ys Zs))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val) (Zs tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))))
% 0.24/0.68 (assert (forall ((N tptp.node) (G tptp.g) (N2 tptp.node)) (let ((_let_1 (@ tptp.member_node N))) (=> (@ _let_1 (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N2))) (=> (@ tptp.invar G) (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))))))))
% 0.24/0.68 (assert (forall ((N tptp.node) (G tptp.g) (N2 tptp.node)) (let ((_let_1 (@ tptp.set_node2 (@ tptp.alpha_n G)))) (let ((_let_2 (@ tptp.member_node N))) (=> (@ _let_2 (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N2))) (=> (@ _let_2 _let_1) (=> (@ tptp.invar G) (@ (@ tptp.member_node N2) _let_1))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node)) (=> (not (= (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N) tptp.nil_node)) (=> (@ tptp.invar G) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ms tptp.list_node) (L tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_2 (@ _let_1 N))) (=> (@ (@ _let_2 Ns) M) (=> (@ (@ (@ _let_1 M) Ms) L) (@ (@ _let_2 (@ (@ tptp.append_node (@ tptp.butlast_node Ns)) Ms)) L)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node)) (= (@ (@ tptp.append_list_node Xs) tptp.nil_list_node) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val)) (= (@ (@ tptp.append_val Xs) tptp.nil_val) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (@ (@ tptp.append_node Xs) tptp.nil_node) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (= (= (@ (@ tptp.append_list_node Xs) Ys) Xs) (= Ys tptp.nil_list_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (= (= (@ (@ tptp.append_val Xs) Ys) Xs) (= Ys tptp.nil_val))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (= (@ (@ tptp.append_node Xs) Ys) Xs) (= Ys tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (= (= Xs (@ (@ tptp.append_list_node Xs) Ys)) (= Ys tptp.nil_list_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (= (= Xs (@ (@ tptp.append_val Xs) Ys)) (= Ys tptp.nil_val))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (= Xs (@ (@ tptp.append_node Xs) Ys)) (= Ys tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (= (= (@ (@ tptp.append_list_node Xs) Ys) Ys) (= Xs tptp.nil_list_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (= (= (@ (@ tptp.append_val Xs) Ys) Ys) (= Xs tptp.nil_val))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (= (@ (@ tptp.append_node Xs) Ys) Ys) (= Xs tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_list_node) (Xs tptp.list_list_node)) (= (= Ys (@ (@ tptp.append_list_node Xs) Ys)) (= Xs tptp.nil_list_node))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_val) (Xs tptp.list_val)) (= (= Ys (@ (@ tptp.append_val Xs) Ys)) (= Xs tptp.nil_val))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Xs tptp.list_node)) (= (= Ys (@ (@ tptp.append_node Xs) Ys)) (= Xs tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (= (= tptp.nil_list_node (@ (@ tptp.append_list_node Xs) Ys)) (and (= Xs tptp.nil_list_node) (= Ys tptp.nil_list_node)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (= (= tptp.nil_val (@ (@ tptp.append_val Xs) Ys)) (and (= Xs tptp.nil_val) (= Ys tptp.nil_val)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (= tptp.nil_node (@ (@ tptp.append_node Xs) Ys)) (and (= Xs tptp.nil_node) (= Ys tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (= (= (@ (@ tptp.append_list_node Xs) Ys) tptp.nil_list_node) (and (= Xs tptp.nil_list_node) (= Ys tptp.nil_list_node)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (= (= (@ (@ tptp.append_val Xs) Ys) tptp.nil_val) (and (= Xs tptp.nil_val) (= Ys tptp.nil_val)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (= (@ (@ tptp.append_node Xs) Ys) tptp.nil_node) (and (= Xs tptp.nil_node) (= Ys tptp.nil_node)))))
% 0.24/0.68 (assert (= (@ tptp.append_list_node tptp.nil_list_node) (lambda ((X3 tptp.list_list_node)) X3)))
% 0.24/0.68 (assert (= (@ tptp.append_val tptp.nil_val) (lambda ((X3 tptp.list_val)) X3)))
% 0.24/0.68 (assert (= (@ tptp.append_node tptp.nil_node) (lambda ((X3 tptp.list_node)) X3)))
% 0.24/0.68 (assert (forall ((A tptp.list_list_node)) (= (@ (@ tptp.append_list_node A) tptp.nil_list_node) A)))
% 0.24/0.68 (assert (forall ((A tptp.list_val)) (= (@ (@ tptp.append_val A) tptp.nil_val) A)))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (= (@ (@ tptp.append_node A) tptp.nil_node) A)))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (X tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Ns)) (not (forall ((Ns_1 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns_1) X) (forall ((Ns_2 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) X) Ns_2) M) (not (= Ns (@ (@ tptp.append_node (@ tptp.butlast_node Ns_1)) Ns_2))))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (M2 tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node M2) (@ tptp.set_node2 Ns)) (not (forall ((Ns3 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns3) M2) (=> (@ (@ tptp.prefix_node Ns3) Ns) (@ (@ tptp.member_node M2) (@ tptp.set_node2 (@ tptp.butlast_node Ns3)))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node Bool))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Ns)) (@ P X2))) (not (forall ((M3 tptp.node) (Ns3 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns3) M3) (=> (@ P M3) (=> (forall ((X2 tptp.node)) (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 (@ tptp.butlast_node Ns3))) (not (@ P X2)))) (not (@ (@ tptp.prefix_node Ns3) Ns)))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node tptp.list_node tptp.node Bool))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (=> (@ tptp.invar G) (@ (@ (@ P M) (@ (@ tptp.cons_node M) tptp.nil_node)) M)) (=> (forall ((Ns4 tptp.list_node) (N3 tptp.node) (N4 tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N4) Ns4) M) (=> (@ (@ (@ P N4) Ns4) M) (=> (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N4))) (@ (@ (@ P N3) (@ (@ tptp.cons_node N3) Ns4)) M))))) (@ (@ (@ P N) Ns) M))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (X tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Ns)) (not (forall ((Ns_1 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns_1) X) (forall ((Ns_2 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) X) Ns_2) M) (=> (= Ns (@ (@ tptp.append_node Ns_1) (@ tptp.tl_node Ns_2))) (not (= Ns (@ (@ tptp.append_node (@ tptp.butlast_node Ns_1)) Ns_2)))))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ns2 tptp.list_node) (M2 tptp.node)) (let ((_let_1 (@ (@ tptp.append_node Ns2) (@ (@ tptp.cons_node M2) tptp.nil_node)))) (let ((_let_2 (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N))) (=> (@ (@ _let_2 Ns) M) (=> (@ (@ tptp.prefix_node _let_1) Ns) (@ (@ _let_2 _let_1) M2)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node tptp.list_node tptp.node Bool))) (let ((_let_1 (@ P N))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ _let_1 (@ (@ tptp.cons_node N) tptp.nil_node)) N)) (=> (forall ((Ns4 tptp.list_node) (M3 tptp.node) (M4 tptp.node)) (let ((_let_1 (@ P N))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns4) M3) (=> (@ (@ _let_1 Ns4) M3) (=> (@ (@ tptp.member_node M3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) M4))) (@ (@ _let_1 (@ (@ tptp.append_node Ns4) (@ (@ tptp.cons_node M4) tptp.nil_node))) M4)))))) (@ (@ _let_1 Ns) M)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (M2 tptp.node)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N))) (=> (@ (@ _let_1 Ns) M) (=> (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) M2))) (@ (@ _let_1 (@ (@ tptp.append_node Ns) (@ (@ tptp.cons_node M2) tptp.nil_node))) M2))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (X tptp.val) (Ys tptp.list_val) (Y tptp.val)) (= (= (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val X) tptp.nil_val)) (@ (@ tptp.append_val Ys) (@ (@ tptp.cons_val Y) tptp.nil_val))) (and (= Xs Ys) (= X Y)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (X tptp.list_node) (Ys tptp.list_list_node) (Y tptp.list_node)) (= (= (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node X) tptp.nil_list_node)) (@ (@ tptp.append_list_node Ys) (@ (@ tptp.cons_list_node Y) tptp.nil_list_node))) (and (= Xs Ys) (= X Y)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (X tptp.node) (Ys tptp.list_node) (Y tptp.node)) (= (= (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node X) tptp.nil_node)) (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node))) (and (= Xs Ys) (= X Y)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (X tptp.val)) (= (@ tptp.butlast_val (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val X) tptp.nil_val))) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (X tptp.list_node)) (= (@ tptp.butlast_list_node (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node X) tptp.nil_list_node))) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (X tptp.node)) (= (@ tptp.butlast_node (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node X) tptp.nil_node))) Xs)))
% 0.24/0.68 (assert (not (forall ((Ms2 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) tptp.m) Ms2) tptp.i) (=> (@ (@ tptp.prefix_node Ms2) tptp.ms) (@ (@ tptp.member_node tptp.i) (@ tptp.set_node2 (@ tptp.butlast_node Ms2))))))))
% 0.24/0.68 (assert (not (forall ((I tptp.node) (Ri tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)) Ri) I) (=> (@ (@ tptp.member_node I) (@ tptp.set_node2 tptp.ms)) (=> (forall ((X2 tptp.node)) (let ((_let_1 (@ tptp.member_node X2))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Ri))) (not (@ _let_1 (@ tptp.set_node2 tptp.ms)))))) (not (@ (@ tptp.prefix_node Ri) tptp.rs2))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (N2 tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_1 N) Ns) M) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N))) (@ (@ (@ _let_1 N2) (@ (@ tptp.cons_node N2) Ns)) M))))))
% 0.24/0.68 (assert (= (@ tptp.butlast_list_node tptp.nil_list_node) tptp.nil_list_node))
% 0.24/0.68 (assert (= (@ tptp.butlast_val tptp.nil_val) tptp.nil_val))
% 0.24/0.68 (assert (= (@ tptp.butlast_node tptp.nil_node) tptp.nil_node))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val Xs))) (@ _let_1 (@ tptp.set_val2 Xs))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Xs))) (@ _let_1 (@ tptp.set_node2 Xs))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val)) (= (@ tptp.butlast_val (@ tptp.tl_val Xs)) (@ tptp.tl_val (@ tptp.butlast_val Xs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (@ tptp.butlast_node (@ tptp.tl_node Xs)) (@ tptp.tl_node (@ tptp.butlast_node Xs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (X tptp.val)) (let ((_let_1 (@ tptp.cons_val X))) (let ((_let_2 (@ tptp.butlast_val (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_val))) (and (=> _let_3 (= _let_2 tptp.nil_val)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_val Xs))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_list_node) (X tptp.list_node)) (let ((_let_1 (@ tptp.cons_list_node X))) (let ((_let_2 (@ tptp.butlast_list_node (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_list_node))) (and (=> _let_3 (= _let_2 tptp.nil_list_node)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_node Xs))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (X tptp.node)) (let ((_let_1 (@ tptp.cons_node X))) (let ((_let_2 (@ tptp.butlast_node (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_node))) (and (=> _let_3 (= _let_2 tptp.nil_node)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_node Xs))))))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_list_node) (Xs tptp.list_list_node)) (let ((_let_1 (@ tptp.append_list_node Xs))) (let ((_let_2 (@ tptp.butlast_list_node (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_list_node))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_list_node Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_node Ys))))))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (let ((_let_2 (@ tptp.butlast_val (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_val))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_val Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_val Ys))))))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (let ((_let_2 (@ tptp.butlast_node (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_node))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_node Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_node Ys))))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val) (Ys tptp.list_val)) (let ((_let_1 (@ tptp.member_val X))) (=> (or (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val Xs))) (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val Ys)))) (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val (@ (@ tptp.append_val Xs) Ys))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (=> (or (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Xs))) (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Ys)))) (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node (@ (@ tptp.append_node Xs) Ys))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_val) (X tptp.val) (Xs tptp.list_val)) (= (= (@ tptp.butlast_val L) (@ (@ tptp.cons_val X) Xs)) (exists ((Xl tptp.val)) (= L (@ (@ tptp.cons_val X) (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val Xl) tptp.nil_val))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_list_node) (X tptp.list_node) (Xs tptp.list_list_node)) (= (= (@ tptp.butlast_list_node L) (@ (@ tptp.cons_list_node X) Xs)) (exists ((Xl tptp.list_node)) (= L (@ (@ tptp.cons_list_node X) (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node Xl) tptp.nil_list_node))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (= (= (@ tptp.butlast_node L) (@ (@ tptp.cons_node X) Xs)) (exists ((Xl tptp.node)) (= L (@ (@ tptp.cons_node X) (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node Xl) tptp.nil_node))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_val) (X tptp.val) (Xs tptp.list_val)) (=> (= (@ tptp.butlast_val L) (@ (@ tptp.cons_val X) Xs)) (not (forall ((Xl2 tptp.val)) (not (= L (@ (@ tptp.cons_val X) (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val Xl2) tptp.nil_val))))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_list_node) (X tptp.list_node) (Xs tptp.list_list_node)) (=> (= (@ tptp.butlast_list_node L) (@ (@ tptp.cons_list_node X) Xs)) (not (forall ((Xl2 tptp.list_node)) (not (= L (@ (@ tptp.cons_list_node X) (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node Xl2) tptp.nil_list_node))))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (=> (= (@ tptp.butlast_node L) (@ (@ tptp.cons_node X) Xs)) (not (forall ((Xl2 tptp.node)) (not (= L (@ (@ tptp.cons_node X) (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node Xl2) tptp.nil_node))))))))))
% 0.24/0.68 (assert (forall ((N1 tptp.val) (R1 tptp.list_val) (N22 tptp.val) (R2 tptp.list_val)) (=> (= (@ (@ tptp.cons_val N1) R1) (@ (@ tptp.cons_val N22) R2)) (and (= N1 N22) (= R1 R2)))))
% 0.24/0.68 (assert (forall ((N1 tptp.list_node) (R1 tptp.list_list_node) (N22 tptp.list_node) (R2 tptp.list_list_node)) (=> (= (@ (@ tptp.cons_list_node N1) R1) (@ (@ tptp.cons_list_node N22) R2)) (and (= N1 N22) (= R1 R2)))))
% 0.24/0.68 (assert (forall ((N1 tptp.node) (R1 tptp.list_node) (N22 tptp.node) (R2 tptp.list_node)) (=> (= (@ (@ tptp.cons_node N1) R1) (@ (@ tptp.cons_node N22) R2)) (and (= N1 N22) (= R1 R2)))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (not (= (@ (@ tptp.cons_val X) Xs) Xs))))
