%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO858^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 : Wed Feb 25 09:54:55 AM UTC 2026
% Result : Theorem 9.46s 2.78s
% Output : Refutation 9.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO858^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:48:57 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.45 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SYO858^1 : TPTP v9.2.1. Released v7.5.0.
% 0.27/0.46 % Domain : Syntactic
% 0.27/0.46 % Problem : ProofGold problem HOUnif_141_pos_th0
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Urb20]
% 0.27/0.46 % Names : HOUnif_141_pos_th0.p [Urb20]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.44 v9.1.0, 0.50 v9.0.0, 0.70 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0
% 0.27/0.46 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.27/0.46 % Number of atoms : 488 ( 143 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 9 ( 4 avg)
% 0.27/0.46 % Number of connectives : 1259 ( 0 ~; 0 |; 0 &;1162 @)
% 0.27/0.46 % ( 0 <=>; 97 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 17 ( 2 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 700 ( 700 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.27/0.46 % Number of variables : 536 ( 370 ^; 129 !; 37 ?; 536 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : See https://proofgold.org
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(c_Eps_i_tp,type,
% 0.27/0.46 c_Eps_i: ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_False_tp,type,
% 0.27/0.46 c_False: $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_True_tp,type,
% 0.27/0.46 c_True: $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_not_tp,type,
% 0.27/0.46 c_not: $o > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_and_tp,type,
% 0.27/0.46 c_and: $o > $o > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_or_tp,type,
% 0.27/0.46 c_or: $o > $o > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_iff_tp,type,
% 0.27/0.46 c_iff: $o > $o > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_In_tp,type,
% 0.27/0.46 c_In: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Subq_tp,type,
% 0.27/0.46 c_Subq: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Empty_tp,type,
% 0.27/0.46 c_Empty: $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Union_tp,type,
% 0.27/0.46 c_Union: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Power_tp,type,
% 0.27/0.46 c_Power: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Repl_tp,type,
% 0.27/0.46 c_Repl: $i > ( $i > $i ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_TransSet_tp,type,
% 0.27/0.46 c_TransSet: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_atleast2_tp,type,
% 0.27/0.46 c_atleast2: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_atleast3_tp,type,
% 0.27/0.46 c_atleast3: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_atleast4_tp,type,
% 0.27/0.46 c_atleast4: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_atleast5_tp,type,
% 0.27/0.46 c_atleast5: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_atleast6_tp,type,
% 0.27/0.46 c_atleast6: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_exactly2_tp,type,
% 0.27/0.46 c_exactly2: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_exactly3_tp,type,
% 0.27/0.46 c_exactly3: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_exactly4_tp,type,
% 0.27/0.46 c_exactly4: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_exactly5_tp,type,
% 0.27/0.46 c_exactly5: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_exu_i_tp,type,
% 0.27/0.46 c_exu_i: ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_reflexive_i_tp,type,
% 0.27/0.46 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_irreflexive_i_tp,type,
% 0.27/0.46 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_symmetric_i_tp,type,
% 0.27/0.46 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_antisymmetric_i_tp,type,
% 0.27/0.46 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_transitive_i_tp,type,
% 0.27/0.46 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_eqreln_i_tp,type,
% 0.27/0.46 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_per_i_tp,type,
% 0.27/0.46 c_per_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_linear_i_tp,type,
% 0.27/0.46 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_trichotomous_or_i_tp,type,
% 0.27/0.46 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_partialorder_i_tp,type,
% 0.27/0.46 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_totalorder_i_tp,type,
% 0.27/0.46 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_strictpartialorder_i_tp,type,
% 0.27/0.46 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_stricttotalorder_i_tp,type,
% 0.27/0.46 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_If_i_tp,type,
% 0.27/0.46 c_If_i: $o > $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_exactly1of2_tp,type,
% 0.27/0.46 c_exactly1of2: $o > $o > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_exactly1of3_tp,type,
% 0.27/0.46 c_exactly1of3: $o > $o > $o > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_nIn_tp,type,
% 0.27/0.46 c_nIn: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_nSubq_tp,type,
% 0.27/0.46 c_nSubq: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_UPair_tp,type,
% 0.27/0.46 c_UPair: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Sing_tp,type,
% 0.27/0.46 c_Sing: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_binunion_tp,type,
% 0.27/0.46 c_binunion: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_SetAdjoin_tp,type,
% 0.27/0.46 c_SetAdjoin: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_famunion_tp,type,
% 0.27/0.46 c_famunion: $i > ( $i > $i ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Sep_tp,type,
% 0.27/0.46 c_Sep: $i > ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_ReplSep_tp,type,
% 0.27/0.46 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_binintersect_tp,type,
% 0.27/0.46 c_binintersect: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_setminus_tp,type,
% 0.27/0.46 c_setminus: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_inj_tp,type,
% 0.27/0.46 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_bij_tp,type,
% 0.27/0.46 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_atleastp_tp,type,
% 0.27/0.46 c_atleastp: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_equip_tp,type,
% 0.27/0.46 c_equip: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_In_rec_poly_G_i_tp,type,
% 0.27/0.46 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_In_rec_poly_i_tp,type,
% 0.27/0.46 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_ordsucc_tp,type,
% 0.27/0.46 c_ordsucc: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_nat_p_tp,type,
% 0.27/0.46 c_nat_p: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_nat_primrec_tp,type,
% 0.27/0.46 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_add_nat_tp,type,
% 0.27/0.46 c_add_nat: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_mul_nat_tp,type,
% 0.27/0.46 c_mul_nat: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_ordinal_tp,type,
% 0.27/0.46 c_ordinal: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_V__tp,type,
% 0.27/0.46 c_V_: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Inj1_tp,type,
% 0.27/0.46 c_Inj1: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Inj0_tp,type,
% 0.27/0.46 c_Inj0: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Unj_tp,type,
% 0.27/0.46 c_Unj: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_combine_funcs_tp,type,
% 0.27/0.46 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_setsum_tp,type,
% 0.27/0.46 c_setsum: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_proj0_tp,type,
% 0.27/0.46 c_proj0: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_proj1_tp,type,
% 0.27/0.46 c_proj1: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_binrep_tp,type,
% 0.27/0.46 c_binrep: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_lam_tp,type,
% 0.27/0.46 c_lam: $i > ( $i > $i ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_setprod_tp,type,
% 0.27/0.46 c_setprod: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_ap_tp,type,
% 0.27/0.46 c_ap: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_setsum_p_tp,type,
% 0.27/0.46 c_setsum_p: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_tuple_p_tp,type,
% 0.27/0.46 c_tuple_p: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Pi_tp,type,
% 0.27/0.46 c_Pi: $i > ( $i > $i ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_setexp_tp,type,
% 0.27/0.46 c_setexp: $i > $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_Sep2_tp,type,
% 0.27/0.46 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_set_of_pairs_tp,type,
% 0.27/0.46 c_set_of_pairs: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_lam2_tp,type,
% 0.27/0.46 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_PNoEq__tp,type,
% 0.27/0.46 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_PNoLt__tp,type,
% 0.27/0.46 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_PNoLt_tp,type,
% 0.27/0.46 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_PNoLe_tp,type,
% 0.27/0.46 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_PNo_downc_tp,type,
% 0.27/0.46 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_PNo_upc_tp,type,
% 0.27/0.46 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNoElts__tp,type,
% 0.27/0.46 c_SNoElts_: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNo__tp,type,
% 0.27/0.46 c_SNo_: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_PSNo_tp,type,
% 0.27/0.46 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNo_tp,type,
% 0.27/0.46 c_SNo: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNoLev_tp,type,
% 0.27/0.46 c_SNoLev: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNoEq__tp,type,
% 0.27/0.46 c_SNoEq_: $i > $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNoLt_tp,type,
% 0.27/0.46 c_SNoLt: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_SNoLe_tp,type,
% 0.27/0.46 c_SNoLe: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_binop_on_tp,type,
% 0.27/0.46 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Loop_tp,type,
% 0.27/0.46 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Loop_with_defs_tp,type,
% 0.27/0.46 c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Loop_with_defs_cex1_tp,type,
% 0.27/0.46 c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_Loop_with_defs_cex2_tp,type,
% 0.27/0.46 c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_combinator_tp,type,
% 0.27/0.46 c_combinator: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_combinator_equiv_tp,type,
% 0.27/0.46 c_combinator_equiv: $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(c_equip_mod_tp,type,
% 0.27/0.46 c_equip_mod: $i > $i > $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(ax1,axiom,
% 0.27/0.46 ! [X0: $i > $o,X1: $i] :
% 0.27/0.46 ( ( X0 @ X1 )
% 0.27/0.46 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax2,axiom,
% 0.27/0.46 ! [X0: $o] :
% 0.27/0.46 ( ( c_not @ ( c_not @ X0 ) )
% 0.27/0.46 => X0 ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax3,axiom,
% 0.27/0.46 ! [X0: $o,X1: $o] :
% 0.27/0.46 ( ( c_iff @ X0 @ X1 )
% 0.27/0.46 => ( X0 = X1 ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax4,axiom,
% 0.27/0.46 ! [X0: $i,X1: $i] :
% 0.27/0.46 ( ( c_Subq @ X0 @ X1 )
% 0.27/0.46 => ( ( c_Subq @ X1 @ X0 )
% 0.27/0.46 => ( X0 = X1 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax5,axiom,
% 0.27/0.46 ( c_not
% 0.27/0.46 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax6,axiom,
% 0.27/0.46 ! [X0: $i,X1: $i] :
% 0.27/0.46 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.27/0.46 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax7,axiom,
% 0.27/0.46 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax8,axiom,
% 0.27/0.46 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.27/0.46 ( c_iff
% 0.27/0.46 @ ( c_In @ X2
% 0.27/0.46 @ ( c_Repl @ X0
% 0.27/0.46 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.27/0.46 @ ? [X3: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X3 @ X0 )
% 0.27/0.46 @ ( X2
% 0.27/0.46 = ( X1 @ X3 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax9,axiom,
% 0.27/0.46 ! [X0: $i > $o] :
% 0.27/0.46 ( ! [X1: $i] :
% 0.27/0.46 ( ( X0 @ X1 )
% 0.27/0.46 => ! [X2: $i] :
% 0.27/0.46 ( ( c_In @ X2 @ X1 )
% 0.27/0.46 => ( X0 @ X2 ) ) )
% 0.27/0.46 => ( ( X0 @ c_Empty )
% 0.27/0.46 => ( ! [X1: $i] :
% 0.27/0.46 ( ( X0 @ X1 )
% 0.27/0.46 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.27/0.46 => ( ! [X1: $i] :
% 0.27/0.46 ( ( X0 @ X1 )
% 0.27/0.46 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.27/0.46 => ( ! [X1: $i] :
% 0.27/0.46 ( ( X0 @ X1 )
% 0.27/0.46 => ! [X2: $i > $i] :
% 0.27/0.46 ( ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X1 )
% 0.27/0.46 => ( X0 @ ( X2 @ X3 ) ) )
% 0.27/0.46 => ( X0
% 0.27/0.46 @ ( c_Repl @ X1
% 0.27/0.46 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.27/0.46 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax10,axiom,
% 0.27/0.46 ! [X0: $i > $o] :
% 0.27/0.46 ( ! [X1: $i] :
% 0.27/0.46 ( ! [X2: $i] :
% 0.27/0.46 ( ( c_In @ X2 @ X1 )
% 0.27/0.46 => ( X0 @ X2 ) )
% 0.27/0.46 => ( X0 @ X1 ) )
% 0.27/0.46 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax11,axiom,
% 0.27/0.46 ( c_False
% 0.27/0.46 = ( ! [X0: $o] : X0 ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax12,axiom,
% 0.27/0.46 ( c_True
% 0.27/0.46 = ( ! [X0: $o] :
% 0.27/0.46 ( X0
% 0.27/0.46 => X0 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax13,axiom,
% 0.27/0.46 ( c_not
% 0.27/0.46 = ( ^ [X0: $o] :
% 0.27/0.46 ( X0
% 0.27/0.46 => c_False ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax14,axiom,
% 0.27/0.46 ( c_and
% 0.27/0.46 = ( ^ [X0: $o,X1: $o] :
% 0.27/0.46 ! [X2: $o] :
% 0.27/0.46 ( ( X0
% 0.27/0.46 => ( X1
% 0.27/0.46 => X2 ) )
% 0.27/0.46 => X2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax15,axiom,
% 0.27/0.46 ( c_or
% 0.27/0.46 = ( ^ [X0: $o,X1: $o] :
% 0.27/0.46 ! [X2: $o] :
% 0.27/0.46 ( ( X0
% 0.27/0.46 => X2 )
% 0.27/0.46 => ( ( X1
% 0.27/0.46 => X2 )
% 0.27/0.46 => X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax16,axiom,
% 0.27/0.46 ( c_iff
% 0.27/0.46 = ( ^ [X0: $o,X1: $o] :
% 0.27/0.46 ( c_and
% 0.27/0.46 @ ( X0
% 0.27/0.46 => X1 )
% 0.27/0.46 @ ( X1
% 0.27/0.46 => X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax17,axiom,
% 0.27/0.46 ( c_Subq
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ! [X2: $i] :
% 0.27/0.46 ( ( c_In @ X2 @ X0 )
% 0.27/0.46 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax18,axiom,
% 0.27/0.46 ( c_TransSet
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ! [X1: $i] :
% 0.27/0.46 ( ( c_In @ X1 @ X0 )
% 0.27/0.46 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax19,axiom,
% 0.27/0.46 ( c_atleast2
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax20,axiom,
% 0.27/0.46 ( c_atleast3
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax21,axiom,
% 0.27/0.46 ( c_atleast4
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax22,axiom,
% 0.27/0.46 ( c_atleast5
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax23,axiom,
% 0.27/0.46 ( c_atleast6
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax24,axiom,
% 0.27/0.46 ( c_exactly2
% 0.27/0.46 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax25,axiom,
% 0.27/0.46 ( c_exactly3
% 0.27/0.46 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax26,axiom,
% 0.27/0.46 ( c_exactly4
% 0.27/0.46 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax27,axiom,
% 0.27/0.46 ( c_exactly5
% 0.27/0.46 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax28,axiom,
% 0.27/0.46 ( c_exu_i
% 0.27/0.46 = ( ^ [X0: $i > $o] :
% 0.27/0.46 ( c_and
% 0.27/0.46 @ ? [X1: $i] : ( X0 @ X1 )
% 0.27/0.46 @ ! [X1: $i,X2: $i] :
% 0.27/0.46 ( ( X0 @ X1 )
% 0.27/0.46 => ( ( X0 @ X2 )
% 0.27/0.46 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax29,axiom,
% 0.27/0.46 ( c_reflexive_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax30,axiom,
% 0.27/0.46 ( c_irreflexive_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax31,axiom,
% 0.27/0.46 ( c_symmetric_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i,X2: $i] :
% 0.27/0.46 ( ( X0 @ X1 @ X2 )
% 0.27/0.46 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax32,axiom,
% 0.27/0.46 ( c_antisymmetric_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i,X2: $i] :
% 0.27/0.46 ( ( X0 @ X1 @ X2 )
% 0.27/0.46 => ( ( X0 @ X2 @ X1 )
% 0.27/0.46 => ( X1 = X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax33,axiom,
% 0.27/0.46 ( c_transitive_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i,X2: $i,X3: $i] :
% 0.27/0.46 ( ( X0 @ X1 @ X2 )
% 0.27/0.46 => ( ( X0 @ X2 @ X3 )
% 0.27/0.46 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax34,axiom,
% 0.27/0.46 ( c_eqreln_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax35,axiom,