% 0.24/0.68 (assert (forall ((X tptp.list_node) (Xs tptp.list_list_node)) (not (= (@ (@ tptp.cons_list_node X) Xs) Xs))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (not (= (@ (@ tptp.cons_node X) Xs) Xs))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Xs1 tptp.list_val) (Zs tptp.list_val) (Ys tptp.list_val) (Us tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_val Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_val Zs) Us)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Xs1 tptp.list_node) (Zs tptp.list_node) (Ys tptp.list_node) (Us tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_node Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_node Zs) Us)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (Ys tptp.list_val) (Zs tptp.list_val) (Ts tptp.list_val)) (= (= (@ (@ tptp.append_val Xs) Ys) (@ (@ tptp.append_val Zs) Ts)) (exists ((Us2 tptp.list_val)) (let ((_let_1 (@ tptp.append_val Us2))) (or (and (= Xs (@ (@ tptp.append_val Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_val Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node) (Ts tptp.list_node)) (= (= (@ (@ tptp.append_node Xs) Ys) (@ (@ tptp.append_node Zs) Ts)) (exists ((Us2 tptp.list_node)) (let ((_let_1 (@ tptp.append_node Us2))) (or (and (= Xs (@ (@ tptp.append_node Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_node Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_val Bool)) (A0 tptp.list_val)) (=> (@ P tptp.nil_val) (=> (forall ((X4 tptp.val) (Ys2 tptp.list_val)) (=> (@ P Ys2) (@ P (@ (@ tptp.cons_val X4) Ys2)))) (@ P A0)))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (A0 tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node) (Ys2 tptp.list_node)) (=> (@ P Ys2) (@ P (@ (@ tptp.cons_node X4) Ys2)))) (@ P A0)))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_val Bool)) (R (-> tptp.node tptp.val Bool)) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_val)) (=> (forall ((X_1 tptp.list_val)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_val Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_val tptp.list_val Bool)) (R (-> tptp.val tptp.val Bool)) (Xs tptp.list_val) (Ys tptp.list_val)) (=> (forall ((Xs2 tptp.list_val)) (@ (@ P Xs2) tptp.nil_val)) (=> (forall ((X_1 tptp.list_val)) (@ (@ P tptp.nil_val) X_1)) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_val X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ P (@ (@ tptp.cons_val X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_val Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_list_node tptp.list_val Bool)) (R (-> tptp.list_node tptp.val Bool)) (Xs tptp.list_list_node) (Ys tptp.list_val)) (=> (forall ((Xs2 tptp.list_list_node)) (@ (@ P Xs2) tptp.nil_val)) (=> (forall ((X_1 tptp.list_val)) (@ (@ P tptp.nil_list_node) X_1)) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_list_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ P (@ (@ tptp.cons_list_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_val Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_list_node Bool)) (R (-> tptp.node tptp.list_node Bool)) (Xs tptp.list_node) (Ys tptp.list_list_node)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_list_node)) (=> (forall ((X_1 tptp.list_list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_list_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_val tptp.list_list_node Bool)) (R (-> tptp.val tptp.list_node Bool)) (Xs tptp.list_val) (Ys tptp.list_list_node)) (=> (forall ((Xs2 tptp.list_val)) (@ (@ P Xs2) tptp.nil_list_node)) (=> (forall ((X_1 tptp.list_list_node)) (@ (@ P tptp.nil_val) X_1)) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_val X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_val X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_list_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_list_node tptp.list_list_node Bool)) (R (-> tptp.list_node tptp.list_node Bool)) (Xs tptp.list_list_node) (Ys tptp.list_list_node)) (=> (forall ((Xs2 tptp.list_list_node)) (@ (@ P Xs2) tptp.nil_list_node)) (=> (forall ((X_1 tptp.list_list_node)) (@ (@ P tptp.nil_list_node) X_1)) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_list_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_list_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_list_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (R (-> tptp.node tptp.node Bool)) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_node)) (=> (forall ((X_1 tptp.list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((P (-> (-> tptp.node tptp.node Bool) tptp.list_node tptp.list_node Bool)) (A0 (-> tptp.node tptp.node Bool)) (A1 tptp.list_node) (A22 tptp.list_node)) (=> (forall ((R3 (-> tptp.node tptp.node Bool)) (X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Ys2))) (let ((_let_2 (@ P R3))) (let ((_let_3 (@ _let_2 (@ (@ tptp.cons_node X4) Xs2)))) (let ((_let_4 (@ (@ R3 X4) Y2))) (=> (=> _let_4 (@ (@ _let_2 Xs2) _let_1)) (=> (=> (not _let_4) (@ _let_3 Ys2)) (@ _let_3 _let_1)))))))) (=> (forall ((R3 (-> tptp.node tptp.node Bool)) (Xs2 tptp.list_node)) (@ (@ (@ P R3) Xs2) tptp.nil_node)) (=> (forall ((R3 (-> tptp.node tptp.node Bool)) (V tptp.node) (Va tptp.list_node)) (@ (@ (@ P R3) tptp.nil_node) (@ (@ tptp.cons_node V) Va))) (@ (@ (@ P A0) A1) A22))))))
% 0.24/0.68 (assert (forall ((P (-> (-> tptp.node tptp.node) tptp.list_node tptp.list_node Bool)) (A0 (-> tptp.node tptp.node)) (A1 tptp.list_node) (A22 tptp.list_node)) (=> (forall ((F (-> tptp.node tptp.node)) (X_1 tptp.list_node)) (@ (@ (@ P F) tptp.nil_node) X_1)) (=> (forall ((F (-> tptp.node tptp.node)) (A3 tptp.node) (As tptp.list_node) (Bs tptp.list_node)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_node (@ F A3)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_node A3) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.list_node Bool))) (=> (not (= Xs tptp.nil_node)) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (not (= Xs2 tptp.nil_node)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_node X4) Xs2))))) (@ P Xs))))))
% 0.24/0.68 (assert (forall ((P (-> (-> tptp.node tptp.node Bool) tptp.list_node tptp.list_node Bool)) (A0 (-> tptp.node tptp.node Bool)) (A1 tptp.list_node) (A22 tptp.list_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool))) (@ (@ (@ P P2) tptp.nil_node) tptp.nil_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool)) (A3 tptp.node) (As tptp.list_node) (B2 tptp.node) (Bs tptp.list_node)) (let ((_let_1 (@ P P2))) (=> (@ (@ _let_1 As) Bs) (@ (@ _let_1 (@ (@ tptp.cons_node A3) As)) (@ (@ tptp.cons_node B2) Bs))))) (=> (forall ((P2 (-> tptp.node tptp.node Bool)) (V tptp.node) (Va tptp.list_node)) (@ (@ (@ P P2) (@ (@ tptp.cons_node V) Va)) tptp.nil_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool)) (V tptp.node) (Va tptp.list_node)) (@ (@ (@ P P2) tptp.nil_node) (@ (@ tptp.cons_node V) Va))) (@ (@ (@ P A0) A1) A22)))))))
% 0.24/0.68 (assert (forall ((P (-> (-> tptp.node tptp.node Bool) tptp.list_node Bool)) (A0 (-> tptp.node tptp.node Bool)) (A1 tptp.list_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool))) (@ (@ P P2) tptp.nil_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool)) (X4 tptp.node)) (@ (@ P P2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((P2 (-> tptp.node tptp.node Bool)) (X4 tptp.node) (Y2 tptp.node) (Xs2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_node X4) _let_1)))))) (@ (@ P A0) A1))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (Xs tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X1 tptp.node) (X23 tptp.node) (Xs2 tptp.list_node)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_node X1) (@ (@ tptp.cons_node X23) Xs2))))) (@ P Xs))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (A0 tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Y2 tptp.node) (Xs2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Xs2))) (let ((_let_2 (@ tptp.cons_node X4))) (let ((_let_3 (= X4 Y2))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.24/0.68 (assert (forall ((P (-> (-> tptp.node tptp.node Bool) tptp.list_node Bool)) (A0 (-> tptp.node tptp.node Bool)) (A1 tptp.list_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool))) (@ (@ P P2) tptp.nil_node)) (=> (forall ((P2 (-> tptp.node tptp.node Bool)) (X4 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_node X4) Ys2))))) (@ (@ P A0) A1)))))
% 0.24/0.68 (assert (forall ((X tptp.list_node)) (=> (not (= X tptp.nil_node)) (=> (forall ((X4 tptp.node)) (not (= X (@ (@ tptp.cons_node X4) tptp.nil_node)))) (not (forall ((X4 tptp.node) (Y2 tptp.node) (Xs2 tptp.list_node)) (not (= X (@ (@ tptp.cons_node X4) (@ (@ tptp.cons_node Y2) Xs2))))))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (W1 tptp.list_node) (W2 tptp.list_node)) (=> (@ (@ P tptp.nil_node) tptp.nil_node) (=> (forall ((E3 tptp.node) (W12 tptp.list_node) (W22 tptp.list_node)) (=> (@ (@ P W12) W22) (@ (@ P (@ (@ tptp.cons_node E3) W12)) W22))) (=> (forall ((E3 tptp.node) (W13 tptp.list_node) (W23 tptp.list_node)) (let ((_let_1 (@ P W13))) (=> (@ _let_1 W23) (@ _let_1 (@ (@ tptp.cons_node E3) W23))))) (@ (@ P W1) W2))))))
% 0.24/0.68 (assert (forall ((X tptp.list_list_node)) (=> (not (= X tptp.nil_list_node)) (=> (forall ((Xss tptp.list_list_node)) (not (= X (@ (@ tptp.cons_list_node tptp.nil_node) Xss)))) (not (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Xss tptp.list_list_node)) (not (= X (@ (@ tptp.cons_list_node (@ (@ tptp.cons_node X4) Xs2)) Xss)))))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (A0 tptp.list_node) (A1 tptp.list_node)) (=> (forall ((X_1 tptp.list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_node)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (A0 tptp.list_node)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (forall ((X212 tptp.node) (X222 tptp.list_node)) (=> (= Xs2 (@ (@ tptp.cons_node X212) X222)) (@ P Xs2))) (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (@ P tptp.nil_node) (@ P A0)))))
% 0.24/0.68 (assert (forall ((X tptp.list_node)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (not (= X (@ (@ tptp.cons_node X4) Xs2)))) (= X tptp.nil_node))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (Xs tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Y2 tptp.node) (Zs2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Zs2))) (=> (@ P Zs2) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_node X4) _let_1)))))) (@ P Xs))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (A0 tptp.list_node) (A1 tptp.list_node)) (=> (forall ((X_1 tptp.list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Ys2 tptp.list_node)) (=> (@ (@ P Ys2) Xs2) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) Ys2))) (@ (@ P A0) A1)))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ P tptp.nil_node) tptp.nil_node) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) tptp.nil_node)) (=> (forall ((Y2 tptp.node) (Ys2 tptp.list_node)) (@ (@ P tptp.nil_node) (@ (@ tptp.cons_node Y2) Ys2))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) (@ (@ tptp.cons_node Y2) Ys2)))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (not (= Xs tptp.nil_node)) (exists ((Y3 tptp.node) (Ys3 tptp.list_node)) (= Xs (@ (@ tptp.cons_node Y3) Ys3))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (List tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X1 tptp.node) (X23 tptp.list_node)) (=> (@ P X23) (@ P (@ (@ tptp.cons_node X1) X23)))) (@ P List)))))
% 0.24/0.68 (assert (forall ((Y tptp.list_node)) (=> (not (= Y tptp.nil_node)) (not (forall ((X213 tptp.node) (X223 tptp.list_node)) (not (= Y (@ (@ tptp.cons_node X213) X223))))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (A0 tptp.list_node) (A1 tptp.list_node)) (=> (forall ((X_1 tptp.list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((A3 tptp.node) (As tptp.list_node) (B2 tptp.list_node)) (let ((_let_1 (@ tptp.cons_node A3))) (=> (@ (@ P As) (@ _let_1 B2)) (@ (@ P (@ _let_1 As)) B2)))) (@ (@ P A0) A1)))))
% 0.24/0.68 (assert (forall ((List tptp.list_node) (X21 tptp.node) (X22 tptp.list_node)) (=> (= List (@ (@ tptp.cons_node X21) X22)) (not (= List tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((L tptp.list_node)) (=> (not (= L tptp.nil_node)) (not (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (not (= L (@ (@ tptp.cons_node X4) Xs2))))))))
% 0.24/0.68 (assert (forall ((X21 tptp.node) (X22 tptp.list_node)) (not (= tptp.nil_node (@ (@ tptp.cons_node X21) X22)))))
% 0.24/0.68 (assert (forall ((E2 tptp.val) (A tptp.list_val)) (=> (@ (@ tptp.member_val E2) (@ tptp.set_val2 A)) (=> (forall ((Z2 tptp.list_val)) (not (= A (@ (@ tptp.cons_val E2) Z2)))) (not (forall ((Z1 tptp.val) (Z2 tptp.list_val)) (=> (= A (@ (@ tptp.cons_val Z1) Z2)) (not (@ (@ tptp.member_val E2) (@ tptp.set_val2 Z2))))))))))
% 0.24/0.68 (assert (forall ((E2 tptp.node) (A tptp.list_node)) (=> (@ (@ tptp.member_node E2) (@ tptp.set_node2 A)) (=> (forall ((Z2 tptp.list_node)) (not (= A (@ (@ tptp.cons_node E2) Z2)))) (not (forall ((Z1 tptp.node) (Z2 tptp.list_node)) (=> (= A (@ (@ tptp.cons_node Z1) Z2)) (not (@ (@ tptp.member_node E2) (@ tptp.set_node2 Z2))))))))))
% 0.24/0.68 (assert (forall ((Y tptp.val) (X tptp.val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.member_val Y))) (=> (@ _let_1 (@ tptp.set_val2 (@ (@ tptp.cons_val X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_val2 Xs)))))))
% 0.24/0.68 (assert (forall ((Y tptp.node) (X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.member_node Y))) (=> (@ _let_1 (@ tptp.set_node2 (@ (@ tptp.cons_node X) Xs))) (or (= Y X) (@ _let_1 (@ tptp.set_node2 Xs)))))))
% 0.24/0.68 (assert (forall ((X21 tptp.val) (X22 tptp.list_val)) (@ (@ tptp.member_val X21) (@ tptp.set_val2 (@ (@ tptp.cons_val X21) X22)))))
% 0.24/0.68 (assert (forall ((X21 tptp.node) (X22 tptp.list_node)) (@ (@ tptp.member_node X21) (@ tptp.set_node2 (@ (@ tptp.cons_node X21) X22)))))
% 0.24/0.68 (assert (forall ((Y tptp.val) (X22 tptp.list_val) (X21 tptp.val)) (let ((_let_1 (@ tptp.member_val Y))) (=> (@ _let_1 (@ tptp.set_val2 X22)) (@ _let_1 (@ tptp.set_val2 (@ (@ tptp.cons_val X21) X22)))))))
% 0.24/0.68 (assert (forall ((Y tptp.node) (X22 tptp.list_node) (X21 tptp.node)) (let ((_let_1 (@ tptp.member_node Y))) (=> (@ _let_1 (@ tptp.set_node2 X22)) (@ _let_1 (@ tptp.set_node2 (@ (@ tptp.cons_node X21) X22)))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs1 tptp.list_node) (Ys tptp.list_node) (Xs tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.cons_node X))) (=> (= (@ _let_1 Xs1) Ys) (=> (= Xs (@ (@ tptp.append_node Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_node Ys) Zs)))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.cons_node X))) (= (@ (@ tptp.append_node (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_node Xs) Ys))))))
% 0.24/0.68 (assert (forall ((C1 tptp.list_node) (Qs tptp.node) (C2 tptp.list_node) (C12 tptp.list_node) (Qs2 tptp.node) (C22 tptp.list_node)) (=> (= (@ (@ tptp.append_node C1) (@ (@ tptp.cons_node Qs) C2)) (@ (@ tptp.append_node C12) (@ (@ tptp.cons_node Qs2) C22))) (=> (forall ((C21 tptp.list_node)) (=> (= C1 (@ (@ tptp.append_node C12) (@ (@ tptp.cons_node Qs2) C21))) (not (= C22 (@ (@ tptp.append_node C21) (@ (@ tptp.cons_node Qs) C2)))))) (=> (=> (= C12 C1) (=> (= Qs2 Qs) (not (= C22 C2)))) (not (forall ((C212 tptp.list_node)) (=> (= C12 (@ (@ tptp.append_node C1) (@ (@ tptp.cons_node Qs) C212))) (not (= C2 (@ (@ tptp.append_node C212) (@ (@ tptp.cons_node Qs2) C22))))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_node tptp.nil_node) Ys)))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node)) (= (@ (@ tptp.append_node tptp.nil_node) Ys) Ys)))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (= (@ (@ tptp.append_node tptp.nil_node) A) A)))
% 0.24/0.68 (assert (forall ((X21 tptp.node) (X22 tptp.list_node)) (= (@ tptp.tl_node (@ (@ tptp.cons_node X21) X22)) X22)))
% 0.24/0.68 (assert (= (@ tptp.tl_node tptp.nil_node) tptp.nil_node))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Zs tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (=> (= (@ (@ tptp.append_node Ys) Zs) _let_1) (=> (=> (= Ys tptp.nil_node) (not (= Zs _let_1))) (not (forall ((Ys4 tptp.list_node)) (=> (= Ys (@ (@ tptp.cons_node X) Ys4)) (not (= (@ (@ tptp.append_node Ys4) Zs) Xs))))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (=> (= _let_1 (@ (@ tptp.append_node Ys) Zs)) (=> (=> (= Ys tptp.nil_node) (not (= Zs _let_1))) (not (forall ((Ys4 tptp.list_node)) (=> (= Ys (@ (@ tptp.cons_node X) Ys4)) (not (= (@ (@ tptp.append_node Ys4) Zs) Xs))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (P (-> tptp.list_node tptp.list_node Bool))) (=> (not (= Xs tptp.nil_node)) (=> (not (= Ys tptp.nil_node)) (=> (forall ((X4 tptp.node) (Y2 tptp.node)) (@ (@ P (@ (@ tptp.cons_node X4) tptp.nil_node)) (@ (@ tptp.cons_node Y2) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node)) (=> (not (= Xs2 tptp.nil_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.cons_node Y2) tptp.nil_node)))) (=> (forall ((X4 tptp.node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (not (= Ys2 tptp.nil_node)) (@ (@ P (@ (@ tptp.cons_node X4) tptp.nil_node)) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (@ (@ P Xs2) Ys2) (=> (not (= Xs2 tptp.nil_node)) (=> (not (= Ys2 tptp.nil_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))))) (@ (@ P Xs) Ys)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.list_node Bool))) (=> (not (= Xs tptp.nil_node)) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (not (= Xs2 tptp.nil_node)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node)))))) (@ P Xs))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Zs tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (= (= (@ (@ tptp.append_node Ys) Zs) _let_1) (or (and (= Ys tptp.nil_node) (= Zs _let_1)) (exists ((Ys5 tptp.list_node)) (and (= Ys (@ (@ tptp.cons_node X) Ys5)) (= (@ (@ tptp.append_node Ys5) Zs) Xs))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (= (= _let_1 (@ (@ tptp.append_node Ys) Zs)) (or (and (= Ys tptp.nil_node) (= _let_1 Zs)) (exists ((Ys5 tptp.list_node)) (and (= (@ (@ tptp.cons_node X) Ys5) Ys) (= Xs (@ (@ tptp.append_node Ys5) Zs)))))))))