% 0.27/0.46 ( c_per_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax36,axiom,
% 0.27/0.46 ( c_linear_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax37,axiom,
% 0.27/0.46 ( c_trichotomous_or_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] :
% 0.27/0.46 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax38,axiom,
% 0.27/0.46 ( c_partialorder_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax39,axiom,
% 0.27/0.46 ( c_totalorder_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax40,axiom,
% 0.27/0.46 ( c_strictpartialorder_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax41,axiom,
% 0.27/0.46 ( c_stricttotalorder_i
% 0.27/0.46 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax42,axiom,
% 0.27/0.46 ( c_If_i
% 0.27/0.46 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.27/0.46 ( c_Eps_i
% 0.27/0.46 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax43,axiom,
% 0.27/0.46 ( c_exactly1of2
% 0.27/0.46 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax44,axiom,
% 0.27/0.46 ( c_exactly1of3
% 0.27/0.46 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax45,axiom,
% 0.27/0.46 ( c_nIn
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax46,axiom,
% 0.27/0.46 ( c_nSubq
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax47,axiom,
% 0.27/0.46 ( c_UPair
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.27/0.46 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax48,axiom,
% 0.27/0.46 ( c_Sing
% 0.27/0.46 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax49,axiom,
% 0.27/0.46 ( c_binunion
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax50,axiom,
% 0.27/0.46 ( c_SetAdjoin
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax51,axiom,
% 0.27/0.46 ( c_famunion
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i] :
% 0.27/0.46 ( c_Union
% 0.27/0.46 @ ( c_Repl @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax52,axiom,
% 0.27/0.46 ( c_Sep
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o] :
% 0.27/0.46 ( c_If_i
% 0.27/0.46 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.27/0.46 @ ( c_Repl @ X0
% 0.27/0.46 @ ^ [X2: $i] :
% 0.27/0.46 ( ^ [X3: $i] :
% 0.27/0.46 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.27/0.46 @ ( c_Eps_i
% 0.27/0.46 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.27/0.46 @ X2 ) )
% 0.27/0.46 @ c_Empty ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax53,axiom,
% 0.27/0.46 ( c_ReplSep
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.27/0.46 ( c_Repl
% 0.27/0.46 @ ( c_Sep @ X0
% 0.27/0.46 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.27/0.46 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax54,axiom,
% 0.27/0.46 ( c_binintersect
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_Sep @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax55,axiom,
% 0.27/0.46 ( c_setminus
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_Sep @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax56,axiom,
% 0.27/0.46 ( c_inj
% 0.27/0.46 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.27/0.46 ( c_and
% 0.27/0.46 @ ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X0 )
% 0.27/0.46 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.27/0.46 @ ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X0 )
% 0.27/0.46 => ! [X4: $i] :
% 0.27/0.46 ( ( c_In @ X4 @ X0 )
% 0.27/0.46 => ( ( ( X2 @ X3 )
% 0.27/0.46 = ( X2 @ X4 ) )
% 0.27/0.46 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax57,axiom,
% 0.27/0.46 ( c_bij
% 0.27/0.46 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.27/0.46 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.27/0.46 @ ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X1 )
% 0.27/0.46 => ? [X4: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X4 @ X0 )
% 0.27/0.46 @ ( ( X2 @ X4 )
% 0.27/0.46 = X3 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax58,axiom,
% 0.27/0.46 ( c_atleastp
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax59,axiom,
% 0.27/0.46 ( c_equip
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax60,axiom,
% 0.27/0.46 ( c_In_rec_poly_G_i
% 0.27/0.46 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.27/0.46 ! [X3: $i > $i > $o] :
% 0.27/0.46 ( ! [X4: $i,X5: $i > $i] :
% 0.27/0.46 ( ! [X6: $i] :
% 0.27/0.46 ( ( c_In @ X6 @ X4 )
% 0.27/0.46 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.27/0.46 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.27/0.46 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax61,axiom,
% 0.27/0.46 ( c_In_rec_poly_i
% 0.27/0.46 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.27/0.46 ( c_Eps_i
% 0.27/0.46 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax62,axiom,
% 0.27/0.46 ( c_ordsucc
% 0.27/0.46 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax63,axiom,
% 0.27/0.46 ( c_nat_p
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ! [X1: $i > $o] :
% 0.27/0.46 ( ( X1 @ c_Empty )
% 0.27/0.46 => ( ! [X2: $i] :
% 0.27/0.46 ( ( X1 @ X2 )
% 0.27/0.46 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.27/0.46 => ( X1 @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax64,axiom,
% 0.27/0.46 ( c_nat_primrec
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.27/0.46 ( c_In_rec_poly_i
% 0.27/0.46 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax65,axiom,
% 0.27/0.46 ( c_add_nat
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_nat_primrec @ X0
% 0.27/0.46 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.27/0.46 @ X1 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax66,axiom,
% 0.27/0.46 ( c_mul_nat
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_nat_primrec @ c_Empty
% 0.27/0.46 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.27/0.46 @ X1 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax67,axiom,
% 0.27/0.46 ( c_ordinal
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( c_and @ ( c_TransSet @ X0 )
% 0.27/0.46 @ ! [X1: $i] :
% 0.27/0.46 ( ( c_In @ X1 @ X0 )
% 0.27/0.46 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax68,axiom,
% 0.27/0.46 ( c_V_
% 0.27/0.46 = ( c_In_rec_poly_i
% 0.27/0.46 @ ^ [X0: $i,X1: $i > $i] :
% 0.27/0.46 ( c_famunion @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax69,axiom,
% 0.27/0.46 ( c_Inj1
% 0.27/0.46 = ( c_In_rec_poly_i
% 0.27/0.46 @ ^ [X0: $i,X1: $i > $i] :
% 0.27/0.46 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.27/0.46 @ ( c_Repl @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax70,axiom,
% 0.27/0.46 ( c_Inj0
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( c_Repl @ X0
% 0.27/0.46 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax71,axiom,
% 0.27/0.46 ( c_Unj
% 0.27/0.46 = ( c_In_rec_poly_i
% 0.27/0.46 @ ^ [X0: $i,X1: $i > $i] :
% 0.27/0.46 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.27/0.46 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax72,axiom,
% 0.27/0.46 ( c_combine_funcs
% 0.27/0.46 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.27/0.46 ( c_If_i
% 0.27/0.46 @ ( X4
% 0.27/0.46 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.27/0.46 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.27/0.46 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax73,axiom,
% 0.27/0.46 ( c_setsum
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_binunion
% 0.27/0.46 @ ( c_Repl @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.27/0.46 @ ( c_Repl @ X1
% 0.27/0.46 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax74,axiom,
% 0.27/0.46 ( c_proj0
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( c_ReplSep @ X0
% 0.27/0.46 @ ^ [X1: $i] :
% 0.27/0.46 ? [X2: $i] :
% 0.27/0.46 ( ( c_Inj0 @ X2 )
% 0.27/0.46 = X1 )
% 0.27/0.46 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax75,axiom,
% 0.27/0.46 ( c_proj1
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( c_ReplSep @ X0
% 0.27/0.46 @ ^ [X1: $i] :
% 0.27/0.46 ? [X2: $i] :
% 0.27/0.46 ( ( c_Inj1 @ X2 )
% 0.27/0.46 = X1 )
% 0.27/0.46 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax76,axiom,
% 0.27/0.46 ( c_binrep
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax77,axiom,
% 0.27/0.46 ( c_lam
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i] :
% 0.27/0.46 ( c_famunion @ X0
% 0.27/0.46 @ ^ [X2: $i] :
% 0.27/0.46 ( c_Repl @ ( X1 @ X2 )
% 0.27/0.46 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax78,axiom,
% 0.27/0.46 ( c_setprod
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_lam @ X0
% 0.27/0.46 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax79,axiom,
% 0.27/0.46 ( c_ap
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_ReplSep @ X0
% 0.27/0.46 @ ^ [X2: $i] :
% 0.27/0.46 ? [X3: $i] :
% 0.27/0.46 ( X2
% 0.27/0.46 = ( c_setsum @ X1 @ X3 ) )
% 0.27/0.46 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax80,axiom,
% 0.27/0.46 ( c_setsum_p
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.27/0.46 = X0 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax81,axiom,
% 0.27/0.46 ( c_tuple_p
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ! [X2: $i] :
% 0.27/0.46 ( ( c_In @ X2 @ X1 )
% 0.27/0.46 => ? [X3: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X3 @ X0 )
% 0.27/0.46 @ ? [X4: $i] :
% 0.27/0.46 ( X2
% 0.27/0.46 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax82,axiom,
% 0.27/0.46 ( c_Pi
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i] :
% 0.27/0.46 ( c_Sep
% 0.27/0.46 @ ( c_Power
% 0.27/0.46 @ ( c_lam @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.27/0.46 @ ^ [X2: $i] :
% 0.27/0.46 ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X0 )
% 0.27/0.46 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax83,axiom,
% 0.27/0.46 ( c_setexp
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_Pi @ X1
% 0.27/0.46 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax84,axiom,
% 0.27/0.46 ( c_Sep2
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.27/0.46 ( c_Sep
% 0.27/0.46 @ ( c_lam @ X0
% 0.27/0.46 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.27/0.46 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax85,axiom,
% 0.27/0.46 ( c_set_of_pairs
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ! [X1: $i] :
% 0.27/0.46 ( ( c_In @ X1 @ X0 )
% 0.27/0.46 => ? [X2: $i,X3: $i] :
% 0.27/0.46 ( X1
% 0.27/0.46 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.27/0.46 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax86,axiom,
% 0.27/0.46 ( c_lam2
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.27/0.46 ( c_lam @ X0
% 0.27/0.46 @ ^ [X3: $i] :
% 0.27/0.46 ( c_lam @ ( X1 @ X3 )
% 0.27/0.46 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax87,axiom,
% 0.27/0.46 ( c_PNoEq_
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.27/0.46 ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X0 )
% 0.27/0.46 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax88,axiom,
% 0.27/0.46 ( c_PNoLt_
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.27/0.46 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax89,axiom,
% 0.27/0.46 ( c_PNoLt
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax90,axiom,
% 0.27/0.46 ( c_PNoLe
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax91,axiom,
% 0.27/0.46 ( c_PNo_downc
% 0.27/0.46 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.27/0.46 ? [X3: $i] :
% 0.27/0.46 ( c_and @ ( c_ordinal @ X3 )
% 0.27/0.46 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax92,axiom,
% 0.27/0.46 ( c_PNo_upc
% 0.27/0.46 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.27/0.46 ? [X3: $i] :
% 0.27/0.46 ( c_and @ ( c_ordinal @ X3 )
% 0.27/0.46 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax93,axiom,
% 0.27/0.46 ( c_SNoElts_
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( c_binunion @ X0
% 0.27/0.46 @ ( c_Repl @ X0
% 0.27/0.46 @ ^ [X1: $i] :
% 0.27/0.46 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.27/0.46 @ X1 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax94,axiom,
% 0.27/0.46 ( c_SNo_
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.27/0.46 @ ! [X2: $i] :
% 0.27/0.46 ( ( c_In @ X2 @ X0 )
% 0.27/0.46 => ( c_exactly1of2
% 0.27/0.46 @ ( c_In
% 0.27/0.46 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.27/0.46 @ X2 )
% 0.27/0.46 @ X1 )
% 0.27/0.46 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax95,axiom,
% 0.27/0.46 ( c_PSNo
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $o] :
% 0.27/0.46 ( c_binunion
% 0.27/0.46 @ ( c_Sep @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.27/0.46 @ ( c_ReplSep @ X0
% 0.27/0.46 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.27/0.46 @ ^ [X2: $i] :
% 0.27/0.46 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.27/0.46 @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax96,axiom,
% 0.27/0.46 ( c_SNo
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax97,axiom,
% 0.27/0.46 ( c_SNoLev
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ( c_Eps_i
% 0.27/0.46 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax98,axiom,
% 0.27/0.46 ( c_SNoEq_
% 0.27/0.46 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.27/0.46 ( c_PNoEq_ @ X0
% 0.27/0.46 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.27/0.46 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax99,axiom,
% 0.27/0.46 ( c_SNoLt
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.27/0.46 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.27/0.46 @ ( c_SNoLev @ X1 )
% 0.27/0.46 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax100,axiom,
% 0.27/0.46 ( c_SNoLe
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.27/0.46 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.27/0.46 @ ( c_SNoLev @ X1 )
% 0.27/0.46 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax101,axiom,
% 0.27/0.46 ( c_binop_on
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.27/0.46 ! [X2: $i] :
% 0.27/0.46 ( ( c_In @ X2 @ X0 )
% 0.27/0.46 => ! [X3: $i] :
% 0.27/0.46 ( ( c_In @ X3 @ X0 )
% 0.27/0.46 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax102,axiom,
% 0.27/0.46 ( c_Loop
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.27/0.46 ( c_and
% 0.27/0.46 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.27/0.46 @ ! [X5: $i] :
% 0.27/0.46 ( ( c_In @ X5 @ X0 )
% 0.27/0.46 => ( c_and
% 0.27/0.46 @ ( ( X1 @ X4 @ X5 )
% 0.27/0.46 = X5 )
% 0.27/0.46 @ ( ( X1 @ X5 @ X4 )
% 0.27/0.46 = X5 ) ) ) )
% 0.27/0.46 @ ! [X5: $i] :
% 0.27/0.46 ( ( c_In @ X5 @ X0 )
% 0.27/0.46 => ! [X6: $i] :
% 0.27/0.46 ( ( c_In @ X6 @ X0 )
% 0.27/0.46 => ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.27/0.46 = X6 )
% 0.27/0.46 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.27/0.46 = X6 ) )
% 0.27/0.46 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.27/0.46 = X5 ) )
% 0.27/0.46 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.27/0.46 = X5 ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax103,axiom,
% 0.27/0.46 ( c_Loop_with_defs
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.27/0.46 ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.27/0.46 @ ! [X14: $i] :
% 0.27/0.46 ( ( c_In @ X14 @ X0 )
% 0.27/0.46 => ! [X15: $i] :
% 0.27/0.46 ( ( c_In @ X15 @ X0 )
% 0.27/0.46 => ( ( X5 @ X14 @ X15 )
% 0.27/0.46 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.27/0.46 @ ! [X14: $i] :
% 0.27/0.46 ( ( c_In @ X14 @ X0 )
% 0.27/0.46 => ! [X15: $i] :
% 0.27/0.46 ( ( c_In @ X15 @ X0 )
% 0.27/0.46 => ! [X16: $i] :
% 0.27/0.46 ( ( c_In @ X16 @ X0 )
% 0.27/0.46 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.27/0.46 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.27/0.46 @ ! [X14: $i] :
% 0.27/0.46 ( ( c_In @ X14 @ X0 )
% 0.27/0.46 => ! [X15: $i] :
% 0.27/0.46 ( ( c_In @ X15 @ X0 )
% 0.27/0.46 => ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( c_and
% 0.27/0.46 @ ( ( X7 @ X14 @ X15 )
% 0.27/0.46 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.27/0.46 @ ( ( X10 @ X14 @ X15 )
% 0.27/0.46 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.27/0.46 @ ( ( X11 @ X14 @ X15 )
% 0.27/0.46 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.27/0.46 @ ( ( X12 @ X14 @ X15 )
% 0.27/0.46 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.27/0.46 @ ( ( X13 @ X14 @ X15 )
% 0.27/0.46 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.27/0.46 @ ! [X14: $i] :
% 0.27/0.46 ( ( c_In @ X14 @ X0 )
% 0.27/0.46 => ! [X15: $i] :
% 0.27/0.46 ( ( c_In @ X15 @ X0 )
% 0.27/0.46 => ! [X16: $i] :
% 0.27/0.46 ( ( c_In @ X16 @ X0 )
% 0.27/0.46 => ( c_and
% 0.27/0.46 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.27/0.46 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.27/0.46 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.27/0.46 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax104,axiom,
% 0.27/0.46 ( c_Loop_with_defs_cex1
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.27/0.46 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.27/0.46 @ ? [X14: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X14 @ X0 )
% 0.27/0.46 @ ? [X15: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X15 @ X0 )