% 0.24/0.68 (assert (forall ((L tptp.list_node)) (= (not (= L tptp.nil_node)) (exists ((Xs3 tptp.list_node) (X3 tptp.node)) (= L (@ (@ tptp.append_node Xs3) (@ (@ tptp.cons_node X3) tptp.nil_node)))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node tptp.list_node Bool)) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ P tptp.nil_node) tptp.nil_node) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) tptp.nil_node)) (=> (forall ((Y2 tptp.node) (Ys2 tptp.list_node)) (@ (@ P tptp.nil_node) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node)))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))) (@ (@ P Xs) Ys)))))))
% 0.24/0.68 (assert (forall ((L tptp.list_node)) (=> (not (= L tptp.nil_node)) (not (forall ((Ll tptp.list_node) (E3 tptp.node)) (not (= L (@ (@ tptp.append_node Ll) (@ (@ tptp.cons_node E3) tptp.nil_node)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (not (forall ((Ys2 tptp.list_node) (Y2 tptp.node)) (not (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node)))))))))
% 0.24/0.68 (assert (forall ((P (-> tptp.list_node Bool)) (Xs tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))))) (@ P Xs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (= (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 Xs)) (@ P X3))) (exists ((Ys3 tptp.list_node) (X3 tptp.node)) (and (exists ((Zs3 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X3) Zs3)))) (@ P X3) (forall ((Y3 tptp.node)) (=> (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys3)) (not (@ P Y3)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (= (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 Xs)) (@ P X3))) (exists ((Ys3 tptp.list_node) (X3 tptp.node) (Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X3) Zs3))) (@ P X3) (forall ((Y3 tptp.node)) (=> (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Zs3)) (not (@ P Y3)))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys3 tptp.list_val) (Zs3 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys3) (@ (@ tptp.cons_val X) Zs3))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Ys3))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys3 tptp.list_node) (Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X) Zs3))) (not (@ (@ tptp.member_node X) (@ tptp.set_node2 Ys3))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys3 tptp.list_val) (Zs3 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys3) (@ (@ tptp.cons_val X) Zs3))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Zs3))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys3 tptp.list_node) (Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X) Zs3))) (not (@ (@ tptp.member_node X) (@ tptp.set_node2 Zs3))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (not (forall ((Ys2 tptp.list_node) (X4 tptp.node)) (=> (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (=> (@ P X4) (not (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Ys2)) (not (@ P Xa))))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (not (forall ((Ys2 tptp.list_node) (X4 tptp.node) (Zs2 tptp.list_node)) (=> (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2))) (=> (@ P X4) (not (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Zs2)) (not (@ P Xa))))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (exists ((Ys2 tptp.list_node) (X4 tptp.node)) (and (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (@ P X4) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Ys2)) (not (@ P Xa)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (exists ((Ys2 tptp.list_node) (X4 tptp.node) (Zs2 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2))) (@ P X4) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Zs2)) (not (@ P Xa)))))))))
% 0.24/0.68 (assert (forall ((E2 tptp.val) (L tptp.list_val)) (=> (@ (@ tptp.member_val E2) (@ tptp.set_val2 L)) (not (forall ((L12 tptp.list_val) (L22 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val E2) L22)))))))))
% 0.24/0.68 (assert (forall ((E2 tptp.node) (L tptp.list_node)) (=> (@ (@ tptp.member_node E2) (@ tptp.set_node2 L)) (not (forall ((L12 tptp.list_node) (L22 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node E2) L22)))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys3 tptp.list_val) (Zs3 tptp.list_val)) (= Xs (@ (@ tptp.append_val Ys3) (@ (@ tptp.cons_val X) Zs3)))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys3 tptp.list_node) (Zs3 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X) Zs3)))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val) (Ys tptp.list_val) (Xs4 tptp.list_val) (Ys6 tptp.list_val)) (let ((_let_1 (@ tptp.cons_val X))) (let ((_let_2 (@ tptp.member_val X))) (=> (not (@ _let_2 (@ tptp.set_val2 Xs))) (=> (not (@ _let_2 (@ tptp.set_val2 Ys))) (= (= (@ (@ tptp.append_val Xs) (@ _let_1 Ys)) (@ (@ tptp.append_val Xs4) (@ _let_1 Ys6))) (and (= Xs Xs4) (= Ys Ys6)))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Xs4 tptp.list_node) (Ys6 tptp.list_node)) (let ((_let_1 (@ tptp.cons_node X))) (let ((_let_2 (@ tptp.member_node X))) (=> (not (@ _let_2 (@ tptp.set_node2 Xs))) (=> (not (@ _let_2 (@ tptp.set_node2 Ys))) (= (= (@ (@ tptp.append_node Xs) (@ _let_1 Ys)) (@ (@ tptp.append_node Xs4) (@ _let_1 Ys6))) (and (= Xs Xs4) (= Ys Ys6)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (not (forall ((Ys2 tptp.list_node) (X4 tptp.node)) (=> (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (not (@ P X4))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (=> (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys2 tptp.list_val) (Zs2 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys2) (@ (@ tptp.cons_val X) Zs2))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Ys2))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys2 tptp.list_node) (Zs2 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X) Zs2))) (not (@ (@ tptp.member_node X) (@ tptp.set_node2 Ys2))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (L tptp.list_val) (Y tptp.val)) (let ((_let_1 (= X Y))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.set_val2 L))) (=> (@ (@ tptp.member_val X) _let_3) (=> (@ (@ tptp.member_val Y) _let_3) (=> (=> _let_1 (forall ((L12 tptp.list_val) (L22 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val Y) L22)))))) (=> (=> _let_2 (forall ((L12 tptp.list_val) (L22 tptp.list_val) (L3 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val X) (@ (@ tptp.append_val L22) (@ (@ tptp.cons_val Y) L3)))))))) (not (=> _let_2 (forall ((L12 tptp.list_val) (L22 tptp.list_val) (L3 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val Y) (@ (@ tptp.append_val L22) (@ (@ tptp.cons_val X) L3))))))))))))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (L tptp.list_node) (Y tptp.node)) (let ((_let_1 (= X Y))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.set_node2 L))) (=> (@ (@ tptp.member_node X) _let_3) (=> (@ (@ tptp.member_node Y) _let_3) (=> (=> _let_1 (forall ((L12 tptp.list_node) (L22 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node Y) L22)))))) (=> (=> _let_2 (forall ((L12 tptp.list_node) (L22 tptp.list_node) (L3 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node X) (@ (@ tptp.append_node L22) (@ (@ tptp.cons_node Y) L3)))))))) (not (=> _let_2 (forall ((L12 tptp.list_node) (L22 tptp.list_node) (L3 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node Y) (@ (@ tptp.append_node L22) (@ (@ tptp.cons_node X) L3))))))))))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (exists ((Ys2 tptp.list_node) (X4 tptp.node)) (and (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (@ P X4))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (=> (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys2 tptp.list_val) (Zs2 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys2) (@ (@ tptp.cons_val X) Zs2))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Zs2))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys2 tptp.list_node) (Zs2 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X) Zs2))) (not (@ (@ tptp.member_node X) (@ tptp.set_node2 Zs2))))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (=> (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys2 tptp.list_val) (Zs2 tptp.list_val)) (= Xs (@ (@ tptp.append_val Ys2) (@ (@ tptp.cons_val X) Zs2)))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys2 tptp.list_node) (Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X) Zs2)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (=> (= (@ tptp.tl_node Xs) tptp.nil_node) (not (forall ((E3 tptp.node)) (not (= Xs (@ (@ tptp.cons_node E3) tptp.nil_node)))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (= (@ tptp.tl_node Xs) tptp.nil_node) (or (= Xs tptp.nil_node) (exists ((X3 tptp.node)) (= Xs (@ (@ tptp.cons_node X3) tptp.nil_node)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (= tptp.nil_node (@ tptp.tl_node Xs)) (or (= Xs tptp.nil_node) (exists ((X3 tptp.node)) (= Xs (@ (@ tptp.cons_node X3) tptp.nil_node)))))))
% 0.24/0.68 (assert (forall ((A tptp.list_val) (X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (not (= A tptp.nil_val)) (=> (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val A))) (@ _let_1 (@ tptp.set_val2 A)))))))
% 0.24/0.68 (assert (forall ((A tptp.list_node) (X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (not (= A tptp.nil_node)) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node A))) (@ _let_1 (@ tptp.set_node2 A)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (let ((_let_1 (@ tptp.prefix_node Xs))) (let ((_let_2 (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node)))) (= (@ _let_1 _let_2) (or (= Xs _let_2) (@ _let_1 Ys)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (X tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Ns)) (not (forall ((Ns_1 tptp.list_node) (Ns_3 tptp.list_node) (Ns_2 tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (let ((_let_2 (@ tptp.cons_node X))) (let ((_let_3 (@ _let_2 Ns_2))) (let ((_let_4 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_5 (@ _let_4 X))) (let ((_let_6 (@ tptp.append_node Ns_1))) (let ((_let_7 (@ _let_6 (@ _let_2 tptp.nil_node)))) (=> (= Ns (@ _let_6 (@ (@ tptp.append_node Ns_3) Ns_2))) (=> (@ (@ tptp.prefix_node _let_7) Ns) (=> (@ (@ tptp.suffix_node _let_3) Ns) (=> (@ (@ (@ _let_4 N) _let_7) X) (=> (not (@ _let_1 (@ tptp.set_node2 Ns_1))) (=> (@ (@ _let_5 Ns_3) X) (=> (@ (@ _let_5 _let_3) M) (@ _let_1 (@ tptp.set_node2 Ns_2))))))))))))))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (@ (@ tptp.prefix_node (@ (@ tptp.append_node Xs) Ys)) Xs) (= Ys tptp.nil_node))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (N2 tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) N) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 Ns)) (not (forall ((Ns3 tptp.list_node)) (let ((_let_1 (@ tptp.set_node2 Ns3))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns3) N) (=> (@ (@ tptp.member_node N2) _let_1) (=> (not (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.tl_node (@ tptp.butlast_node Ns3))))) (not (@ (@ tptp.ord_less_eq_set_node _let_1) (@ tptp.set_node2 Ns)))))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (let ((_let_1 (@ tptp.tl_node Ns))) (let ((_let_2 (@ tptp.hd_node _let_1))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_3 N) Ns) M) (=> (=> (= Ns (@ (@ tptp.cons_node N) tptp.nil_node)) (not (= M N))) (not (=> (@ (@ (@ _let_3 _let_2) _let_1) M) (not (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) _let_2)))))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node) (N tptp.node) (M tptp.node)) (let ((_let_1 (@ tptp.cons_node N))) (let ((_let_2 (@ tptp.append_node Ns))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_node))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) M))) (@ _let_3 (@ _let_2 (@ _let_1 (@ (@ tptp.cons_node M) tptp.nil_node)))))))))))
% 0.24/0.68 (assert (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node Bool))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Ns)) (@ P X2))) (not (forall ((N3 tptp.node) (Ns3 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N3) Ns3) M) (=> (@ P N3) (=> (forall ((X2 tptp.node)) (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 (@ tptp.tl_node Ns3))) (not (@ P X2)))) (not (@ (@ tptp.suffix_node Ns3) Ns)))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ tptp.defs G) N))))
% 0.24/0.68 (assert (forall ((X tptp.list_node)) (@ (@ tptp.prefix_node X) X)))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (@ (@ tptp.prefix_node A) A)))
% 0.24/0.68 (assert (forall ((X tptp.list_node)) (@ (@ tptp.suffix_node X) X)))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (@ (@ tptp.suffix_node A) A)))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns) (not (= Ns tptp.nil_node)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (= N (@ tptp.hd_node Ns)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_1 N) Ns) M) (@ (@ (@ _let_1 (@ tptp.hd_node Ns)) Ns) M)))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node)) (let ((_let_1 (@ tptp.cons_node N))) (let ((_let_2 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_2 (@ _let_1 Ns)) (@ _let_2 (@ _let_1 tptp.nil_node)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node) (M tptp.node) (Ns2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node M) Ns2))) (let ((_let_2 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_2 (@ (@ tptp.append_node Ns) _let_1)) (@ _let_2 _let_1))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (@ tptp.finite_finite_node (@ tptp.set_node2 Xs))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val)) (@ tptp.finite_finite_val (@ tptp.set_val2 Xs))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Y tptp.node) (Ys tptp.list_node)) (= (@ (@ tptp.prefix_node (@ (@ tptp.cons_node X) Xs)) (@ (@ tptp.cons_node Y) Ys)) (and (= X Y) (@ (@ tptp.prefix_node Xs) Ys)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (@ (@ tptp.prefix_node tptp.nil_node) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (@ (@ tptp.prefix_node Xs) tptp.nil_node) (= Xs tptp.nil_node))))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (= (@ (@ tptp.prefix_node A) tptp.nil_node) (= A tptp.nil_node))))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (= (@ (@ tptp.suffix_node A) tptp.nil_node) (= A tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (= (@ (@ tptp.suffix_node Xs) tptp.nil_node) (= Xs tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (= (@ (@ tptp.prefix_node (@ _let_1 Ys)) (@ _let_1 Zs)) (@ (@ tptp.prefix_node Ys) Zs)))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Xs tptp.list_node) (Zs tptp.list_node)) (= (@ (@ tptp.suffix_node (@ (@ tptp.append_node Ys) Xs)) (@ (@ tptp.append_node Zs) Xs)) (@ (@ tptp.suffix_node Ys) Zs))))
% 0.24/0.68 (assert (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ tptp.invar G) (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) (@ (@ tptp.cons_node N) tptp.nil_node))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node) (M tptp.node) (Ns2 tptp.list_node)) (let ((_let_1 (@ tptp.cons_node M))) (let ((_let_2 (@ tptp.append_node Ns))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_3 (@ _let_2 (@ _let_1 Ns2))) (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_node)))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node) (N2 tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_1 Ns) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns)))) (@ _let_1 (@ (@ tptp.cons_node N2) Ns)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (A tptp.list_node)) (= (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) A) (or (exists ((N5 tptp.node)) (and (= A (@ (@ tptp.cons_node N5) tptp.nil_node)) (@ (@ tptp.member_node N5) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.invar G))) (exists ((Ns5 tptp.list_node) (N6 tptp.node)) (and (= A (@ (@ tptp.cons_node N6) Ns5)) (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns5) (@ (@ tptp.member_node N6) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns5))))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (X tptp.list_node) (P (-> tptp.list_node Bool))) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) X) (=> (forall ((N4 tptp.node)) (=> (@ (@ tptp.member_node N4) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ tptp.invar G) (@ P (@ (@ tptp.cons_node N4) tptp.nil_node))))) (=> (forall ((Ns4 tptp.list_node) (N3 tptp.node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns4) (=> (@ P Ns4) (=> (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns4)))) (@ P (@ (@ tptp.cons_node N3) Ns4)))))) (@ P X))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (A tptp.list_node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) A) (=> (forall ((N4 tptp.node)) (=> (= A (@ (@ tptp.cons_node N4) tptp.nil_node)) (=> (@ (@ tptp.member_node N4) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (@ tptp.invar G))))) (not (forall ((Ns4 tptp.list_node) (N3 tptp.node)) (=> (= A (@ (@ tptp.cons_node N3) Ns4)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns4) (not (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns4)))))))))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Xs tptp.list_node)) (= (@ (@ tptp.suffix_node (@ (@ tptp.append_node Ys) Xs)) Xs) (= Ys tptp.nil_node))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (= (@ tptp.hd_node (@ (@ tptp.append_node Xs) Ys)) (@ tptp.hd_node Xs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (= (@ (@ tptp.suffix_node Xs) (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node))) (or (= Xs tptp.nil_node) (exists ((Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Zs3) (@ (@ tptp.cons_node Y) tptp.nil_node))) (@ (@ tptp.suffix_node Zs3) Ys)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (X tptp.node) (Ys tptp.list_node) (Y tptp.node)) (= (@ (@ tptp.suffix_node (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node X) tptp.nil_node))) (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node))) (and (= X Y) (@ (@ tptp.suffix_node Xs) Ys)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (= (@ (@ tptp.cons_node (@ tptp.hd_node Xs)) (@ tptp.tl_node Xs)) Xs))))
% 0.24/0.68 (assert (forall ((List tptp.list_node)) (=> (not (= List tptp.nil_node)) (= (@ (@ tptp.cons_node (@ tptp.hd_node List)) (@ tptp.tl_node List)) List))))
% 0.24/0.68 (assert (forall ((L tptp.list_val) (X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (not (= L tptp.nil_val)) (= (or (= X (@ tptp.hd_val L)) (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val L)))) (@ _let_1 (@ tptp.set_val2 L)))))))
% 0.24/0.68 (assert (forall ((L tptp.list_node) (X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (not (= L tptp.nil_node)) (= (or (= X (@ tptp.hd_node L)) (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node L)))) (@ _let_1 (@ tptp.set_node2 L)))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns) (@ tptp.invar G))))
% 0.24/0.68 (assert (forall ((G tptp.g) (Ns tptp.list_node) (N tptp.node)) (let ((_let_1 (@ tptp.member_node N))) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns) (=> (@ _let_1 (@ tptp.set_node2 Ns)) (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))))))))
% 0.24/0.68 (assert (forall ((G tptp.g) (N tptp.node) (N2 tptp.node) (Ns tptp.list_node) (Ms tptp.list_node)) (let ((_let_1 (@ tptp.cons_node N2))) (let ((_let_2 (@ _let_1 Ms))) (let ((_let_3 (@ tptp.cons_node N))) (let ((_let_4 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_5 (@ _let_1 Ns))) (=> (@ _let_4 (@ _let_3 _let_5)) (=> (=> (@ _let_4 _let_5) (@ _let_4 _let_2)) (@ _let_4 (@ _let_3 _let_2)))))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node Xs) Ys) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) (@ tptp.set_node2 Ys)))))
% 0.24/0.68 (assert (forall ((S tptp.set_node) (P (-> tptp.node Bool))) (= (@ (@ tptp.ord_less_eq_set_node S) (@ tptp.collect_node P)) (forall ((X3 tptp.node)) (=> (@ (@ tptp.member_node X3) S) (@ P X3))))))
% 0.24/0.68 (assert (forall ((A tptp.set_node) (B tptp.set_node) (C tptp.set_node) (D tptp.set_node)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_node B) C) (=> (= C D) (@ (@ tptp.ord_less_eq_set_node A) D))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Y tptp.node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node (@ (@ tptp.cons_node X) Xs)) (@ (@ tptp.cons_node Y) Ys)) (@ (@ tptp.suffix_node Xs) Ys))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_node Y) Ys))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node (@ (@ tptp.cons_node X) Xs)) Ys) (@ (@ tptp.suffix_node Xs) Ys))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Y tptp.node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (let ((_let_2 (@ (@ tptp.cons_node Y) Ys))) (= (@ _let_1 _let_2) (or (= Xs _let_2) (@ _let_1 Ys)))))))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (=> (@ (@ tptp.suffix_node A) tptp.nil_node) (= A tptp.nil_node))))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (@ (@ tptp.suffix_node tptp.nil_node) A)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (@ (@ tptp.suffix_node tptp.nil_node) Xs)))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node Xs) Ys) (not (forall ((Zs2 tptp.list_node)) (not (= Ys (@ (@ tptp.append_node Zs2) Xs))))))))
% 0.24/0.68 (assert (forall ((Ys tptp.list_node) (Zs tptp.list_node) (Xs tptp.list_node)) (=> (= Ys (@ (@ tptp.append_node Zs) Xs)) (@ (@ tptp.suffix_node Xs) Ys))))
% 0.24/0.68 (assert (= tptp.suffix_node (lambda ((Xs3 tptp.list_node) (Ys3 tptp.list_node)) (exists ((Zs3 tptp.list_node)) (= Ys3 (@ (@ tptp.append_node Zs3) Xs3))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (= (@ _let_1 (@ (@ tptp.append_node Ys) Zs)) (or (@ _let_1 Zs) (exists ((Xs5 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Xs5) Zs)) (@ (@ tptp.suffix_node Xs5) Ys))))))))
% 0.24/0.68 (assert (forall ((Zs tptp.list_node) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node (@ (@ tptp.append_node Zs) Xs)) Ys) (@ (@ tptp.suffix_node Xs) Ys))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.append_node Zs) Ys))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (@ (@ tptp.suffix_node (@ tptp.tl_node Xs)) Xs)))
% 0.24/0.68 (assert (forall ((Xs_1 tptp.list_node) (Ys tptp.list_node) (Xs_2 tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs_2))) (let ((_let_2 (@ tptp.suffix_node Xs_1))) (=> (@ _let_2 Ys) (=> (@ _let_1 Ys) (or (@ _let_2 Xs_2) (@ _let_1 Xs_1))))))))
% 0.24/0.68 (assert (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((X3 tptp.list_node) (Y3 tptp.list_node)) (and (@ (@ tptp.suffix_node X3) Y3) (@ (@ tptp.suffix_node Y3) X3)))))
% 0.24/0.68 (assert (forall ((X tptp.list_node) (Y tptp.list_node)) (=> (@ (@ tptp.suffix_node X) Y) (=> (@ (@ tptp.suffix_node Y) X) (= X Y)))))
% 0.24/0.68 (assert (forall ((X tptp.list_node) (Y tptp.list_node)) (=> (= X Y) (@ (@ tptp.suffix_node X) Y))))
% 0.24/0.68 (assert (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node A))) (=> (@ _let_1 B) (=> (@ (@ tptp.suffix_node B) C) (@ _let_1 C))))))
% 0.24/0.68 (assert (forall ((X tptp.list_node) (Y tptp.list_node) (Z3 tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.suffix_node Y) Z3) (@ _let_1 Z3))))))
% 0.24/0.68 (assert (forall ((Y tptp.list_node) (X tptp.list_node)) (=> (@ (@ tptp.suffix_node Y) X) (= (@ (@ tptp.suffix_node X) Y) (= X Y)))))
% 0.24/0.68 (assert (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((A4 tptp.list_node) (B3 tptp.list_node)) (and (@ (@ tptp.suffix_node A4) B3) (@ (@ tptp.suffix_node B3) A4)))))
% 0.24/0.68 (assert (forall ((A tptp.list_node) (B tptp.list_node)) (=> (@ (@ tptp.suffix_node A) B) (=> (@ (@ tptp.suffix_node B) A) (= A B)))))
% 0.24/0.68 (assert (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (=> (= A B) (=> (@ (@ tptp.suffix_node B) C) (@ (@ tptp.suffix_node A) C)))))
% 0.24/0.68 (assert (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.24/0.68 (assert (forall ((B tptp.list_node) (A tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node C))) (=> (@ (@ tptp.suffix_node B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.24/0.68 (assert (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((A4 tptp.list_node) (B3 tptp.list_node)) (and (@ (@ tptp.suffix_node B3) A4) (@ (@ tptp.suffix_node A4) B3)))))
% 0.24/0.68 (assert (forall ((B tptp.list_node) (A tptp.list_node)) (=> (@ (@ tptp.suffix_node B) A) (=> (@ (@ tptp.suffix_node A) B) (= A B)))))
% 0.24/0.68 (assert (forall ((X21 tptp.node) (X22 tptp.list_node)) (= (@ tptp.hd_node (@ (@ tptp.cons_node X21) X22)) X21)))
% 0.24/0.68 (assert (forall ((A2 tptp.set_node)) (=> (@ tptp.finite_finite_node A2) (exists ((Xs2 tptp.list_node)) (= (@ tptp.set_node2 Xs2) A2)))))
% 0.24/0.68 (assert (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (exists ((Xs2 tptp.list_val)) (= (@ tptp.set_val2 Xs2) A2)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val) (B4 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_val2 Xs)) B4) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 B4)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (B4 tptp.set_node)) (= (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) B4) (forall ((X3 tptp.node)) (let ((_let_1 (@ tptp.member_node X3))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 B4)))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.prefix_node Xs) Ys) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) (@ tptp.set_node2 Ys)))))
% 0.24/0.68 (assert (forall ((A tptp.list_val)) (=> (not (= A tptp.nil_val)) (@ (@ tptp.member_val (@ tptp.hd_val A)) (@ tptp.set_val2 A)))))
% 0.24/0.68 (assert (forall ((A tptp.list_node)) (=> (not (= A tptp.nil_node)) (@ (@ tptp.member_node (@ tptp.hd_node A)) (@ tptp.set_node2 A)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_val)) (=> (not (= Xs tptp.nil_val)) (@ (@ tptp.member_val (@ tptp.hd_val Xs)) (@ tptp.set_val2 Xs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (@ (@ tptp.member_node (@ tptp.hd_node Xs)) (@ tptp.set_node2 Xs)))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.hd_node (@ (@ tptp.append_node Xs) Ys)))) (let ((_let_2 (= Xs tptp.nil_node))) (and (=> _let_2 (= _let_1 (@ tptp.hd_node Ys))) (=> (not _let_2) (= _let_1 (@ tptp.hd_node Xs))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (exists ((Ps tptp.list_node) (Xs6 tptp.list_node) (Ys4 tptp.list_node)) (let ((_let_1 (@ tptp.append_node Ps))) (and (= Xs (@ _let_1 Xs6)) (= Ys (@ _let_1 Ys4)) (or (= Xs6 tptp.nil_node) (= Ys4 tptp.nil_node) (not (= (@ tptp.hd_node Xs6) (@ tptp.hd_node Ys4)))))))))
% 0.24/0.68 (assert (forall ((Ps2 tptp.list_node) (Ls tptp.list_node)) (=> (not (@ (@ tptp.suffix_node Ps2) Ls)) (=> (=> (not (= Ps2 tptp.nil_node)) (not (= Ls tptp.nil_node))) (=> (forall ((A3 tptp.node) (As tptp.list_node)) (=> (= Ps2 (@ (@ tptp.append_node As) (@ (@ tptp.cons_node A3) tptp.nil_node))) (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (= Ls (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (= X4 A3) (@ (@ tptp.suffix_node As) Xs2)))))) (not (forall ((A3 tptp.node)) (=> (exists ((As tptp.list_node)) (= Ps2 (@ (@ tptp.append_node As) (@ (@ tptp.cons_node A3) tptp.nil_node)))) (forall ((X4 tptp.node)) (=> (exists ((Xs2 tptp.list_node)) (= Ls (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node)))) (= X4 A3)))))))))))
% 0.24/0.68 (assert (forall ((Ps2 tptp.list_node) (Ls tptp.list_node) (P (-> tptp.list_node tptp.list_node Bool))) (=> (not (@ (@ tptp.suffix_node Ps2) Ls)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) tptp.nil_node)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (not (= X4 Y2)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (= X4 Y2) (=> (not (@ (@ tptp.suffix_node Xs2) Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))))) (@ (@ P Ps2) Ls)))))))
% 0.24/0.68 (assert (forall ((List tptp.list_node) (List2 tptp.list_node)) (let ((_let_1 (= List2 tptp.nil_node))) (let ((_let_2 (= List tptp.nil_node))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_node List) (@ tptp.hd_node List2)) (= (@ tptp.tl_node List) (@ tptp.tl_node List2))))) (= List List2)))))))
% 0.24/0.68 (assert (forall ((X tptp.val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.member_val X))) (=> (not (= X (@ tptp.hd_val Xs))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val Xs))))))))
% 0.24/0.68 (assert (forall ((X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (=> (not (= X (@ tptp.hd_node Xs))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node Xs))))))))
% 0.24/0.68 (assert (forall ((Xs tptp.list_node) (X tptp.node)) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) (@ tptp.set_node2 (@ (@ tptp.cons_node X) Xs)))))
% 0.72/0.96 (assert (forall ((List tptp.list_node)) (=> (not (= List tptp.nil_node)) (= List (@ (@ tptp.cons_node (@ tptp.hd_node List)) (@ tptp.tl_node List))))))
% 0.72/0.96 (assert (forall ((Xs tptp.list_node) (A2 tptp.set_node)) (=> (not (= Xs tptp.nil_node)) (=> (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) A2) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 (@ tptp.tl_node Xs))) A2)))))
% 0.72/0.96 (assert (forall ((Xs tptp.list_node) (A2 tptp.set_node)) (=> (not (= Xs tptp.nil_node)) (=> (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) A2) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 (@ tptp.butlast_node Xs))) A2)))))
% 0.72/0.96 (assert (forall ((Xs_1 tptp.list_node) (Ys tptp.list_node) (Xs_2 tptp.list_node)) (let ((_let_1 (@ tptp.prefix_node Xs_2))) (let ((_let_2 (@ tptp.prefix_node Xs_1))) (=> (@ _let_2 Ys) (=> (@ _let_1 Ys) (or (@ _let_2 Xs_2) (@ _let_1 Xs_1))))))))
% 0.72/0.96 (assert (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((X3 tptp.list_node) (Y3 tptp.list_node)) (and (@ (@ tptp.prefix_node X3) Y3) (@ (@ tptp.prefix_node Y3) X3)))))
% 0.72/0.96 (assert (forall ((X tptp.list_node) (Y tptp.list_node)) (=> (@ (@ tptp.prefix_node X) Y) (=> (@ (@ tptp.prefix_node Y) X) (= X Y)))))
% 0.72/0.96 (assert (not (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) tptp.n) (@ (@ tptp.append_node tptp.ns) (@ tptp.tl_node tptp.ri))) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r))))
% 0.72/0.96 (set-info :filename cvc5---1.0.5_28241)
% 0.72/0.96 (check-sat-assuming ( true ))
% 0.72/0.96 ------- get file name : TPTP file name is ITP081^1
% 0.72/0.96 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_28241.smt2...
% 0.72/0.96 --- Run --ho-elim --full-saturate-quant at 10...
% 0.72/0.96 % SZS status Theorem for ITP081^1
% 0.72/0.96 % SZS output start Proof for ITP081^1
% 0.72/0.96 (