% 0.27/0.46 @ ? [X16: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X16 @ X0 )
% 0.27/0.46 @ ? [X17: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X17 @ X0 )
% 0.27/0.46 @ ( c_not
% 0.27/0.46 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.27/0.46 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax105,axiom,
% 0.27/0.46 ( c_Loop_with_defs_cex2
% 0.27/0.46 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.27/0.46 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.27/0.46 @ ? [X14: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X14 @ X0 )
% 0.27/0.46 @ ? [X15: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X15 @ X0 )
% 0.27/0.46 @ ? [X16: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X16 @ X0 )
% 0.27/0.46 @ ? [X17: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X17 @ X0 )
% 0.27/0.46 @ ? [X18: $i] :
% 0.27/0.46 ( c_and @ ( c_In @ X18 @ X0 )
% 0.27/0.46 @ ( c_not
% 0.27/0.46 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.27/0.46 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax106,axiom,
% 0.27/0.46 ( c_combinator
% 0.27/0.46 = ( ^ [X0: $i] :
% 0.27/0.46 ! [X1: $i > $o] :
% 0.27/0.46 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.27/0.46 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.27/0.46 => ( ! [X2: $i,X3: $i] :
% 0.27/0.46 ( ( X1 @ X2 )
% 0.27/0.46 => ( ( X1 @ X3 )
% 0.27/0.46 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.27/0.46 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax107,axiom,
% 0.27/0.46 ( c_combinator_equiv
% 0.27/0.46 = ( ^ [X0: $i,X1: $i] :
% 0.27/0.46 ! [X2: $i > $i > $o] :
% 0.27/0.46 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.27/0.46 ( ( c_per_i @ X2 )
% 0.27/0.46 => ( ! [X6: $i] :
% 0.27/0.46 ( ( c_combinator @ X6 )
% 0.27/0.46 => ( X2 @ X6 @ X6 ) )
% 0.27/0.46 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.27/0.46 ( ( c_combinator @ X6 )
% 0.27/0.46 => ( ( c_combinator @ X7 )
% 0.27/0.46 => ( ( c_combinator @ X8 )
% 0.27/0.46 => ( ( c_combinator @ X9 )
% 0.27/0.46 => ( ( X2 @ X6 @ X8 )
% 0.27/0.46 => ( ( X2 @ X7 @ X9 )
% 0.27/0.46 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.27/0.46 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.27/0.46 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.27/0.46 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.27/0.46 @ ( c_Inj0 @ c_Empty )
% 0.27/0.46 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.27/0.46 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(ax108,axiom,
% 0.27/0.46 ( c_equip_mod
% 0.27/0.46 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.27/0.46 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf(conj,conjecture,
% 0.27/0.46 ! [X0: ( $i > $i > $i > $i ) > ( $i > $i ) > ( ( $i > $i > $i ) > $i ) > $i,X1: ( $i > $i ) > $i > $i,X2: ( ( ( $i > $i > $i > $i ) > $i ) > $i > $i ) > $i > $i,X3: ( $i > $i ) > ( $i > $i ) > $i] :
% 0.27/0.46 ( ! [X4: $i > ( ( $i > $i ) > $i ) > $i,X5: ( $i > $i ) > $i,X6: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i,X7: $i] :
% 0.27/0.46 ( ( X3
% 0.27/0.46 @ ^ [X8: $i] : ( c_Inj1 @ c_Empty )
% 0.27/0.46 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ c_Empty ) )
% 0.27/0.46 = ( c_Inj1 @ c_Empty ) )
% 0.27/0.46 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 0.27/0.46 ( ( X3
% 0.27/0.46 @ ^ [X8: $i] : X6
% 0.27/0.46 @ ^ [X8: $i] : X7 )
% 0.27/0.46 = ( c_setsum
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : c_Empty
% 0.27/0.46 @ ( X0
% 0.27/0.46 @ ^ [X8: $i,X9: $i,X10: $i] :
% 0.27/0.46 ( X3
% 0.27/0.46 @ ^ [X11: $i] : X10
% 0.27/0.46 @ ^ [X11: $i] : c_Empty )
% 0.27/0.46 @ ^ [X8: $i] : c_Empty
% 0.27/0.46 @ ^ [X8: $i > $i > $i] : c_Empty ) )
% 0.27/0.46 @ c_Empty ) )
% 0.27/0.46 => ( ! [X4: $i > $i,X5: $i > $i > $i,X6: $i > $i,X7: $i] :
% 0.27/0.46 ( ( X2
% 0.27/0.46 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : X7
% 0.27/0.46 @ c_Empty )
% 0.27/0.46 = X7 )
% 0.27/0.46 => ( ! [X4: $i > ( $i > $i > $i ) > $i,X5: $i > $i,X6: ( ( ( $i > $i ) > $i ) > $i ) > $i,X7: $i > $i] :
% 0.27/0.46 ( ( X2
% 0.27/0.46 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] :
% 0.27/0.46 ( X7
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X10: ( $i > $i > $i > $i ) > $i,X11: $i] :
% 0.27/0.46 ( X0
% 0.27/0.46 @ ^ [X12: $i,X13: $i,X14: $i] : ( c_Inj1 @ c_Empty )
% 0.27/0.46 @ ^ [X12: $i] : ( c_Inj0 @ c_Empty )
% 0.27/0.46 @ ^ [X12: $i > $i > $i] :
% 0.27/0.46 ( X3
% 0.27/0.46 @ ^ [X13: $i] : c_Empty
% 0.27/0.46 @ ^ [X13: $i] : c_Empty ) )
% 0.27/0.46 @ ( c_Inj0
% 0.27/0.46 @ ( X0
% 0.27/0.46 @ ^ [X10: $i,X11: $i,X12: $i] : c_Empty
% 0.27/0.46 @ ^ [X10: $i] : c_Empty
% 0.27/0.46 @ ^ [X10: $i > $i > $i] : c_Empty ) ) ) )
% 0.27/0.46 @ ( X3
% 0.27/0.46 @ ^ [X8: $i] : ( c_setsum @ X8 @ c_Empty )
% 0.27/0.46 @ ^ [X8: $i] : c_Empty ) )
% 0.27/0.46 = ( c_setsum
% 0.27/0.46 @ ( X7
% 0.27/0.46 @ ( X5
% 0.27/0.46 @ ( X0
% 0.27/0.46 @ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ c_Empty )
% 0.27/0.46 @ ^ [X8: $i] :
% 0.27/0.46 ( X0
% 0.27/0.46 @ ^ [X9: $i,X10: $i,X11: $i] : c_Empty
% 0.27/0.46 @ ^ [X9: $i] : c_Empty
% 0.27/0.46 @ ^ [X9: $i > $i > $i] : c_Empty )
% 0.27/0.46 @ ^ [X8: $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 0.27/0.46 @ ( X1
% 0.27/0.46 @ ^ [X8: $i] : ( X7 @ c_Empty )
% 0.27/0.46 @ ( X5
% 0.27/0.46 @ ( X4
% 0.27/0.46 @ ( X1
% 0.27/0.46 @ ^ [X8: $i] : c_Empty
% 0.27/0.46 @ c_Empty )
% 0.27/0.46 @ ^ [X8: $i,X9: $i] : c_Empty ) ) ) ) )
% 0.27/0.46 => ( ! [X4: ( ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i,X7: $i] :
% 0.27/0.46 ( ( X1
% 0.27/0.46 @ ^ [X8: $i] :
% 0.27/0.46 ( c_Inj1
% 0.27/0.46 @ ( X1
% 0.27/0.46 @ ^ [X9: $i] :
% 0.27/0.46 ( c_Inj0
% 0.27/0.46 @ ( X0
% 0.27/0.46 @ ^ [X10: $i,X11: $i,X12: $i] : c_Empty
% 0.27/0.46 @ ^ [X10: $i] : c_Empty
% 0.27/0.46 @ ^ [X10: $i > $i > $i] : c_Empty ) )
% 0.27/0.46 @ ( c_Inj1 @ X7 ) ) )
% 0.27/0.46 @ ( c_Inj0
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : X9
% 0.27/0.46 @ X5 ) ) )
% 0.27/0.46 = ( c_Inj0
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : X7
% 0.27/0.46 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 0.27/0.46 => ( ! [X4: ( ( $i > $i ) > $i ) > $i,X5: $i > $i > ( $i > $i ) > $i,X6: $i,X7: ( $i > $i ) > ( $i > $i ) > $i] :
% 0.27/0.46 ( ( X1
% 0.27/0.46 @ ^ [X8: $i] :
% 0.27/0.46 ( X7
% 0.27/0.46 @ ^ [X9: $i] : ( c_setsum @ X9 @ X8 )
% 0.27/0.46 @ ^ [X9: $i] : c_Empty )
% 0.27/0.46 @ c_Empty )
% 0.27/0.46 = ( X7
% 0.27/0.46 @ ^ [X8: $i] :
% 0.27/0.46 ( c_setsum
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : c_Empty
% 0.27/0.46 @ ( X3
% 0.27/0.46 @ ^ [X9: $i] :
% 0.27/0.46 ( X2
% 0.27/0.46 @ ^ [X10: ( $i > $i > $i > $i ) > $i,X11: $i] : c_Empty
% 0.27/0.46 @ c_Empty )
% 0.27/0.46 @ ^ [X9: $i] :
% 0.27/0.46 ( X1
% 0.27/0.46 @ ^ [X10: $i] : c_Empty
% 0.27/0.46 @ c_Empty ) ) )
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : c_Empty
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : ( c_setsum @ c_Empty @ c_Empty )
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : c_Empty
% 0.27/0.46 @ c_Empty ) ) ) )
% 0.27/0.46 @ ^ [X8: $i] :
% 0.27/0.46 ( c_Inj1
% 0.27/0.46 @ ( X1
% 0.27/0.46 @ ^ [X9: $i] :
% 0.27/0.46 ( X7
% 0.27/0.46 @ ^ [X10: $i] :
% 0.27/0.46 ( X1
% 0.27/0.46 @ ^ [X11: $i] : c_Empty
% 0.27/0.46 @ c_Empty )
% 0.27/0.46 @ ^ [X10: $i] : ( c_Inj1 @ c_Empty ) )
% 0.27/0.46 @ X6 ) ) ) )
% 0.27/0.46 => ( ! [X4: $i > ( ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i,X7: $i] :
% 0.27/0.46 ( ( X0
% 0.27/0.46 @ ^ [X8: $i,X9: $i,X10: $i] : X7
% 0.27/0.46 @ ^ [X8: $i] : X6
% 0.27/0.46 @ ^ [X8: $i > $i > $i] : c_Empty )
% 0.27/0.46 = X6 )
% 0.27/0.46 => ( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i > $i] :
% 0.27/0.46 ( ( X0
% 0.27/0.46 @ ^ [X8: $i,X9: $i,X10: $i] :
% 0.27/0.46 ( X1
% 0.27/0.46 @ ^ [X11: $i] :
% 0.27/0.46 ( X2
% 0.27/0.46 @ ^ [X12: ( $i > $i > $i > $i ) > $i,X13: $i] : X10
% 0.27/0.46 @ ( X2
% 0.27/0.46 @ ^ [X12: ( $i > $i > $i > $i ) > $i,X13: $i] : ( c_setsum @ c_Empty @ c_Empty )
% 0.27/0.46 @ X11 ) )
% 0.27/0.46 @ ( c_Inj1 @ c_Empty ) )
% 0.27/0.46 @ ^ [X8: $i] : ( X7 @ c_Empty )
% 0.27/0.46 @ ^ [X8: $i > $i > $i] : c_Empty )
% 0.27/0.46 = ( X7 @ X4 ) )
% 0.27/0.46 => c_False ) ) ) ) ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 2.08/1.39 ---- Embedded in THF ---
% 2.08/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.08/1.39 %%% Generated on Tue Feb 24 14:48:58 EST 2026
% 2.08/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 2.08/1.39 %%% Logic specification used:
% 2.08/1.39 %%% thf(spec, logic, $$dhol).