% 0.72/0.96 (let ((_let_1 (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2))) (let ((_let_2 (@ _let_1 tptp.phi_r))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2))) (let ((_let_4 (@ _let_3 tptp.n))) (let ((_let_5 (not (@ (@ _let_4 (@ (@ tptp.append_node tptp.ns) (@ tptp.tl_node tptp.ri))) _let_2)))) (let ((_let_6 (@ _let_3 tptp.m))) (let ((_let_7 (@ tptp.member_node tptp.i))) (let ((_let_8 (@ _let_1 tptp.r))) (let ((_let_9 (@ tptp.member_node _let_8))) (let ((_let_10 (= tptp.m tptp.i))) (let ((_let_11 (= tptp.i _let_2))) (let ((_let_12 (not _let_11))) (let ((_let_13 (@ _let_3 _let_8))) (let ((_let_14 (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ms tptp.list_node) (L tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_2 (@ _let_1 N))) (=> (@ (@ _let_2 Ns) M) (=> (@ (@ (@ _let_1 M) Ms) L) (@ (@ _let_2 (@ (@ tptp.append_node Ns) (@ tptp.tl_node Ms))) L)))))))) (let ((_let_15 (@ _let_13 tptp.ri))) (let ((_let_16 (@ _let_15 tptp.i))) (let ((_let_17 (@ (@ _let_4 tptp.ns) _let_8))) (let ((_let_18 (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ms tptp.list_node) (L tptp.node)) (let ((_let_1 (ho_66 (ho_65 (ho_64 (ho_63 k_62 k_52) k_46) k_60) G))) (let ((_let_2 (ho_67 _let_1 N))) (or (not (ho_36 (ho_68 _let_2 Ns) M)) (not (ho_36 (ho_68 (ho_67 _let_1 M) Ms) L)) (ho_36 (ho_68 _let_2 (ho_24 (ho_23 k_22 Ns) (ho_24 k_69 Ms))) L))))))) (let ((_let_19 (ho_58 (ho_57 (ho_56 (ho_55 k_54 k_52) k_50) k_48) tptp.g2))) (let ((_let_20 (ho_59 _let_19 tptp.phi_r))) (let ((_let_21 (ho_66 (ho_65 (ho_64 (ho_63 k_62 k_52) k_46) k_60) tptp.g2))) (let ((_let_22 (ho_67 _let_21 tptp.n))) (let ((_let_23 (ho_36 (ho_68 _let_22 (ho_24 (ho_23 k_22 tptp.ns) (ho_24 k_69 tptp.ri))) _let_20))) (let ((_let_24 (ho_59 _let_19 tptp.r))) (let ((_let_25 (ho_36 (ho_68 (ho_67 _let_21 _let_24) tptp.ri) _let_20))) (let ((_let_26 (not _let_25))) (let ((_let_27 (ho_36 (ho_68 _let_22 tptp.ns) _let_24))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_23))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ms tptp.list_node) (L tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_2 (@ _let_1 N))) (or (not (@ (@ _let_2 Ns) M)) (not (@ (@ (@ _let_1 M) Ms) L)) (@ (@ _let_2 (@ (@ tptp.append_node Ns) (@ tptp.tl_node Ms))) L))))) _let_18))))))) (let ((_let_31 (not _let_29))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.g2 tptp.n tptp.ns _let_24 tptp.ri _let_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_23 _let_28 _let_26 _let_31))) (EQ_RESOLVE (ASSUME :args (_let_5)) (PREPROCESS :args ((= _let_5 (not _let_23))))) (EQ_RESOLVE (ASSUME :args (_let_17)) (PREPROCESS :args ((= _let_17 _let_27)))) (EQ_RESOLVE (ASSUME :args (_let_16)) (TRANS (MACRO_SR_EQ_INTRO (ASSUME :args (_let_11)) :args (_let_16 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ _let_15 _let_2) _let_25))))) :args (_let_31 true _let_23 false _let_27 false _let_25)) _let_30 :args (false true _let_29 false _let_18)) :args ((not (= tptp.r tptp.phi_r)) _let_11 (forall ((G tptp.g)) (@ tptp.invar G)) _let_17 _let_16 _let_14 (not (= _let_2 _let_8)) (@ (@ _let_13 tptp.rs) tptp.pred_phi_r) (@ (@ (@ (@ (@ (@ tptp.sSA_CF1252180629de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.phi_r) tptp.r) (@ (@ _let_13 tptp.rs2) _let_2) (@ (@ _let_6 tptp.ms2) tptp.i) (=> _let_12 (=> (=> _let_12 (not _let_10)) (not (=> _let_12 _let_10)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (N2 tptp.node) (Ns2 tptp.list_node) (M tptp.node)) (let ((_let_1 (@ (@ tptp.cons_node N2) Ns2))) (let ((_let_2 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_2 N) (@ (@ tptp.append_node Ns) _let_1)) M) (@ (@ (@ _let_2 N2) _let_1) M))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (not (= Ns tptp.nil_node)))) (forall ((G tptp.g) (N tptp.node) (M tptp.node)) (not (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) tptp.nil_node) M))) (@ (@ tptp.member_val tptp.r) (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) tptp.g2) tptp.pred_phi_r)) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node N) (@ tptp.set_node2 Ns)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (L tptp.node)) (let ((_let_1 (@ tptp.member_node L))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ _let_1 (@ tptp.set_node2 Ns)) (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))))))) (forall ((X tptp.list_node) (Xs tptp.list_list_node) (Ys tptp.list_list_node) (Y tptp.list_node)) (let ((_let_1 (@ tptp.member_list_node X))) (=> (@ _let_1 (@ tptp.set_list_node2 Xs)) (@ _let_1 (@ tptp.set_list_node2 (@ tptp.tl_list_node (@ (@ tptp.append_list_node Ys) (@ (@ tptp.cons_list_node Y) Xs)))))))) (forall ((X tptp.val) (Xs tptp.list_val) (Ys tptp.list_val) (Y tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val (@ (@ tptp.append_val Ys) (@ (@ tptp.cons_val Y) Xs)))))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) Xs)))))))) (@ _let_7 (@ tptp.set_node2 tptp.ms)) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ tptp.alpha_n G))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (@ (@ tptp.member_node M) (@ tptp.set_node2 Ns)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (N2 tptp.node) (Ns2 tptp.list_node) (M tptp.node)) (let ((_let_1 (@ tptp.cons_node N2))) (let ((_let_2 (@ tptp.append_node Ns))) (let ((_let_3 (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N))) (=> (@ (@ _let_3 (@ _let_2 (@ _let_1 Ns2))) M) (@ (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_node))) N2)))))) (not (@ _let_9 (@ tptp.set_node2 (@ tptp.tl_node tptp.rs2)))) (not (@ _let_9 (@ tptp.set_node2 (@ tptp.tl_node tptp.rs)))) (= tptp.rs2 (@ (@ tptp.append_node tptp.rs) (@ (@ tptp.cons_node _let_2) tptp.nil_node))) (@ (@ tptp.prefix_node tptp.ri) tptp.rs2) (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ tptp.invar G) (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) (@ (@ tptp.cons_node N) tptp.nil_node)) N)))) (not (@ _let_7 (@ tptp.set_node2 (@ tptp.butlast_node tptp.ms2)))) (@ (@ tptp.member_node tptp.pred_phi_r) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) tptp.g2) _let_2))) (@ (@ _let_6 tptp.ms) (@ _let_1 tptp.s)) (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (=> (not (= Xs tptp.nil_list_node)) (= (@ tptp.tl_list_node (@ (@ tptp.append_list_node Xs) Ys)) (@ (@ tptp.append_list_node (@ tptp.tl_list_node Xs)) Ys)))) (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (=> (not (= Xs tptp.nil_val)) (= (@ tptp.tl_val (@ (@ tptp.append_val Xs) Ys)) (@ (@ tptp.append_val (@ tptp.tl_val Xs)) Ys)))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (= (@ tptp.tl_node (@ (@ tptp.append_node Xs) Ys)) (@ (@ tptp.append_node (@ tptp.tl_node Xs)) Ys)))) (forall ((L1 tptp.list_val) (E tptp.val) (L2 tptp.list_val) (E2 tptp.val)) (= (= (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E) L2)) (@ (@ tptp.cons_val E2) tptp.nil_val)) (and (= L1 tptp.nil_val) (= E E2) (= L2 tptp.nil_val)))) (forall ((L1 tptp.list_list_node) (E tptp.list_node) (L2 tptp.list_list_node) (E2 tptp.list_node)) (= (= (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E) L2)) (@ (@ tptp.cons_list_node E2) tptp.nil_list_node)) (and (= L1 tptp.nil_list_node) (= E E2) (= L2 tptp.nil_list_node)))) (forall ((L1 tptp.list_node) (E tptp.node) (L2 tptp.list_node) (E2 tptp.node)) (= (= (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E) L2)) (@ (@ tptp.cons_node E2) tptp.nil_node)) (and (= L1 tptp.nil_node) (= E E2) (= L2 tptp.nil_node)))) (forall ((E2 tptp.val) (L1 tptp.list_val) (E tptp.val) (L2 tptp.list_val)) (= (= (@ (@ tptp.cons_val E2) tptp.nil_val) (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E) L2))) (and (= L1 tptp.nil_val) (= E E2) (= L2 tptp.nil_val)))) (forall ((E2 tptp.list_node) (L1 tptp.list_list_node) (E tptp.list_node) (L2 tptp.list_list_node)) (= (= (@ (@ tptp.cons_list_node E2) tptp.nil_list_node) (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E) L2))) (and (= L1 tptp.nil_list_node) (= E E2) (= L2 tptp.nil_list_node)))) (forall ((E2 tptp.node) (L1 tptp.list_node) (E tptp.node) (L2 tptp.list_node)) (= (= (@ (@ tptp.cons_node E2) tptp.nil_node) (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E) L2))) (and (= L1 tptp.nil_node) (= E E2) (= L2 tptp.nil_node)))) (forall ((L2 tptp.list_val) (A tptp.val) (L1 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L2 tptp.nil_val)) (= (= _let_1 (@ (@ tptp.append_val L1) L2)) (and (= L1 tptp.nil_val) (= L2 _let_1)))))) (forall ((L2 tptp.list_list_node) (A tptp.list_node) (L1 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L2 tptp.nil_list_node)) (= (= _let_1 (@ (@ tptp.append_list_node L1) L2)) (and (= L1 tptp.nil_list_node) (= L2 _let_1)))))) (forall ((L2 tptp.list_node) (A tptp.node) (L1 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L2 tptp.nil_node)) (= (= _let_1 (@ (@ tptp.append_node L1) L2)) (and (= L1 tptp.nil_node) (= L2 _let_1)))))) (forall ((L1 tptp.list_val) (A tptp.val) (L2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L1 tptp.nil_val)) (= (= _let_1 (@ (@ tptp.append_val L1) L2)) (and (= L1 _let_1) (= L2 tptp.nil_val)))))) (forall ((L1 tptp.list_list_node) (A tptp.list_node) (L2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L1 tptp.nil_list_node)) (= (= _let_1 (@ (@ tptp.append_list_node L1) L2)) (and (= L1 _let_1) (= L2 tptp.nil_list_node)))))) (forall ((L1 tptp.list_node) (A tptp.node) (L2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L1 tptp.nil_node)) (= (= _let_1 (@ (@ tptp.append_node L1) L2)) (and (= L1 _let_1) (= L2 tptp.nil_node)))))) (forall ((L2 tptp.list_val) (L1 tptp.list_val) (A tptp.val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L2 tptp.nil_val)) (= (= (@ (@ tptp.append_val L1) L2) _let_1) (and (= L1 tptp.nil_val) (= L2 _let_1)))))) (forall ((L2 tptp.list_list_node) (L1 tptp.list_list_node) (A tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L2 tptp.nil_list_node)) (= (= (@ (@ tptp.append_list_node L1) L2) _let_1) (and (= L1 tptp.nil_list_node) (= L2 _let_1)))))) (forall ((L2 tptp.list_node) (L1 tptp.list_node) (A tptp.node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L2 tptp.nil_node)) (= (= (@ (@ tptp.append_node L1) L2) _let_1) (and (= L1 tptp.nil_node) (= L2 _let_1)))))) (forall ((L1 tptp.list_val) (L2 tptp.list_val) (A tptp.val)) (let ((_let_1 (@ (@ tptp.cons_val A) tptp.nil_val))) (=> (not (= L1 tptp.nil_val)) (= (= (@ (@ tptp.append_val L1) L2) _let_1) (and (= L1 _let_1) (= L2 tptp.nil_val)))))) (forall ((L1 tptp.list_list_node) (L2 tptp.list_list_node) (A tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node A) tptp.nil_list_node))) (=> (not (= L1 tptp.nil_list_node)) (= (= (@ (@ tptp.append_list_node L1) L2) _let_1) (and (= L1 _let_1) (= L2 tptp.nil_list_node)))))) (forall ((L1 tptp.list_node) (L2 tptp.list_node) (A tptp.node)) (let ((_let_1 (@ (@ tptp.cons_node A) tptp.nil_node))) (=> (not (= L1 tptp.nil_node)) (= (= (@ (@ tptp.append_node L1) L2) _let_1) (and (= L1 _let_1) (= L2 tptp.nil_node)))))) (forall ((L1 tptp.list_val) (E1 tptp.val) (E22 tptp.val) (L2 tptp.list_val) (E12 tptp.val) (E23 tptp.val)) (= (= (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E1) (@ (@ tptp.cons_val E22) L2))) (@ (@ tptp.cons_val E12) (@ (@ tptp.cons_val E23) tptp.nil_val))) (and (= L1 tptp.nil_val) (= E12 E1) (= E23 E22) (= L2 tptp.nil_val)))) (forall ((L1 tptp.list_list_node) (E1 tptp.list_node) (E22 tptp.list_node) (L2 tptp.list_list_node) (E12 tptp.list_node) (E23 tptp.list_node)) (= (= (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E1) (@ (@ tptp.cons_list_node E22) L2))) (@ (@ tptp.cons_list_node E12) (@ (@ tptp.cons_list_node E23) tptp.nil_list_node))) (and (= L1 tptp.nil_list_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_list_node)))) (forall ((L1 tptp.list_node) (E1 tptp.node) (E22 tptp.node) (L2 tptp.list_node) (E12 tptp.node) (E23 tptp.node)) (= (= (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E1) (@ (@ tptp.cons_node E22) L2))) (@ (@ tptp.cons_node E12) (@ (@ tptp.cons_node E23) tptp.nil_node))) (and (= L1 tptp.nil_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_node)))) (forall ((E12 tptp.val) (E23 tptp.val) (L1 tptp.list_val) (E1 tptp.val) (E22 tptp.val) (L2 tptp.list_val)) (= (= (@ (@ tptp.cons_val E12) (@ (@ tptp.cons_val E23) tptp.nil_val)) (@ (@ tptp.append_val L1) (@ (@ tptp.cons_val E1) (@ (@ tptp.cons_val E22) L2)))) (and (= L1 tptp.nil_val) (= E12 E1) (= E23 E22) (= L2 tptp.nil_val)))) (forall ((E12 tptp.list_node) (E23 tptp.list_node) (L1 tptp.list_list_node) (E1 tptp.list_node) (E22 tptp.list_node) (L2 tptp.list_list_node)) (= (= (@ (@ tptp.cons_list_node E12) (@ (@ tptp.cons_list_node E23) tptp.nil_list_node)) (@ (@ tptp.append_list_node L1) (@ (@ tptp.cons_list_node E1) (@ (@ tptp.cons_list_node E22) L2)))) (and (= L1 tptp.nil_list_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_list_node)))) (forall ((E12 tptp.node) (E23 tptp.node) (L1 tptp.list_node) (E1 tptp.node) (E22 tptp.node) (L2 tptp.list_node)) (= (= (@ (@ tptp.cons_node E12) (@ (@ tptp.cons_node E23) tptp.nil_node)) (@ (@ tptp.append_node L1) (@ (@ tptp.cons_node E1) (@ (@ tptp.cons_node E22) L2)))) (and (= L1 tptp.nil_node) (= E12 E1) (= E23 E22) (= L2 tptp.nil_node)))) (@ (@ tptp.prefix_node tptp.ms2) tptp.ms) (forall ((X2 tptp.node)) (let ((_let_1 (@ tptp.member_node X2))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node tptp.ri))) (not (@ _let_1 (@ tptp.set_node2 tptp.ms)))))) (forall ((X21 tptp.val) (X22 tptp.list_val) (Y21 tptp.val) (Y22 tptp.list_val)) (= (= (@ (@ tptp.cons_val X21) X22) (@ (@ tptp.cons_val Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 tptp.list_node) (X22 tptp.list_list_node) (Y21 tptp.list_node) (Y22 tptp.list_list_node)) (= (= (@ (@ tptp.cons_list_node X21) X22) (@ (@ tptp.cons_list_node Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((X21 tptp.node) (X22 tptp.list_node) (Y21 tptp.node) (Y22 tptp.list_node)) (= (= (@ (@ tptp.cons_node X21) X22) (@ (@ tptp.cons_node Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))) (forall ((A tptp.list_val) (B tptp.list_val) (C tptp.list_val)) (let ((_let_1 (@ tptp.append_val A))) (= (@ (@ tptp.append_val (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_val B) C))))) (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.append_node A))) (= (@ (@ tptp.append_node (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.append_node B) C))))) (forall ((A tptp.val) (P (-> tptp.val Bool))) (= (@ (@ tptp.member_val A) (@ tptp.collect_val P)) (@ P A))) (forall ((A tptp.node) (P (-> tptp.node Bool))) (= (@ (@ tptp.member_node A) (@ tptp.collect_node P)) (@ P A))) (forall ((A2 tptp.set_val)) (= (@ tptp.collect_val (lambda ((X3 tptp.val)) (@ (@ tptp.member_val X3) A2))) A2)) (forall ((A2 tptp.set_node)) (= (@ tptp.collect_node (lambda ((X3 tptp.node)) (@ (@ tptp.member_node X3) A2))) A2)) (forall ((P (-> tptp.node Bool)) (Q (-> tptp.node Bool))) (=> (forall ((X4 tptp.node)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_node P) (@ tptp.collect_node Q)))) (forall ((P (-> tptp.val Bool)) (Q (-> tptp.val Bool))) (=> (forall ((X4 tptp.val)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_val P) (@ tptp.collect_val Q)))) (forall ((Xs tptp.list_val) (Ys tptp.list_val) (Zs tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (= (@ (@ tptp.append_val (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_val Ys) Zs))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (= (@ (@ tptp.append_node (@ _let_1 Ys)) Zs) (@ _let_1 (@ (@ tptp.append_node Ys) Zs))))) (forall ((Ys tptp.list_val) (Xs tptp.list_val) (Zs tptp.list_val)) (= (= (@ (@ tptp.append_val Ys) Xs) (@ (@ tptp.append_val Zs) Xs)) (= Ys Zs))) (forall ((Ys tptp.list_node) (Xs tptp.list_node) (Zs tptp.list_node)) (= (= (@ (@ tptp.append_node Ys) Xs) (@ (@ tptp.append_node Zs) Xs)) (= Ys Zs))) (forall ((Xs tptp.list_val) (Ys tptp.list_val) (Zs tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (= (= (@ _let_1 Ys) (@ _let_1 Zs)) (= Ys Zs)))) (forall ((N tptp.node) (G tptp.g) (N2 tptp.node)) (let ((_let_1 (@ tptp.member_node N))) (=> (@ _let_1 (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N2))) (=> (@ tptp.invar G) (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))))))) (forall ((N tptp.node) (G tptp.g) (N2 tptp.node)) (let ((_let_1 (@ tptp.set_node2 (@ tptp.alpha_n G)))) (let ((_let_2 (@ tptp.member_node N))) (=> (@ _let_2 (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N2))) (=> (@ _let_2 _let_1) (=> (@ tptp.invar G) (@ (@ tptp.member_node N2) _let_1))))))) (forall ((G tptp.g) (N tptp.node)) (=> (not (= (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N) tptp.nil_node)) (=> (@ tptp.invar G) (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G)))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ms tptp.list_node) (L tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_2 (@ _let_1 N))) (=> (@ (@ _let_2 Ns) M) (=> (@ (@ (@ _let_1 M) Ms) L) (@ (@ _let_2 (@ (@ tptp.append_node (@ tptp.butlast_node Ns)) Ms)) L)))))) (forall ((Xs tptp.list_list_node)) (= (@ (@ tptp.append_list_node Xs) tptp.nil_list_node) Xs)) (forall ((Xs tptp.list_val)) (= (@ (@ tptp.append_val Xs) tptp.nil_val) Xs)) (forall ((Xs tptp.list_node)) (= (@ (@ tptp.append_node Xs) tptp.nil_node) Xs)) (forall ((Xs tptp.list_list_node) (Ys tptp.list_list_node)) (= (= (@ (@ tptp.append_list_node Xs) Ys) Xs) (= Ys tptp.nil_list_node))) (forall ((Xs tptp.list_val) (Ys tptp.list_val)) (= (= (@ (@ tptp.append_val Xs) Ys) Xs) (= Ys tptp.nil_val))) (forall ((Xs tptp.list_node) (Ys 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(Ys tptp.list_node)) (= (= (@ (@ tptp.append_node Xs) Ys) tptp.nil_node) (and (= Xs tptp.nil_node) (= Ys tptp.nil_node)))) (= (@ tptp.append_list_node tptp.nil_list_node) (lambda ((X3 tptp.list_list_node)) X3)) (= (@ tptp.append_val tptp.nil_val) (lambda ((X3 tptp.list_val)) X3)) (= (@ tptp.append_node tptp.nil_node) (lambda ((X3 tptp.list_node)) X3)) (forall ((A tptp.list_list_node)) (= (@ (@ tptp.append_list_node A) tptp.nil_list_node) A)) (forall ((A tptp.list_val)) (= (@ (@ tptp.append_val A) tptp.nil_val) A)) (forall ((A tptp.list_node)) (= (@ (@ tptp.append_node A) tptp.nil_node) A)) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (X tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Ns)) (not (forall ((Ns_1 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns_1) X) (forall ((Ns_2 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(not (forall ((M3 tptp.node) (Ns3 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns3) M3) (=> (@ P M3) (=> (forall ((X2 tptp.node)) (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 (@ tptp.butlast_node Ns3))) (not (@ P X2)))) (not (@ (@ tptp.prefix_node Ns3) Ns)))))))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node tptp.list_node tptp.node Bool))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (=> (@ tptp.invar G) (@ (@ (@ P M) (@ (@ tptp.cons_node M) tptp.nil_node)) M)) (=> (forall ((Ns4 tptp.list_node) (N3 tptp.node) (N4 tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N4) Ns4) M) (=> (@ (@ (@ P N4) Ns4) M) (=> (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N4))) (@ (@ (@ P N3) (@ (@ tptp.cons_node N3) Ns4)) M))))) (@ (@ (@ P N) Ns) M))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (X tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Ns)) (not (forall ((Ns_1 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns_1) X) (forall ((Ns_2 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) X) Ns_2) M) (=> (= Ns (@ (@ tptp.append_node Ns_1) (@ tptp.tl_node Ns_2))) (not (= Ns (@ (@ tptp.append_node (@ tptp.butlast_node Ns_1)) Ns_2)))))))))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (Ns2 tptp.list_node) (M2 tptp.node)) (let ((_let_1 (@ (@ tptp.append_node Ns2) (@ (@ tptp.cons_node M2) tptp.nil_node)))) (let ((_let_2 (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N))) (=> (@ (@ _let_2 Ns) M) (=> (@ (@ tptp.prefix_node _let_1) Ns) (@ (@ _let_2 _let_1) M2)))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node tptp.list_node tptp.node Bool))) (let ((_let_1 (@ P N))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ (@ _let_1 (@ (@ tptp.cons_node N) tptp.nil_node)) N)) (=> (forall ((Ns4 tptp.list_node) (M3 tptp.node) (M4 tptp.node)) (let ((_let_1 (@ P N))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns4) M3) (=> (@ (@ _let_1 Ns4) M3) (=> (@ (@ tptp.member_node M3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) M4))) (@ (@ _let_1 (@ (@ tptp.append_node Ns4) (@ (@ tptp.cons_node M4) tptp.nil_node))) M4)))))) (@ (@ _let_1 Ns) M)))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (M2 tptp.node)) (let ((_let_1 (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N))) (=> (@ (@ _let_1 Ns) M) (=> (@ (@ tptp.member_node M) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) M2))) (@ (@ _let_1 (@ (@ tptp.append_node Ns) (@ (@ tptp.cons_node M2) tptp.nil_node))) M2))))) (forall ((Xs tptp.list_val) (X tptp.val) (Ys tptp.list_val) (Y tptp.val)) (= (= (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val X) tptp.nil_val)) (@ (@ tptp.append_val Ys) (@ (@ tptp.cons_val Y) tptp.nil_val))) (and (= Xs Ys) (= X Y)))) (forall ((Xs tptp.list_list_node) (X tptp.list_node) (Ys tptp.list_list_node) (Y tptp.list_node)) (= (= (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node X) tptp.nil_list_node)) (@ (@ tptp.append_list_node Ys) (@ (@ tptp.cons_list_node Y) tptp.nil_list_node))) (and (= Xs Ys) (= X Y)))) (forall ((Xs tptp.list_node) (X tptp.node) (Ys tptp.list_node) (Y tptp.node)) (= (= (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node X) tptp.nil_node)) (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node))) (and (= Xs Ys) (= X Y)))) (forall ((Xs tptp.list_val) (X tptp.val)) (= (@ tptp.butlast_val (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val X) tptp.nil_val))) Xs)) (forall ((Xs tptp.list_list_node) (X tptp.list_node)) (= (@ tptp.butlast_list_node (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node X) tptp.nil_list_node))) Xs)) (forall ((Xs tptp.list_node) (X tptp.node)) (= (@ tptp.butlast_node (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node X) tptp.nil_node))) Xs)) (not (forall ((Ms2 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) tptp.m) Ms2) tptp.i) (=> (@ (@ tptp.prefix_node Ms2) tptp.ms) (@ (@ tptp.member_node tptp.i) (@ tptp.set_node2 (@ tptp.butlast_node Ms2))))))) (not (forall ((I tptp.node) (Ri tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) tptp.g2) (@ (@ (@ (@ (@ tptp.sSA_CF551432799de_val tptp.alpha_n) tptp.defs) tptp.phis) tptp.g2) tptp.r)) Ri) I) (=> (@ (@ tptp.member_node I) (@ tptp.set_node2 tptp.ms)) (=> (forall ((X2 tptp.node)) (let ((_let_1 (@ tptp.member_node X2))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Ri))) (not (@ _let_1 (@ tptp.set_node2 tptp.ms)))))) (not (@ (@ tptp.prefix_node Ri) tptp.rs2))))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (N2 tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_1 N) Ns) M) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) N))) (@ (@ (@ _let_1 N2) (@ (@ tptp.cons_node N2) Ns)) M))))) (= (@ tptp.butlast_list_node tptp.nil_list_node) tptp.nil_list_node) (= (@ tptp.butlast_val tptp.nil_val) tptp.nil_val) (= (@ tptp.butlast_node tptp.nil_node) tptp.nil_node) (forall ((X tptp.val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.member_val X))) (=> (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val Xs))) (@ _let_1 (@ tptp.set_val2 Xs))))) (forall ((X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Xs))) (@ _let_1 (@ tptp.set_node2 Xs))))) (forall ((Xs tptp.list_val)) (= (@ tptp.butlast_val (@ tptp.tl_val Xs)) (@ tptp.tl_val (@ tptp.butlast_val Xs)))) (forall ((Xs tptp.list_node)) (= (@ tptp.butlast_node (@ tptp.tl_node Xs)) (@ tptp.tl_node (@ tptp.butlast_node Xs)))) (forall ((Xs tptp.list_val) (X tptp.val)) (let ((_let_1 (@ tptp.cons_val X))) (let ((_let_2 (@ tptp.butlast_val (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_val))) (and (=> _let_3 (= _let_2 tptp.nil_val)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_val Xs))))))))) (forall ((Xs tptp.list_list_node) (X tptp.list_node)) (let ((_let_1 (@ tptp.cons_list_node X))) (let ((_let_2 (@ tptp.butlast_list_node (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_list_node))) (and (=> _let_3 (= _let_2 tptp.nil_list_node)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_node Xs))))))))) (forall ((Xs tptp.list_node) (X tptp.node)) (let ((_let_1 (@ tptp.cons_node X))) (let ((_let_2 (@ tptp.butlast_node (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_node))) (and (=> _let_3 (= _let_2 tptp.nil_node)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_node Xs))))))))) (forall ((Ys tptp.list_list_node) (Xs tptp.list_list_node)) (let ((_let_1 (@ tptp.append_list_node Xs))) (let ((_let_2 (@ tptp.butlast_list_node (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_list_node))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_list_node Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_list_node Ys))))))))) (forall ((Ys tptp.list_val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (let ((_let_2 (@ tptp.butlast_val (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_val))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_val Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_val Ys))))))))) (forall ((Ys tptp.list_node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (let ((_let_2 (@ tptp.butlast_node (@ _let_1 Ys)))) (let ((_let_3 (= Ys tptp.nil_node))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_node Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_node Ys))))))))) (forall ((X tptp.val) (Xs tptp.list_val) (Ys tptp.list_val)) (let ((_let_1 (@ tptp.member_val X))) (=> (or (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val Xs))) (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val Ys)))) (@ _let_1 (@ tptp.set_val2 (@ tptp.butlast_val (@ (@ tptp.append_val Xs) Ys))))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (=> (or (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Xs))) (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node Ys)))) (@ _let_1 (@ tptp.set_node2 (@ tptp.butlast_node (@ (@ tptp.append_node Xs) Ys))))))) (forall ((L tptp.list_val) (X tptp.val) (Xs tptp.list_val)) (= (= (@ tptp.butlast_val L) (@ (@ tptp.cons_val X) Xs)) (exists ((Xl tptp.val)) (= L (@ (@ tptp.cons_val X) (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val Xl) tptp.nil_val))))))) (forall ((L tptp.list_list_node) (X tptp.list_node) (Xs tptp.list_list_node)) (= (= (@ tptp.butlast_list_node L) (@ (@ tptp.cons_list_node X) Xs)) (exists ((Xl tptp.list_node)) (= L (@ (@ tptp.cons_list_node X) (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node Xl) tptp.nil_list_node))))))) (forall ((L tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (= (= (@ tptp.butlast_node L) (@ (@ tptp.cons_node X) Xs)) (exists ((Xl tptp.node)) (= L (@ (@ tptp.cons_node X) (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node Xl) tptp.nil_node))))))) (forall ((L tptp.list_val) (X tptp.val) (Xs tptp.list_val)) (=> (= (@ tptp.butlast_val L) (@ (@ tptp.cons_val X) Xs)) (not (forall ((Xl2 tptp.val)) (not (= L (@ (@ tptp.cons_val X) (@ (@ tptp.append_val Xs) (@ (@ tptp.cons_val Xl2) tptp.nil_val))))))))) (forall ((L tptp.list_list_node) (X tptp.list_node) (Xs tptp.list_list_node)) (=> (= (@ tptp.butlast_list_node L) (@ (@ tptp.cons_list_node X) Xs)) (not (forall ((Xl2 tptp.list_node)) (not (= L (@ (@ tptp.cons_list_node X) (@ (@ tptp.append_list_node Xs) (@ (@ tptp.cons_list_node Xl2) tptp.nil_list_node))))))))) (forall ((L tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (=> (= (@ tptp.butlast_node L) (@ (@ tptp.cons_node X) Xs)) (not (forall ((Xl2 tptp.node)) (not (= L (@ (@ tptp.cons_node X) (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node Xl2) tptp.nil_node))))))))) (forall ((N1 tptp.val) (R1 tptp.list_val) (N22 tptp.val) (R2 tptp.list_val)) (=> (= (@ (@ tptp.cons_val N1) R1) (@ (@ tptp.cons_val N22) R2)) (and (= N1 N22) (= R1 R2)))) (forall ((N1 tptp.list_node) (R1 tptp.list_list_node) (N22 tptp.list_node) (R2 tptp.list_list_node)) (=> (= (@ (@ tptp.cons_list_node N1) R1) (@ (@ tptp.cons_list_node N22) R2)) (and (= N1 N22) (= R1 R2)))) (forall ((N1 tptp.node) (R1 tptp.list_node) (N22 tptp.node) (R2 tptp.list_node)) (=> (= (@ (@ tptp.cons_node N1) R1) (@ (@ tptp.cons_node N22) R2)) (and (= N1 N22) (= R1 R2)))) (forall ((X tptp.val) (Xs tptp.list_val)) (not (= (@ (@ tptp.cons_val X) Xs) Xs))) (forall ((X tptp.list_node) (Xs tptp.list_list_node)) (not (= (@ (@ tptp.cons_list_node X) Xs) Xs))) (forall ((X tptp.node) (Xs tptp.list_node)) (not (= (@ (@ tptp.cons_node X) Xs) Xs))) (forall ((Xs tptp.list_val) (Xs1 tptp.list_val) (Zs tptp.list_val) (Ys tptp.list_val) (Us tptp.list_val)) (let ((_let_1 (@ tptp.append_val Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_val Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_val Zs) Us)))))) (forall ((Xs tptp.list_node) (Xs1 tptp.list_node) (Zs tptp.list_node) (Ys tptp.list_node) (Us tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (=> (= (@ _let_1 Xs1) Zs) (=> (= Ys (@ (@ tptp.append_node Xs1) Us)) (= (@ _let_1 Ys) (@ (@ tptp.append_node Zs) Us)))))) (forall ((Xs tptp.list_val) (Ys tptp.list_val) (Zs tptp.list_val) (Ts tptp.list_val)) (= (= (@ (@ tptp.append_val Xs) Ys) (@ (@ tptp.append_val Zs) Ts)) (exists ((Us2 tptp.list_val)) (let ((_let_1 (@ tptp.append_val Us2))) (or (and (= Xs (@ (@ tptp.append_val Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_val Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node) (Ts tptp.list_node)) (= (= (@ (@ tptp.append_node Xs) Ys) (@ (@ tptp.append_node Zs) Ts)) (exists ((Us2 tptp.list_node)) (let ((_let_1 (@ tptp.append_node Us2))) (or (and (= Xs (@ (@ tptp.append_node Zs) Us2)) (= (@ _let_1 Ys) Ts)) (and (= (@ (@ tptp.append_node Xs) Us2) Zs) (= Ys (@ _let_1 Ts)))))))) (forall ((P (-> tptp.list_val Bool)) (A0 tptp.list_val)) (=> (@ P tptp.nil_val) (=> (forall ((X4 tptp.val) (Ys2 tptp.list_val)) (=> (@ P Ys2) (@ P (@ (@ tptp.cons_val X4) Ys2)))) (@ P A0)))) (forall ((P (-> tptp.list_node Bool)) (A0 tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node) (Ys2 tptp.list_node)) (=> (@ P Ys2) (@ P (@ (@ tptp.cons_node X4) Ys2)))) (@ P A0)))) (forall ((P (-> tptp.list_node tptp.list_val Bool)) (R (-> tptp.node tptp.val Bool)) (Xs tptp.list_node) (Ys tptp.list_val)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_val)) (=> (forall ((X_1 tptp.list_val)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_val Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_val tptp.list_val Bool)) (R (-> tptp.val tptp.val Bool)) (Xs tptp.list_val) (Ys tptp.list_val)) (=> (forall ((Xs2 tptp.list_val)) (@ (@ P Xs2) tptp.nil_val)) (=> (forall ((X_1 tptp.list_val)) (@ (@ P tptp.nil_val) X_1)) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_val X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ P (@ (@ tptp.cons_val X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_val Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_list_node tptp.list_val Bool)) (R (-> tptp.list_node tptp.val Bool)) (Xs tptp.list_list_node) (Ys tptp.list_val)) (=> (forall ((Xs2 tptp.list_list_node)) (@ (@ P Xs2) tptp.nil_val)) (=> (forall ((X_1 tptp.list_val)) (@ (@ P tptp.nil_list_node) X_1)) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ (@ tptp.cons_val Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_list_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.val) (Ys2 tptp.list_val)) (let ((_let_1 (@ P (@ (@ tptp.cons_list_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_val Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_node tptp.list_list_node Bool)) (R (-> tptp.node tptp.list_node Bool)) (Xs tptp.list_node) (Ys tptp.list_list_node)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_list_node)) (=> (forall ((X_1 tptp.list_list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_list_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_val tptp.list_list_node Bool)) (R (-> tptp.val tptp.list_node Bool)) (Xs tptp.list_val) (Ys tptp.list_list_node)) (=> (forall ((Xs2 tptp.list_val)) (@ (@ P Xs2) tptp.nil_list_node)) (=> (forall ((X_1 tptp.list_list_node)) (@ (@ P tptp.nil_val) X_1)) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_val X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.val) (Xs2 tptp.list_val) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_val X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_list_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_list_node tptp.list_list_node Bool)) (R (-> tptp.list_node tptp.list_node Bool)) (Xs tptp.list_list_node) (Ys tptp.list_list_node)) (=> (forall ((Xs2 tptp.list_list_node)) (@ (@ P Xs2) tptp.nil_list_node)) (=> (forall ((X_1 tptp.list_list_node)) (@ (@ P tptp.nil_list_node) X_1)) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ (@ tptp.cons_list_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_list_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.list_node) (Xs2 tptp.list_list_node) (Y2 tptp.list_node) (Ys2 tptp.list_list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_list_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_list_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_node tptp.list_node Bool)) (R (-> tptp.node tptp.node Bool)) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (forall ((Xs2 tptp.list_node)) (@ (@ P Xs2) tptp.nil_node)) (=> (forall ((X_1 tptp.list_node)) (@ (@ P tptp.nil_node) X_1)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Ys2))) (=> (@ (@ R X4) Y2) (=> (@ (@ P Xs2) _let_1) (@ (@ P (@ (@ tptp.cons_node X4) Xs2)) _let_1))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ P (@ (@ tptp.cons_node X4) Xs2)))) (=> (not (@ (@ R X4) Y2)) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_node Y2) Ys2)))))) (@ (@ P Xs) Ys)))))) (forall ((P (-> (-> tptp.node tptp.node Bool) tptp.list_node tptp.list_node Bool)) (A0 (-> tptp.node tptp.node Bool)) (A1 tptp.list_node) (A22 tptp.list_node)) (=> (forall ((R3 (-> tptp.node tptp.node Bool)) (X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node Y2) Ys2))) (let ((_let_2 (@ P R3))) (let ((_let_3 (@ _let_2 (@ (@ tptp.cons_node X4) Xs2)))) (let ((_let_4 (@ (@ R3 X4) Y2))) (=> (=> _let_4 (@ (@ _let_2 Xs2) _let_1)) (=> (=> (not _let_4) (@ _let_3 Ys2)) (@ _let_3 _let_1)))))))) (=> (forall ((R3 (-> tptp.node tptp.node Bool)) (Xs2 tptp.list_node)) (@ (@ (@ P R3) Xs2) tptp.nil_node)) (=> (forall ((R3 (-> tptp.node tptp.node Bool)) (V tptp.node) (Va tptp.list_node)) (@ (@ (@ P R3) tptp.nil_node) (@ (@ tptp.cons_node V) Va))) (@ (@ (@ P A0) A1) A22))))) (forall ((P (-> (-> tptp.node tptp.node) tptp.list_node tptp.list_node Bool)) (A0 (-> tptp.node tptp.node)) (A1 tptp.list_node) (A22 tptp.list_node)) (=> (forall ((F (-> tptp.node tptp.node)) (X_1 tptp.list_node)) (@ (@ (@ P F) tptp.nil_node) X_1)) (=> (forall ((F (-> tptp.node tptp.node)) (A3 tptp.node) (As