% 2.08/1.39
% 2.08/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2DTF351.p
% 2.08/1.39 thf(c_Eps_i_tp, type, c_Eps_i: (($i > $o) > $i)).
% 2.08/1.39 thf(c_False_tp, type, c_False: $o).
% 2.08/1.39 thf(c_True_tp, type, c_True: $o).
% 2.08/1.39 thf(c_not_tp, type, c_not: ($o > $o)).
% 2.08/1.39 thf(c_and_tp, type, c_and: ($o > ($o > $o))).
% 2.08/1.39 thf(c_or_tp, type, c_or: ($o > ($o > $o))).
% 2.08/1.39 thf(c_iff_tp, type, c_iff: ($o > ($o > $o))).
% 2.08/1.39 thf(c_In_tp, type, c_In: ($i > ($i > $o))).
% 2.08/1.39 thf(c_Subq_tp, type, c_Subq: ($i > ($i > $o))).
% 2.08/1.39 thf(c_Empty_tp, type, c_Empty: $i).
% 2.08/1.39 thf(c_Union_tp, type, c_Union: ($i > $i)).
% 2.08/1.39 thf(c_Power_tp, type, c_Power: ($i > $i)).
% 2.08/1.39 thf(c_Repl_tp, type, c_Repl: ($i > (($i > $i) > $i))).
% 2.08/1.39 thf(c_TransSet_tp, type, c_TransSet: ($i > $o)).
% 2.08/1.39 thf(c_atleast2_tp, type, c_atleast2: ($i > $o)).
% 2.08/1.39 thf(c_atleast3_tp, type, c_atleast3: ($i > $o)).
% 2.08/1.39 thf(c_atleast4_tp, type, c_atleast4: ($i > $o)).
% 2.08/1.39 thf(c_atleast5_tp, type, c_atleast5: ($i > $o)).
% 2.08/1.39 thf(c_atleast6_tp, type, c_atleast6: ($i > $o)).
% 2.08/1.39 thf(c_exactly2_tp, type, c_exactly2: ($i > $o)).
% 2.08/1.39 thf(c_exactly3_tp, type, c_exactly3: ($i > $o)).
% 2.08/1.39 thf(c_exactly4_tp, type, c_exactly4: ($i > $o)).
% 2.08/1.39 thf(c_exactly5_tp, type, c_exactly5: ($i > $o)).
% 2.08/1.39 thf(c_exu_i_tp, type, c_exu_i: (($i > $o) > $o)).
% 2.08/1.39 thf(c_reflexive_i_tp, type, c_reflexive_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_irreflexive_i_tp, type, c_irreflexive_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_symmetric_i_tp, type, c_symmetric_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_antisymmetric_i_tp, type, c_antisymmetric_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_transitive_i_tp, type, c_transitive_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_eqreln_i_tp, type, c_eqreln_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_per_i_tp, type, c_per_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_linear_i_tp, type, c_linear_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_trichotomous_or_i_tp, type, c_trichotomous_or_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_partialorder_i_tp, type, c_partialorder_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_totalorder_i_tp, type, c_totalorder_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_strictpartialorder_i_tp, type, c_strictpartialorder_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_stricttotalorder_i_tp, type, c_stricttotalorder_i: (($i > ($i > $o)) > $o)).
% 2.08/1.39 thf(c_If_i_tp, type, c_If_i: ($o > ($i > ($i > $i)))).
% 2.08/1.39 thf(c_exactly1of2_tp, type, c_exactly1of2: ($o > ($o > $o))).
% 2.08/1.39 thf(c_exactly1of3_tp, type, c_exactly1of3: ($o > ($o > ($o > $o)))).
% 2.08/1.39 thf(c_nIn_tp, type, c_nIn: ($i > ($i > $o))).
% 2.08/1.39 thf(c_nSubq_tp, type, c_nSubq: ($i > ($i > $o))).
% 2.08/1.39 thf(c_UPair_tp, type, c_UPair: ($i > ($i > $i))).
% 2.08/1.39 thf(c_Sing_tp, type, c_Sing: ($i > $i)).
% 2.08/1.39 thf(c_binunion_tp, type, c_binunion: ($i > ($i > $i))).
% 2.08/1.39 thf(c_SetAdjoin_tp, type, c_SetAdjoin: ($i > ($i > $i))).
% 2.08/1.39 thf(c_famunion_tp, type, c_famunion: ($i > (($i > $i) > $i))).
% 2.08/1.39 thf(c_Sep_tp, type, c_Sep: ($i > (($i > $o) > $i))).
% 2.08/1.39 thf(c_ReplSep_tp, type, c_ReplSep: ($i > (($i > $o) > (($i > $i) > $i)))).
% 2.08/1.39 thf(c_binintersect_tp, type, c_binintersect: ($i > ($i > $i))).
% 2.08/1.39 thf(c_setminus_tp, type, c_setminus: ($i > ($i > $i))).
% 2.08/1.39 thf(c_inj_tp, type, c_inj: ($i > ($i > (($i > $i) > $o)))).
% 2.08/1.39 thf(c_bij_tp, type, c_bij: ($i > ($i > (($i > $i) > $o)))).
% 2.08/1.39 thf(c_atleastp_tp, type, c_atleastp: ($i > ($i > $o))).
% 2.08/1.39 thf(c_equip_tp, type, c_equip: ($i > ($i > $o))).
% 2.08/1.39 thf(c_In_rec_poly_G_i_tp, type, c_In_rec_poly_G_i: (($i > (($i > $i) > $i)) > ($i > ($i > $o)))).
% 2.08/1.39 thf(c_In_rec_poly_i_tp, type, c_In_rec_poly_i: (($i > (($i > $i) > $i)) > ($i > $i))).
% 2.08/1.39 thf(c_ordsucc_tp, type, c_ordsucc: ($i > $i)).
% 2.08/1.39 thf(c_nat_p_tp, type, c_nat_p: ($i > $o)).
% 2.08/1.39 thf(c_nat_primrec_tp, type, c_nat_primrec: ($i > (($i > ($i > $i)) > ($i > $i)))).
% 2.08/1.39 thf(c_add_nat_tp, type, c_add_nat: ($i > ($i > $i))).
% 2.08/1.39 thf(c_mul_nat_tp, type, c_mul_nat: ($i > ($i > $i))).
% 2.08/1.39 thf(c_ordinal_tp, type, c_ordinal: ($i > $o)).
% 2.08/1.39 thf(c_V__tp, type, c_V_: ($i > $i)).
% 2.08/1.39 thf(c_Inj1_tp, type, c_Inj1: ($i > $i)).
% 2.08/1.39 thf(c_Inj0_tp, type, c_Inj0: ($i > $i)).
% 2.08/1.39 thf(c_Unj_tp, type, c_Unj: ($i > $i)).
% 2.08/1.39 thf(c_combine_funcs_tp, type, c_combine_funcs: ($i > ($i > (($i > $i) > (($i > $i) > ($i > $i)))))).
% 2.08/1.39 thf(c_setsum_tp, type, c_setsum: ($i > ($i > $i))).
% 2.08/1.39 thf(c_proj0_tp, type, c_proj0: ($i > $i)).
% 2.08/1.39 thf(c_proj1_tp, type, c_proj1: ($i > $i)).