tptp.list_node) (Bs tptp.list_node)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_node (@ F A3)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_node A3) As)) Bs)))) (@ (@ (@ P A0) A1) A22)))) (forall ((Xs tptp.list_node) (P (-> tptp.list_node Bool))) (=> (not (= Xs tptp.nil_node)) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> 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(=> (= Xs (@ (@ tptp.append_node Xs1) Zs)) (= (@ _let_1 Xs) (@ (@ tptp.append_node Ys) Zs)))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.cons_node X))) (= (@ (@ tptp.append_node (@ _let_1 Xs)) Ys) (@ _let_1 (@ (@ tptp.append_node Xs) Ys))))) (forall ((C1 tptp.list_node) (Qs tptp.node) (C2 tptp.list_node) (C12 tptp.list_node) (Qs2 tptp.node) (C22 tptp.list_node)) (=> (= (@ (@ tptp.append_node C1) (@ (@ tptp.cons_node Qs) C2)) (@ (@ tptp.append_node C12) (@ (@ tptp.cons_node Qs2) C22))) (=> (forall ((C21 tptp.list_node)) (=> (= C1 (@ (@ tptp.append_node C12) (@ (@ tptp.cons_node Qs2) C21))) (not (= C22 (@ (@ tptp.append_node C21) (@ (@ tptp.cons_node Qs) C2)))))) (=> (=> (= C12 C1) (=> (= Qs2 Qs) (not (= C22 C2)))) (not (forall ((C212 tptp.list_node)) (=> (= C12 (@ (@ tptp.append_node C1) (@ (@ tptp.cons_node Qs) C212))) (not (= C2 (@ (@ tptp.append_node C212) (@ (@ tptp.cons_node Qs2) C22))))))))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (= Xs Ys) (= Xs (@ (@ tptp.append_node tptp.nil_node) Ys)))) (forall ((Ys tptp.list_node)) (= (@ (@ tptp.append_node tptp.nil_node) Ys) Ys)) (forall ((A tptp.list_node)) (= (@ (@ tptp.append_node tptp.nil_node) A) A)) (forall ((X21 tptp.node) (X22 tptp.list_node)) (= (@ tptp.tl_node (@ (@ tptp.cons_node X21) X22)) X22)) (= (@ tptp.tl_node tptp.nil_node) tptp.nil_node) (forall ((Ys tptp.list_node) (Zs tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (=> (= (@ (@ tptp.append_node Ys) Zs) _let_1) (=> (=> (= Ys tptp.nil_node) (not (= Zs _let_1))) (not (forall ((Ys4 tptp.list_node)) (=> (= Ys (@ (@ tptp.cons_node X) Ys4)) (not (= (@ (@ tptp.append_node Ys4) Zs) Xs))))))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (=> (= _let_1 (@ (@ tptp.append_node Ys) Zs)) (=> (=> (= Ys tptp.nil_node) (not (= Zs _let_1))) (not (forall ((Ys4 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tptp.nil_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))))) (@ (@ P Xs) Ys)))))))) (forall ((Xs tptp.list_node) (P (-> tptp.list_node Bool))) (=> (not (= Xs tptp.nil_node)) (=> (forall ((X4 tptp.node)) (@ P (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (not (= Xs2 tptp.nil_node)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node)))))) (@ P Xs))))) (forall ((Ys tptp.list_node) (Zs tptp.list_node) (X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (= (= (@ (@ tptp.append_node Ys) Zs) _let_1) (or (and (= Ys tptp.nil_node) (= Zs _let_1)) (exists ((Ys5 tptp.list_node)) (and (= Ys (@ (@ tptp.cons_node X) Ys5)) (= (@ (@ tptp.append_node Ys5) Zs) Xs))))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node X) Xs))) (= (= _let_1 (@ (@ tptp.append_node Ys) Zs)) (or (and (= Ys tptp.nil_node) (= _let_1 Zs)) (exists ((Ys5 tptp.list_node)) (and (= (@ (@ tptp.cons_node X) Ys5) Ys) (= Xs (@ (@ tptp.append_node Ys5) Zs)))))))) (forall ((L tptp.list_node)) (= (not (= L tptp.nil_node)) (exists ((Xs3 tptp.list_node) (X3 tptp.node)) (= L (@ (@ tptp.append_node Xs3) (@ (@ tptp.cons_node X3) tptp.nil_node)))))) (forall ((P (-> tptp.list_node tptp.list_node Bool)) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ P tptp.nil_node) tptp.nil_node) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) tptp.nil_node)) (=> (forall ((Y2 tptp.node) (Ys2 tptp.list_node)) (@ (@ P tptp.nil_node) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node)))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))) (@ (@ P Xs) Ys)))))) (forall ((L tptp.list_node)) (=> (not (= L tptp.nil_node)) (not (forall ((Ll tptp.list_node) (E3 tptp.node)) (not (= L (@ (@ tptp.append_node Ll) (@ (@ tptp.cons_node E3) tptp.nil_node)))))))) (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (not (forall ((Ys2 tptp.list_node) (Y2 tptp.node)) (not (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node)))))))) (forall ((P (-> tptp.list_node Bool)) (Xs tptp.list_node)) (=> (@ P tptp.nil_node) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))))) (@ P Xs)))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (= (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 Xs)) (@ P X3))) (exists ((Ys3 tptp.list_node) (X3 tptp.node)) (and (exists ((Zs3 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X3) Zs3)))) (@ P X3) (forall ((Y3 tptp.node)) (=> (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Ys3)) (not (@ P Y3)))))))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (= (exists ((X3 tptp.node)) (and (@ (@ tptp.member_node X3) (@ tptp.set_node2 Xs)) (@ P X3))) (exists ((Ys3 tptp.list_node) (X3 tptp.node) (Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X3) Zs3))) (@ P X3) (forall ((Y3 tptp.node)) (=> (@ (@ tptp.member_node Y3) (@ tptp.set_node2 Zs3)) (not (@ P Y3)))))))) (forall ((X tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys3 tptp.list_val) (Zs3 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys3) (@ (@ tptp.cons_val X) Zs3))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Ys3))))))) (forall ((X tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys3 tptp.list_node) (Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys3) (@ (@ 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tptp.member_node Xa) (@ tptp.set_node2 Ys2)) (not (@ P Xa))))))))))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (not (forall ((Ys2 tptp.list_node) (X4 tptp.node) (Zs2 tptp.list_node)) (=> (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2))) (=> (@ P X4) (not (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Zs2)) (not (@ P Xa))))))))))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (exists ((Ys2 tptp.list_node) (X4 tptp.node)) (and (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (@ P X4) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Ys2)) (not (@ P Xa)))))))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (exists ((Ys2 tptp.list_node) (X4 tptp.node) (Zs2 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2))) (@ P X4) (forall ((Xa tptp.node)) (=> (@ (@ tptp.member_node Xa) (@ tptp.set_node2 Zs2)) (not (@ P Xa)))))))) (forall ((E2 tptp.val) (L tptp.list_val)) (=> (@ (@ tptp.member_val E2) (@ tptp.set_val2 L)) (not (forall ((L12 tptp.list_val) (L22 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val E2) L22)))))))) (forall ((E2 tptp.node) (L tptp.list_node)) (=> (@ (@ tptp.member_node E2) (@ tptp.set_node2 L)) (not (forall ((L12 tptp.list_node) (L22 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node E2) L22)))))))) (forall ((X tptp.val) (Xs tptp.list_val)) (= (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys3 tptp.list_val) (Zs3 tptp.list_val)) (= Xs (@ (@ tptp.append_val Ys3) (@ (@ tptp.cons_val X) Zs3)))))) (forall ((X tptp.node) (Xs tptp.list_node)) (= (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys3 tptp.list_node) (Zs3 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys3) (@ (@ tptp.cons_node X) Zs3)))))) (forall ((X tptp.val) (Xs tptp.list_val) (Ys tptp.list_val) (Xs4 tptp.list_val) (Ys6 tptp.list_val)) (let ((_let_1 (@ tptp.cons_val X))) (let ((_let_2 (@ tptp.member_val X))) (=> (not (@ _let_2 (@ tptp.set_val2 Xs))) (=> (not (@ _let_2 (@ tptp.set_val2 Ys))) (= (= (@ (@ tptp.append_val Xs) (@ _let_1 Ys)) (@ (@ tptp.append_val Xs4) (@ _let_1 Ys6))) (and (= Xs Xs4) (= Ys Ys6)))))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node) (Xs4 tptp.list_node) (Ys6 tptp.list_node)) (let ((_let_1 (@ tptp.cons_node X))) (let ((_let_2 (@ tptp.member_node X))) (=> (not (@ _let_2 (@ tptp.set_node2 Xs))) (=> (not (@ _let_2 (@ tptp.set_node2 Ys))) (= (= (@ (@ tptp.append_node Xs) (@ _let_1 Ys)) (@ (@ tptp.append_node Xs4) (@ _let_1 Ys6))) (and (= Xs Xs4) (= Ys Ys6)))))))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (not (forall ((Ys2 tptp.list_node) (X4 tptp.node)) (=> (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (not (@ P X4))))))) (forall ((X tptp.val) (Xs tptp.list_val)) (=> (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys2 tptp.list_val) (Zs2 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys2) (@ (@ tptp.cons_val X) Zs2))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Ys2))))))) (forall ((X tptp.node) (Xs tptp.list_node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys2 tptp.list_node) (Zs2 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X) Zs2))) (not (@ (@ tptp.member_node X) (@ tptp.set_node2 Ys2))))))) (forall ((X tptp.val) (L tptp.list_val) (Y tptp.val)) (let ((_let_1 (= X Y))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.set_val2 L))) (=> (@ (@ tptp.member_val X) _let_3) (=> (@ (@ tptp.member_val Y) _let_3) (=> (=> _let_1 (forall ((L12 tptp.list_val) (L22 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val Y) L22)))))) (=> (=> _let_2 (forall ((L12 tptp.list_val) (L22 tptp.list_val) (L3 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val X) (@ (@ tptp.append_val L22) (@ (@ tptp.cons_val Y) L3)))))))) (not (=> _let_2 (forall ((L12 tptp.list_val) (L22 tptp.list_val) (L3 tptp.list_val)) (not (= L (@ (@ tptp.append_val L12) (@ (@ tptp.cons_val Y) (@ (@ tptp.append_val L22) (@ (@ tptp.cons_val X) L3))))))))))))))))) (forall ((X tptp.node) (L tptp.list_node) (Y tptp.node)) (let ((_let_1 (= X Y))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.set_node2 L))) (=> (@ (@ tptp.member_node X) _let_3) (=> (@ (@ tptp.member_node Y) _let_3) (=> (=> _let_1 (forall ((L12 tptp.list_node) (L22 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node Y) L22)))))) (=> (=> _let_2 (forall ((L12 tptp.list_node) (L22 tptp.list_node) (L3 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node X) (@ (@ tptp.append_node L22) (@ (@ tptp.cons_node Y) L3)))))))) (not (=> _let_2 (forall ((L12 tptp.list_node) (L22 tptp.list_node) (L3 tptp.list_node)) (not (= L (@ (@ tptp.append_node L12) (@ (@ tptp.cons_node Y) (@ (@ tptp.append_node L22) (@ (@ tptp.cons_node X) L3))))))))))))))))) (forall ((Xs tptp.list_node) (P (-> tptp.node Bool))) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Xs)) (@ P X2))) (exists ((Ys2 tptp.list_node) (X4 tptp.node)) (and (exists ((Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X4) Zs2)))) (@ P X4))))) (forall ((X tptp.val) (Xs tptp.list_val)) (=> (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys2 tptp.list_val) (Zs2 tptp.list_val)) (and (= Xs (@ (@ tptp.append_val Ys2) (@ (@ tptp.cons_val X) Zs2))) (not (@ (@ tptp.member_val X) (@ tptp.set_val2 Zs2))))))) (forall ((X tptp.node) (Xs tptp.list_node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys2 tptp.list_node) (Zs2 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X) Zs2))) (not (@ (@ tptp.member_node X) (@ tptp.set_node2 Zs2))))))) (forall ((X tptp.val) (Xs tptp.list_val)) (=> (@ (@ tptp.member_val X) (@ tptp.set_val2 Xs)) (exists ((Ys2 tptp.list_val) (Zs2 tptp.list_val)) (= Xs (@ (@ tptp.append_val Ys2) (@ (@ tptp.cons_val X) Zs2)))))) (forall ((X tptp.node) (Xs tptp.list_node)) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Xs)) (exists ((Ys2 tptp.list_node) (Zs2 tptp.list_node)) (= Xs (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node X) Zs2)))))) (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (=> (= (@ tptp.tl_node Xs) tptp.nil_node) (not (forall ((E3 tptp.node)) (not (= Xs (@ (@ tptp.cons_node E3) tptp.nil_node)))))))) (forall ((Xs tptp.list_node)) (= (= (@ tptp.tl_node Xs) tptp.nil_node) (or (= Xs tptp.nil_node) (exists ((X3 tptp.node)) (= Xs (@ (@ tptp.cons_node X3) tptp.nil_node)))))) (forall ((Xs tptp.list_node)) (= (= tptp.nil_node (@ tptp.tl_node Xs)) (or (= Xs tptp.nil_node) (exists ((X3 tptp.node)) (= Xs (@ (@ tptp.cons_node X3) tptp.nil_node)))))) (forall ((A tptp.list_val) (X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (not (= A tptp.nil_val)) (=> (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val A))) (@ _let_1 (@ tptp.set_val2 A)))))) (forall ((A tptp.list_node) (X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (not (= A tptp.nil_node)) (=> (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node A))) (@ _let_1 (@ tptp.set_node2 A)))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (let ((_let_1 (@ tptp.prefix_node Xs))) (let ((_let_2 (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node)))) (= (@ _let_1 _let_2) (or (= Xs _let_2) (@ _let_1 Ys)))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (X tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (@ (@ tptp.member_node X) (@ tptp.set_node2 Ns)) (not (forall ((Ns_1 tptp.list_node) (Ns_3 tptp.list_node) (Ns_2 tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (let ((_let_2 (@ tptp.cons_node X))) (let ((_let_3 (@ _let_2 Ns_2))) (let ((_let_4 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_5 (@ _let_4 X))) (let ((_let_6 (@ tptp.append_node Ns_1))) (let ((_let_7 (@ _let_6 (@ _let_2 tptp.nil_node)))) (=> (= Ns (@ _let_6 (@ (@ tptp.append_node Ns_3) Ns_2))) (=> (@ (@ tptp.prefix_node _let_7) Ns) (=> (@ (@ tptp.suffix_node _let_3) Ns) (=> (@ (@ (@ _let_4 N) _let_7) X) (=> (not (@ _let_1 (@ tptp.set_node2 Ns_1))) (=> (@ (@ _let_5 Ns_3) X) (=> (@ (@ _let_5 _let_3) M) (@ _let_1 (@ tptp.set_node2 Ns_2))))))))))))))))))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (= (@ (@ tptp.prefix_node (@ (@ tptp.append_node Xs) Ys)) Xs) (= Ys tptp.nil_node))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (N2 tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) N) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 Ns)) (not (forall ((Ns3 tptp.list_node)) (let ((_let_1 (@ tptp.set_node2 Ns3))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns3) N) (=> (@ (@ tptp.member_node N2) _let_1) (=> (not (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.tl_node (@ tptp.butlast_node Ns3))))) (not (@ (@ tptp.ord_less_eq_set_node _let_1) (@ tptp.set_node2 Ns)))))))))))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (let ((_let_1 (@ tptp.tl_node Ns))) (let ((_let_2 (@ tptp.hd_node _let_1))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_3 N) Ns) M) (=> (=> (= Ns (@ (@ tptp.cons_node N) tptp.nil_node)) (not (= M N))) (not (=> (@ (@ (@ _let_3 _let_2) _let_1) M) (not (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) _let_2)))))))))))) (forall ((G tptp.g) (Ns tptp.list_node) (N tptp.node) (M tptp.node)) (let ((_let_1 (@ tptp.cons_node N))) (let ((_let_2 (@ tptp.append_node Ns))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_node))) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) M))) (@ _let_3 (@ _let_2 (@ _let_1 (@ (@ tptp.cons_node M) tptp.nil_node)))))))))) (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.finite_finite_val (@ (@ (@ (@ (@ tptp.sSA_CF848637139eD_val tptp.alpha_n) tptp.inEdges) tptp.phis) G) N)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node) (P (-> tptp.node Bool))) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (=> (exists ((X2 tptp.node)) (and (@ (@ tptp.member_node X2) (@ tptp.set_node2 Ns)) (@ P X2))) (not (forall ((N3 tptp.node) (Ns3 tptp.list_node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N3) Ns3) M) (=> (@ P N3) (=> (forall ((X2 tptp.node)) (=> (@ (@ tptp.member_node X2) (@ tptp.set_node2 (@ tptp.tl_node Ns3))) (not (@ P X2)))) (not (@ (@ tptp.suffix_node Ns3) Ns)))))))))) (forall ((G tptp.g) (N tptp.node)) (@ tptp.finite_finite_val (@ (@ tptp.defs G) N))) (forall ((X tptp.list_node)) (@ (@ tptp.prefix_node X) X)) (forall ((A tptp.list_node)) (@ (@ tptp.prefix_node A) A)) (forall ((X tptp.list_node)) (@ (@ tptp.suffix_node X) X)) (forall ((A tptp.list_node)) (@ (@ tptp.suffix_node A) A)) (forall ((G tptp.g) (Ns tptp.list_node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns) (not (= Ns tptp.nil_node)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (=> (@ (@ (@ (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) N) Ns) M) (= N (@ tptp.hd_node Ns)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node) (M tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_1012773594_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ (@ (@ _let_1 N) Ns) M) (@ (@ (@ _let_1 (@ tptp.hd_node Ns)) Ns) M)))) (forall ((G tptp.g) (N tptp.node) (Ns tptp.list_node)) (let ((_let_1 (@ tptp.cons_node N))) (let ((_let_2 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_2 (@ _let_1 Ns)) (@ _let_2 (@ _let_1 tptp.nil_node)))))) (forall ((G tptp.g) (Ns tptp.list_node) (M tptp.node) (Ns2 tptp.list_node)) (let ((_let_1 (@ (@ tptp.cons_node M) Ns2))) (let ((_let_2 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_2 (@ (@ tptp.append_node Ns) _let_1)) (@ _let_2 _let_1))))) (forall ((Xs tptp.list_node)) (@ tptp.finite_finite_node (@ tptp.set_node2 Xs))) (forall ((Xs tptp.list_val)) (@ tptp.finite_finite_val (@ tptp.set_val2 Xs))) (forall ((X tptp.node) (Xs tptp.list_node) (Y tptp.node) (Ys tptp.list_node)) (= (@ (@ tptp.prefix_node (@ (@ tptp.cons_node X) Xs)) (@ (@ tptp.cons_node Y) Ys)) (and (= X Y) (@ (@ tptp.prefix_node Xs) Ys)))) (forall ((Xs tptp.list_node)) (@ (@ tptp.prefix_node tptp.nil_node) Xs)) (forall ((Xs tptp.list_node)) (= (@ (@ tptp.prefix_node Xs) tptp.nil_node) (= Xs tptp.nil_node))) (forall ((A tptp.list_node)) (= (@ (@ tptp.prefix_node A) tptp.nil_node) (= A tptp.nil_node))) (forall ((A tptp.list_node)) (= (@ (@ tptp.suffix_node A) tptp.nil_node) (= A tptp.nil_node))) (forall ((Xs tptp.list_node)) (= (@ (@ tptp.suffix_node Xs) tptp.nil_node) (= Xs tptp.nil_node))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.append_node Xs))) (= (@ (@ tptp.prefix_node (@ _let_1 Ys)) (@ _let_1 Zs)) (@ (@ tptp.prefix_node Ys) Zs)))) (forall ((Ys tptp.list_node) (Xs tptp.list_node) (Zs tptp.list_node)) (= (@ (@ tptp.suffix_node (@ (@ tptp.append_node Ys) Xs)) (@ (@ tptp.append_node Zs) Xs)) (@ (@ tptp.suffix_node Ys) Zs))) (forall ((N tptp.node) (G tptp.g)) (=> (@ (@ tptp.member_node N) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ tptp.invar G) (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) (@ (@ tptp.cons_node N) tptp.nil_node))))) (forall ((G tptp.g) (Ns tptp.list_node) (M tptp.node) (Ns2 tptp.list_node)) (let ((_let_1 (@ tptp.cons_node M))) (let ((_let_2 (@ tptp.append_node Ns))) (let ((_let_3 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_3 (@ _let_2 (@ _let_1 Ns2))) (@ _let_3 (@ _let_2 (@ _let_1 tptp.nil_node)))))))) (forall ((G tptp.g) (Ns tptp.list_node) (N2 tptp.node)) (let ((_let_1 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (=> (@ _let_1 Ns) (=> (@ (@ tptp.member_node N2) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns)))) (@ _let_1 (@ (@ tptp.cons_node N2) Ns)))))) (forall ((G tptp.g) (A tptp.list_node)) (= (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) A) (or (exists ((N5 tptp.node)) (and (= A (@ (@ tptp.cons_node N5) tptp.nil_node)) (@ (@ tptp.member_node N5) (@ tptp.set_node2 (@ tptp.alpha_n G))) (@ tptp.invar G))) (exists ((Ns5 tptp.list_node) (N6 tptp.node)) (and (= A (@ (@ tptp.cons_node N6) Ns5)) (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns5) (@ (@ tptp.member_node N6) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns5))))))))) (forall ((G tptp.g) (X tptp.list_node) (P (-> tptp.list_node Bool))) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) X) (=> (forall ((N4 tptp.node)) (=> (@ (@ tptp.member_node N4) (@ tptp.set_node2 (@ tptp.alpha_n G))) (=> (@ tptp.invar G) (@ P (@ (@ tptp.cons_node N4) tptp.nil_node))))) (=> (forall ((Ns4 tptp.list_node) (N3 tptp.node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns4) (=> (@ P Ns4) (=> (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns4)))) (@ P (@ (@ tptp.cons_node N3) Ns4)))))) (@ P X))))) (forall ((G tptp.g) (A tptp.list_node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) A) (=> (forall ((N4 tptp.node)) (=> (= A (@ (@ tptp.cons_node N4) tptp.nil_node)) (=> (@ (@ tptp.member_node N4) (@ tptp.set_node2 (@ tptp.alpha_n G))) (not (@ tptp.invar G))))) (not (forall ((Ns4 tptp.list_node) (N3 tptp.node)) (=> (= A (@ (@ tptp.cons_node N3) Ns4)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns4) (not (@ (@ tptp.member_node N3) (@ tptp.set_node2 (@ (@ (@ tptp.graph_272749361_edgeD tptp.inEdges) G) (@ tptp.hd_node Ns4)))))))))))) (forall ((Ys tptp.list_node) (Xs tptp.list_node)) (= (@ (@ tptp.suffix_node (@ (@ tptp.append_node Ys) Xs)) Xs) (= Ys tptp.nil_node))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (= (@ tptp.hd_node (@ (@ tptp.append_node Xs) Ys)) (@ tptp.hd_node Xs)))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (= (@ (@ tptp.suffix_node Xs) (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node))) (or (= Xs tptp.nil_node) (exists ((Zs3 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Zs3) (@ (@ tptp.cons_node Y) tptp.nil_node))) (@ (@ tptp.suffix_node Zs3) Ys)))))) (forall ((Xs tptp.list_node) (X tptp.node) (Ys tptp.list_node) (Y tptp.node)) (= (@ (@ tptp.suffix_node (@ (@ tptp.append_node Xs) (@ (@ tptp.cons_node X) tptp.nil_node))) (@ (@ tptp.append_node Ys) (@ (@ tptp.cons_node Y) tptp.nil_node))) (and (= X Y) (@ (@ tptp.suffix_node Xs) Ys)))) (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (= (@ (@ tptp.cons_node (@ tptp.hd_node Xs)) (@ tptp.tl_node Xs)) Xs))) (forall ((List tptp.list_node)) (=> (not (= List tptp.nil_node)) (= (@ (@ tptp.cons_node (@ tptp.hd_node List)) (@ tptp.tl_node List)) List))) (forall ((L tptp.list_val) (X tptp.val)) (let ((_let_1 (@ tptp.member_val X))) (=> (not (= L tptp.nil_val)) (= (or (= X (@ tptp.hd_val L)) (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val L)))) (@ _let_1 (@ tptp.set_val2 L)))))) (forall ((L tptp.list_node) (X tptp.node)) (let ((_let_1 (@ tptp.member_node X))) (=> (not (= L tptp.nil_node)) (= (or (= X (@ tptp.hd_node L)) (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node L)))) (@ _let_1 (@ tptp.set_node2 L)))))) (forall ((G tptp.g) (Ns tptp.list_node)) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns) (@ tptp.invar G))) (forall ((G tptp.g) (Ns tptp.list_node) (N tptp.node)) (let ((_let_1 (@ tptp.member_node N))) (=> (@ (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G) Ns) (=> (@ _let_1 (@ tptp.set_node2 Ns)) (@ _let_1 (@ tptp.set_node2 (@ tptp.alpha_n G))))))) (forall ((G tptp.g) (N tptp.node) (N2 tptp.node) (Ns tptp.list_node) (Ms tptp.list_node)) (let ((_let_1 (@ tptp.cons_node N2))) (let ((_let_2 (@ _let_1 Ms))) (let ((_let_3 (@ tptp.cons_node N))) (let ((_let_4 (@ (@ (@ (@ tptp.graph_435229452_edgeD tptp.alpha_n) tptp.invar) tptp.inEdges) G))) (let ((_let_5 (@ _let_1 Ns))) (=> (@ _let_4 (@ _let_3 _let_5)) (=> (=> (@ _let_4 _let_5) (@ _let_4 _let_2)) (@ _let_4 (@ _let_3 _let_2)))))))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node Xs) Ys) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) (@ tptp.set_node2 Ys)))) (forall ((S tptp.set_node) (P (-> tptp.node Bool))) (= (@ (@ tptp.ord_less_eq_set_node S) (@ tptp.collect_node P)) (forall ((X3 tptp.node)) (=> (@ (@ tptp.member_node X3) S) (@ P X3))))) (forall ((A tptp.set_node) (B tptp.set_node) (C tptp.set_node) (D tptp.set_node)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_node B) C) (=> (= C D) (@ (@ tptp.ord_less_eq_set_node A) D))))) (forall ((X tptp.node) (Xs tptp.list_node) (Y tptp.node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node (@ (@ tptp.cons_node X) Xs)) (@ (@ tptp.cons_node Y) Ys)) (@ (@ tptp.suffix_node Xs) Ys))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Y tptp.node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.cons_node Y) Ys))))) (forall ((X tptp.node) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node (@ (@ tptp.cons_node X) Xs)) Ys) (@ (@ tptp.suffix_node Xs) Ys))) (forall ((Xs tptp.list_node) (Y tptp.node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (let ((_let_2 (@ (@ tptp.cons_node Y) Ys))) (= (@ _let_1 _let_2) (or (= Xs _let_2) (@ _let_1 Ys)))))) (forall ((A tptp.list_node)) (=> (@ (@ tptp.suffix_node A) tptp.nil_node) (= A tptp.nil_node))) (forall ((A tptp.list_node)) (@ (@ tptp.suffix_node tptp.nil_node) A)) (forall ((Xs tptp.list_node)) (@ (@ tptp.suffix_node tptp.nil_node) Xs)) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node Xs) Ys) (not (forall ((Zs2 tptp.list_node)) (not (= Ys (@ (@ tptp.append_node Zs2) Xs))))))) (forall ((Ys tptp.list_node) (Zs tptp.list_node) (Xs tptp.list_node)) (=> (= Ys (@ (@ tptp.append_node Zs) Xs)) (@ (@ tptp.suffix_node Xs) Ys))) (= tptp.suffix_node (lambda ((Xs3 tptp.list_node) (Ys3 tptp.list_node)) (exists ((Zs3 tptp.list_node)) (= Ys3 (@ (@ tptp.append_node Zs3) Xs3))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (= (@ _let_1 (@ (@ tptp.append_node Ys) Zs)) (or (@ _let_1 Zs) (exists ((Xs5 tptp.list_node)) (and (= Xs (@ (@ tptp.append_node Xs5) Zs)) (@ (@ tptp.suffix_node Xs5) Ys))))))) (forall ((Zs tptp.list_node) (Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.suffix_node (@ (@ tptp.append_node Zs) Xs)) Ys) (@ (@ tptp.suffix_node Xs) Ys))) (forall ((Xs tptp.list_node) (Ys tptp.list_node) (Zs tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs))) (=> (@ _let_1 Ys) (@ _let_1 (@ (@ tptp.append_node Zs) Ys))))) (forall ((Xs tptp.list_node)) (@ (@ tptp.suffix_node (@ tptp.tl_node Xs)) Xs)) (forall ((Xs_1 tptp.list_node) (Ys tptp.list_node) (Xs_2 tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node Xs_2))) (let ((_let_2 (@ tptp.suffix_node Xs_1))) (=> (@ _let_2 Ys) (=> (@ _let_1 Ys) (or (@ _let_2 Xs_2) (@ _let_1 Xs_1))))))) (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((X3 tptp.list_node) (Y3 tptp.list_node)) (and (@ (@ tptp.suffix_node X3) Y3) (@ (@ tptp.suffix_node Y3) X3)))) (forall ((X tptp.list_node) (Y tptp.list_node)) (=> (@ (@ tptp.suffix_node X) Y) (=> (@ (@ tptp.suffix_node Y) X) (= X Y)))) (forall ((X tptp.list_node) (Y tptp.list_node)) (=> (= X Y) (@ (@ tptp.suffix_node X) Y))) (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node A))) (=> (@ _let_1 B) (=> (@ (@ tptp.suffix_node B) C) (@ _let_1 C))))) (forall ((X tptp.list_node) (Y tptp.list_node) (Z3 tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.suffix_node Y) Z3) (@ _let_1 Z3))))) (forall ((Y tptp.list_node) (X tptp.list_node)) (=> (@ (@ tptp.suffix_node Y) X) (= (@ (@ tptp.suffix_node X) Y) (= X Y)))) (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((A4 tptp.list_node) (B3 tptp.list_node)) (and (@ (@ tptp.suffix_node A4) B3) (@ (@ tptp.suffix_node B3) A4)))) (forall ((A tptp.list_node) (B tptp.list_node)) (=> (@ (@ tptp.suffix_node A) B) (=> (@ (@ tptp.suffix_node B) A) (= A B)))) (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (=> (= A B) (=> (@ (@ tptp.suffix_node B) C) (@ (@ tptp.suffix_node A) C)))) (forall ((A tptp.list_node) (B tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((B tptp.list_node) (A tptp.list_node) (C tptp.list_node)) (let ((_let_1 (@ tptp.suffix_node C))) (=> (@ (@ tptp.suffix_node B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((A4 tptp.list_node) (B3 tptp.list_node)) (and (@ (@ tptp.suffix_node B3) A4) (@ (@ tptp.suffix_node A4) B3)))) (forall ((B tptp.list_node) (A tptp.list_node)) (=> (@ (@ tptp.suffix_node B) A) (=> (@ (@ tptp.suffix_node A) B) (= A B)))) (forall ((X21 tptp.node) (X22 tptp.list_node)) (= (@ tptp.hd_node (@ (@ tptp.cons_node X21) X22)) X21)) (forall ((A2 tptp.set_node)) (=> (@ tptp.finite_finite_node A2) (exists ((Xs2 tptp.list_node)) (= (@ tptp.set_node2 Xs2) A2)))) (forall ((A2 tptp.set_val)) (=> (@ tptp.finite_finite_val A2) (exists ((Xs2 tptp.list_val)) (= (@ tptp.set_val2 Xs2) A2)))) (forall ((Xs tptp.list_val) (B4 tptp.set_val)) (= (@ (@ tptp.ord_less_eq_set_val (@ tptp.set_val2 Xs)) B4) (forall ((X3 tptp.val)) (let ((_let_1 (@ tptp.member_val X3))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 B4)))))) (forall ((Xs tptp.list_node) (B4 tptp.set_node)) (= (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) B4) (forall ((X3 tptp.node)) (let ((_let_1 (@ tptp.member_node X3))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 B4)))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (=> (@ (@ tptp.prefix_node Xs) Ys) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) (@ tptp.set_node2 Ys)))) (forall ((A tptp.list_val)) (=> (not (= A tptp.nil_val)) (@ (@ tptp.member_val (@ tptp.hd_val A)) (@ tptp.set_val2 A)))) (forall ((A tptp.list_node)) (=> (not (= A tptp.nil_node)) (@ (@ tptp.member_node (@ tptp.hd_node A)) (@ tptp.set_node2 A)))) (forall ((Xs tptp.list_val)) (=> (not (= Xs tptp.nil_val)) (@ (@ tptp.member_val (@ tptp.hd_val Xs)) (@ tptp.set_val2 Xs)))) (forall ((Xs tptp.list_node)) (=> (not (= Xs tptp.nil_node)) (@ (@ tptp.member_node (@ tptp.hd_node Xs)) (@ tptp.set_node2 Xs)))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (let ((_let_1 (@ tptp.hd_node (@ (@ tptp.append_node Xs) Ys)))) (let ((_let_2 (= Xs tptp.nil_node))) (and (=> _let_2 (= _let_1 (@ tptp.hd_node Ys))) (=> (not _let_2) (= _let_1 (@ tptp.hd_node Xs))))))) (forall ((Xs tptp.list_node) (Ys tptp.list_node)) (exists ((Ps tptp.list_node) (Xs6 tptp.list_node) (Ys4 tptp.list_node)) (let ((_let_1 (@ tptp.append_node Ps))) (and (= Xs (@ _let_1 Xs6)) (= Ys (@ _let_1 Ys4)) (or (= Xs6 tptp.nil_node) (= Ys4 tptp.nil_node) (not (= (@ tptp.hd_node Xs6) (@ tptp.hd_node Ys4)))))))) (forall ((Ps2 tptp.list_node) (Ls tptp.list_node)) (=> (not (@ (@ tptp.suffix_node Ps2) Ls)) (=> (=> (not (= Ps2 tptp.nil_node)) (not (= Ls tptp.nil_node))) (=> (forall ((A3 tptp.node) (As tptp.list_node)) (=> (= Ps2 (@ (@ tptp.append_node As) (@ (@ tptp.cons_node A3) tptp.nil_node))) (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (=> (= Ls (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (=> (= X4 A3) (@ (@ tptp.suffix_node As) Xs2)))))) (not (forall ((A3 tptp.node)) (=> (exists ((As tptp.list_node)) (= Ps2 (@ (@ tptp.append_node As) (@ (@ tptp.cons_node A3) tptp.nil_node)))) (forall ((X4 tptp.node)) (=> (exists ((Xs2 tptp.list_node)) (= Ls (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node)))) (= X4 A3)))))))))) (forall ((Ps2 tptp.list_node) (Ls tptp.list_node) (P (-> tptp.list_node tptp.list_node Bool))) (=> (not (@ (@ tptp.suffix_node Ps2) Ls)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) tptp.nil_node)) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (not (= X4 Y2)) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))) (=> (forall ((X4 tptp.node) (Xs2 tptp.list_node) (Y2 tptp.node) (Ys2 tptp.list_node)) (=> (= X4 Y2) (=> (not (@ (@ tptp.suffix_node Xs2) Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.append_node Xs2) (@ (@ tptp.cons_node X4) tptp.nil_node))) (@ (@ tptp.append_node Ys2) (@ (@ tptp.cons_node Y2) tptp.nil_node))))))) (@ (@ P Ps2) Ls)))))) (forall ((List tptp.list_node) (List2 tptp.list_node)) (let ((_let_1 (= List2 tptp.nil_node))) (let ((_let_2 (= List tptp.nil_node))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_node List) (@ tptp.hd_node List2)) (= (@ tptp.tl_node List) (@ tptp.tl_node List2))))) (= List List2)))))) (forall ((X tptp.val) (Xs tptp.list_val)) (let ((_let_1 (@ tptp.member_val X))) (=> (not (= X (@ tptp.hd_val Xs))) (=> (@ _let_1 (@ tptp.set_val2 Xs)) (@ _let_1 (@ tptp.set_val2 (@ tptp.tl_val Xs))))))) (forall ((X tptp.node) (Xs tptp.list_node)) (let ((_let_1 (@ tptp.member_node X))) (=> (not (= X (@ tptp.hd_node Xs))) (=> (@ _let_1 (@ tptp.set_node2 Xs)) (@ _let_1 (@ tptp.set_node2 (@ tptp.tl_node Xs))))))) (forall ((Xs tptp.list_node) (X tptp.node)) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) (@ tptp.set_node2 (@ (@ tptp.cons_node X) Xs)))) (forall ((List tptp.list_node)) (=> (not (= List tptp.nil_node)) (= List (@ (@ tptp.cons_node (@ tptp.hd_node List)) (@ tptp.tl_node List))))) (forall ((Xs tptp.list_node) (A2 tptp.set_node)) (=> (not (= Xs tptp.nil_node)) (=> (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) A2) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 (@ tptp.tl_node Xs))) A2)))) (forall ((Xs tptp.list_node) (A2 tptp.set_node)) (=> (not (= Xs tptp.nil_node)) (=> (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 Xs)) A2) (@ (@ tptp.ord_less_eq_set_node (@ tptp.set_node2 (@ tptp.butlast_node Xs))) A2)))) (forall ((Xs_1 tptp.list_node) (Ys tptp.list_node) (Xs_2 tptp.list_node)) (let ((_let_1 (@ tptp.prefix_node Xs_2))) (let ((_let_2 (@ tptp.prefix_node Xs_1))) (=> (@ _let_2 Ys) (=> (@ _let_1 Ys) (or (@ _let_2 Xs_2) (@ _let_1 Xs_1))))))) (= (lambda ((Y4 tptp.list_node) (Z tptp.list_node)) (= Y4 Z)) (lambda ((X3 tptp.list_node) (Y3 tptp.list_node)) (and (@ (@ tptp.prefix_node X3) Y3) (@ (@ tptp.prefix_node Y3) X3)))) (forall ((X tptp.list_node) (Y tptp.list_node)) (=> (@ (@ tptp.prefix_node X) Y) (=> (@ (@ tptp.prefix_node Y) X) (= X Y)))) _let_5 true))))))))))))))))))))))))))))))))))
% 0.72/0.97 )
% 0.72/0.97 % SZS output end Proof for ITP081^1
% 0.72/0.97 % cvc5---1.0.5 exiting
% 0.72/0.97 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------