% 2.08/1.39 thf(c_binrep_tp, type, c_binrep: ($i > ($i > $i))).
% 2.08/1.39 thf(c_lam_tp, type, c_lam: ($i > (($i > $i) > $i))).
% 2.08/1.39 thf(c_setprod_tp, type, c_setprod: ($i > ($i > $i))).
% 2.08/1.39 thf(c_ap_tp, type, c_ap: ($i > ($i > $i))).
% 2.08/1.39 thf(c_setsum_p_tp, type, c_setsum_p: ($i > $o)).
% 2.08/1.39 thf(c_tuple_p_tp, type, c_tuple_p: ($i > ($i > $o))).
% 2.08/1.39 thf(c_Pi_tp, type, c_Pi: ($i > (($i > $i) > $i))).
% 2.08/1.39 thf(c_setexp_tp, type, c_setexp: ($i > ($i > $i))).
% 2.08/1.39 thf(c_Sep2_tp, type, c_Sep2: ($i > (($i > $i) > (($i > ($i > $o)) > $i)))).
% 2.08/1.39 thf(c_set_of_pairs_tp, type, c_set_of_pairs: ($i > $o)).
% 2.08/1.39 thf(c_lam2_tp, type, c_lam2: ($i > (($i > $i) > (($i > ($i > $i)) > $i)))).
% 2.08/1.39 thf(c_PNoEq__tp, type, c_PNoEq_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 2.08/1.39 thf(c_PNoLt__tp, type, c_PNoLt_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 2.08/1.39 thf(c_PNoLt_tp, type, c_PNoLt: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 2.08/1.40 thf(c_PNoLe_tp, type, c_PNoLe: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 2.08/1.40 thf(c_PNo_downc_tp, type, c_PNo_downc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 2.08/1.40 thf(c_PNo_upc_tp, type, c_PNo_upc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 2.08/1.40 thf(c_SNoElts__tp, type, c_SNoElts_: ($i > $i)).
% 2.08/1.40 thf(c_SNo__tp, type, c_SNo_: ($i > ($i > $o))).
% 2.08/1.40 thf(c_PSNo_tp, type, c_PSNo: ($i > (($i > $o) > $i))).
% 2.08/1.40 thf(c_SNo_tp, type, c_SNo: ($i > $o)).
% 2.08/1.40 thf(c_SNoLev_tp, type, c_SNoLev: ($i > $i)).
% 2.08/1.40 thf(c_SNoEq__tp, type, c_SNoEq_: ($i > ($i > ($i > $o)))).
% 2.08/1.40 thf(c_SNoLt_tp, type, c_SNoLt: ($i > ($i > $o))).
% 2.08/1.40 thf(c_SNoLe_tp, type, c_SNoLe: ($i > ($i > $o))).
% 2.08/1.40 thf(c_binop_on_tp, type, c_binop_on: ($i > (($i > ($i > $i)) > $o))).
% 2.08/1.40 thf(c_Loop_tp, type, c_Loop: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > $o)))))).
% 2.08/1.40 thf(c_Loop_with_defs_tp, type, c_Loop_with_defs: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.08/1.40 thf(c_Loop_with_defs_cex1_tp, type, c_Loop_with_defs_cex1: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.08/1.40 thf(c_Loop_with_defs_cex2_tp, type, c_Loop_with_defs_cex2: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.08/1.40 thf(c_combinator_tp, type, c_combinator: ($i > $o)).
% 2.08/1.40 thf(c_combinator_equiv_tp, type, c_combinator_equiv: ($i > ($i > $o))).
% 2.08/1.40 thf(c_equip_mod_tp, type, c_equip_mod: ($i > ($i > ($i > $o)))).
% 2.08/1.40 thf(ax1, axiom, (! [X0:($i > $o),X1:$i]: (((X0 @ X1) => (X0 @ (c_Eps_i @ X0)))))).
% 2.08/1.40 thf(ax2, axiom, (! [X0:$o]: (((c_not @ (c_not @ X0)) => X0)))).
% 2.08/1.40 thf(ax3, axiom, (! [X0:$o,X1:$o]: ((((c_iff @ X0) @ X1) => (X0 = X1))))).
% 2.08/1.40 thf(ax4, axiom, (! [X0:$i,X1:$i]: ((((c_Subq @ X0) @ X1) => (((c_Subq @ X1) @ X0) => (X0 = X1)))))).
% 2.08/1.40 thf(ax5, axiom, (c_not @ (? [X0:$i]: (((c_In @ X0) @ c_Empty))))).
% 2.08/1.40 thf(ax6, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ (? [X2:$i]: (((c_and @ ((c_In @ X1) @ X2)) @ ((c_In @ X2) @ X0)))))))).
% 2.08/1.40 thf(ax7, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))))).
% 2.08/1.40 thf(ax8, axiom, (! [X0:$i,X1:($i > $i),X2:$i]: (((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ (^ [X3:$i]: ((X1 @ X3)))))) @ (? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ (X2 = (X1 @ X3))))))))).
% 2.08/1.40 thf(ax9, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((X0 @ X1) => (! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2))))))) => ((X0 @ c_Empty) => ((! [X1:$i]: (((X0 @ X1) => (X0 @ (c_Union @ X1))))) => ((! [X1:$i]: (((X0 @ X1) => (X0 @ (c_Power @ X1))))) => ((! [X1:$i]: (((X0 @ X1) => (! [X2:($i > $i)]: (((! [X3:$i]: ((((c_In @ X3) @ X1) => (X0 @ (X2 @ X3))))) => (X0 @ ((c_Repl @ X1) @ (^ [X3:$i]: ((X2 @ X3))))))))))) => (! [X1:$i]: ((X0 @ X1))))))))))).
% 2.08/1.40 thf(ax10, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2)))) => (X0 @ X1)))) => (! [X1:$i]: ((X0 @ X1))))))).
% 2.08/1.40 thf(ax11, axiom, (c_False = (! [X0:$o]: (X0)))).
% 2.08/1.40 thf(ax12, axiom, (c_True = (! [X0:$o]: ((X0 => X0))))).
% 2.08/1.40 thf(ax13, axiom, (c_not = (^ [X0:$o]: ((X0 => c_False))))).
% 2.08/1.40 thf(ax14, axiom, (c_and = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => (X1 => X2)) => X2))))))).
% 2.08/1.40 thf(ax15, axiom, (c_or = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => X2) => ((X1 => X2) => X2)))))))).
% 2.08/1.40 thf(ax16, axiom, (c_iff = (^ [X0:$o,X1:$o]: (((c_and @ (X0 => X1)) @ (X1 => X0)))))).
% 2.08/1.40 thf(ax17, axiom, (c_Subq = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax18, axiom, (c_TransSet = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => ((c_Subq @ X1) @ X0)))))))).
% 2.08/1.40 thf(ax19, axiom, (c_atleast2 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_In @ X1) @ X0)) @ (c_not @ ((c_Subq @ X0) @ (c_Power @ X1)))))))))).
% 2.08/1.40 thf(ax20, axiom, (c_atleast3 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast2 @ X1))))))))).
% 2.08/1.40 thf(ax21, axiom, (c_atleast4 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast3 @ X1))))))))).
% 2.08/1.40 thf(ax22, axiom, (c_atleast5 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast4 @ X1))))))))).
% 2.08/1.40 thf(ax23, axiom, (c_atleast6 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast5 @ X1))))))))).
% 2.08/1.40 thf(ax24, axiom, (c_exactly2 = (^ [X0:$i]: (((c_and @ (c_atleast2 @ X0)) @ (c_not @ (c_atleast3 @ X0))))))).
% 2.08/1.40 thf(ax25, axiom, (c_exactly3 = (^ [X0:$i]: (((c_and @ (c_atleast3 @ X0)) @ (c_not @ (c_atleast4 @ X0))))))).
% 2.08/1.40 thf(ax26, axiom, (c_exactly4 = (^ [X0:$i]: (((c_and @ (c_atleast4 @ X0)) @ (c_not @ (c_atleast5 @ X0))))))).
% 2.08/1.40 thf(ax27, axiom, (c_exactly5 = (^ [X0:$i]: (((c_and @ (c_atleast5 @ X0)) @ (c_not @ (c_atleast6 @ X0))))))).
% 2.08/1.40 thf(ax28, axiom, (c_exu_i = (^ [X0:($i > $o)]: (((c_and @ (? [X1:$i]: ((X0 @ X1)))) @ (! [X1:$i,X2:$i]: (((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))))))).
% 2.08/1.40 thf(ax29, axiom, (c_reflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: (((X0 @ X1) @ X1))))))).
% 2.08/1.40 thf(ax30, axiom, (c_irreflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: ((c_not @ ((X0 @ X1) @ X1)))))))).
% 2.08/1.40 thf(ax31, axiom, (c_symmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => ((X0 @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax32, axiom, (c_antisymmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X1) => (X1 = X2))))))))).
% 2.08/1.40 thf(ax33, axiom, (c_transitive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i,X3:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X3) => ((X0 @ X1) @ X3))))))))).
% 2.08/1.40 thf(ax34, axiom, (c_eqreln_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_symmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 2.08/1.40 thf(ax35, axiom, (c_per_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_symmetric_i @ X0)) @ (c_transitive_i @ X0)))))).
% 2.08/1.40 thf(ax36, axiom, (c_linear_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((X0 @ X1) @ X2)) @ ((X0 @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax37, axiom, (c_trichotomous_or_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((c_or @ ((X0 @ X1) @ X2)) @ (X1 = X2))) @ ((X0 @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax38, axiom, (c_partialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_antisymmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 2.08/1.40 thf(ax39, axiom, (c_totalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_partialorder_i @ X0)) @ (c_linear_i @ X0)))))).
% 2.08/1.40 thf(ax40, axiom, (c_strictpartialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_irreflexive_i @ X0)) @ (c_transitive_i @ X0)))))).
% 2.08/1.40 thf(ax41, axiom, (c_stricttotalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_strictpartialorder_i @ X0)) @ (c_trichotomous_or_i @ X0)))))).
% 2.08/1.40 thf(ax42, axiom, (c_If_i = (^ [X0:$o,X1:$i,X2:$i]: ((c_Eps_i @ (^ [X3:$i]: (((c_or @ ((c_and @ X0) @ (X3 = X1))) @ ((c_and @ (c_not @ X0)) @ (X3 = X2)))))))))).
% 2.08/1.40 thf(ax43, axiom, (c_exactly1of2 = (^ [X0:$o,X1:$o]: (((c_or @ ((c_and @ X0) @ (c_not @ X1))) @ ((c_and @ (c_not @ X0)) @ X1)))))).
% 2.08/1.40 thf(ax44, axiom, (c_exactly1of3 = (^ [X0:$o,X1:$o,X2:$o]: (((c_or @ ((c_and @ ((c_exactly1of2 @ X0) @ X1)) @ (c_not @ X2))) @ ((c_and @ ((c_and @ (c_not @ X0)) @ (c_not @ X1))) @ X2)))))).
% 2.08/1.40 thf(ax45, axiom, (c_nIn = (^ [X0:$i,X1:$i]: ((c_not @ ((c_In @ X0) @ X1)))))).
% 2.08/1.40 thf(ax46, axiom, (c_nSubq = (^ [X0:$i,X1:$i]: ((c_not @ ((c_Subq @ X0) @ X1)))))).
% 2.08/1.40 thf(ax47, axiom, (c_UPair = (^ [X0:$i,X1:$i]: (((c_Repl @ (c_Power @ (c_Power @ c_Empty))) @ (^ [X2:$i]: ((((c_If_i @ ((c_In @ c_Empty) @ X2)) @ X0) @ X1)))))))).
% 2.08/1.40 thf(ax48, axiom, (c_Sing = (^ [X0:$i]: (((c_UPair @ X0) @ X0))))).
% 2.08/1.40 thf(ax49, axiom, (c_binunion = (^ [X0:$i,X1:$i]: ((c_Union @ ((c_UPair @ X0) @ X1)))))).
% 2.08/1.40 thf(ax50, axiom, (c_SetAdjoin = (^ [X0:$i,X1:$i]: (((c_binunion @ X0) @ (c_Sing @ X1)))))).
% 2.08/1.40 thf(ax51, axiom, (c_famunion = (^ [X0:$i,X1:($i > $i)]: ((c_Union @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 2.08/1.40 thf(ax52, axiom, (c_Sep = (^ [X0:$i,X1:($i > $o)]: ((((c_If_i @ (? [X2:$i]: (((c_and @ ((c_In @ X2) @ X0)) @ (X1 @ X2))))) @ ((c_Repl @ X0) @ (^ [X2:$i]: (((^ [X3:$i]: ((((c_If_i @ (X1 @ X3)) @ X3) @ (c_Eps_i @ (^ [X4:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ (X1 @ X4)))))))) @ X2))))) @ c_Empty))))).
% 2.08/1.40 thf(ax53, axiom, (c_ReplSep = (^ [X0:$i,X1:($i > $o),X2:($i > $i)]: (((c_Repl @ ((c_Sep @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: ((X2 @ X3)))))))).
% 2.08/1.40 thf(ax54, axiom, (c_binintersect = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax55, axiom, (c_setminus = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_nIn @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax56, axiom, (c_inj = (^ [X0:$i,X1:$i,X2:($i > $i)]: (((c_and @ (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ (X2 @ X3)) @ X1))))) @ (! [X3:$i]: ((((c_In @ X3) @ X0) => (! [X4:$i]: ((((c_In @ X4) @ X0) => (((X2 @ X3) = (X2 @ X4)) => (X3 = X4))))))))))))).
% 2.08/1.40 thf(ax57, axiom, (c_bij = (^ [X0:$i,X1:$i,X2:($i > $i)]: (((c_and @ (((c_inj @ X0) @ X1) @ X2)) @ (! [X3:$i]: ((((c_In @ X3) @ X1) => (? [X4:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ ((X2 @ X4) = X3)))))))))))).
% 2.08/1.40 thf(ax58, axiom, (c_atleastp = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_inj @ X0) @ X1) @ X2))))))).
% 2.08/1.40 thf(ax59, axiom, (c_equip = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_bij @ X0) @ X1) @ X2))))))).
% 2.08/1.40 thf(ax60, axiom, (c_In_rec_poly_G_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i,X2:$i]: ((! [X3:($i > ($i > $o))]: (((! [X4:$i,X5:($i > $i)]: (((! [X6:$i]: ((((c_In @ X6) @ X4) => ((X3 @ X6) @ (X5 @ X6))))) => ((X3 @ X4) @ ((X0 @ X4) @ X5))))) => ((X3 @ X1) @ X2)))))))).
% 2.08/1.40 thf(ax61, axiom, (c_In_rec_poly_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i]: ((c_Eps_i @ (^ [X2:$i]: ((((c_In_rec_poly_G_i @ X0) @ X1) @ X2)))))))).
% 2.08/1.40 thf(ax62, axiom, (c_ordsucc = (^ [X0:$i]: (((c_binunion @ X0) @ (c_Sing @ X0)))))).
% 2.08/1.40 thf(ax63, axiom, (c_nat_p = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ c_Empty) => ((! [X2:$i]: (((X1 @ X2) => (X1 @ (c_ordsucc @ X2))))) => (X1 @ X0))))))))).
% 2.08/1.40 thf(ax64, axiom, (c_nat_primrec = (^ [X0:$i,X1:($i > ($i > $i))]: ((c_In_rec_poly_i @ (^ [X2:$i,X3:($i > $i)]: ((((c_If_i @ ((c_In @ (c_Union @ X2)) @ X2)) @ ((X1 @ (c_Union @ X2)) @ (X3 @ (c_Union @ X2)))) @ X0)))))))).
% 2.08/1.40 thf(ax65, axiom, (c_add_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ X0) @ (^ [X2:$i,X3:$i]: ((c_ordsucc @ X3)))) @ X1))))).
% 2.08/1.40 thf(ax66, axiom, (c_mul_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ c_Empty) @ (^ [X2:$i,X3:$i]: (((c_add_nat @ X0) @ X3)))) @ X1))))).
% 2.08/1.40 thf(ax67, axiom, (c_ordinal = (^ [X0:$i]: (((c_and @ (c_TransSet @ X0)) @ (! [X1:$i]: ((((c_In @ X1) @ X0) => (c_TransSet @ X1))))))))).
% 2.08/1.40 thf(ax68, axiom, (c_V_ = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: ((c_Power @ (X1 @ X2)))))))))).
% 2.08/1.40 thf(ax69, axiom, (c_Inj1 = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_binunion @ (c_Sing @ c_Empty)) @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2)))))))))).
% 2.08/1.40 thf(ax70, axiom, (c_Inj0 = (^ [X0:$i]: (((c_Repl @ X0) @ (^ [X1:$i]: ((c_Inj1 @ X1)))))))).
% 2.08/1.40 thf(ax71, axiom, (c_Unj = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_Repl @ ((c_setminus @ X0) @ (c_Sing @ c_Empty))) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 2.08/1.40 thf(ax72, axiom, (c_combine_funcs = (^ [X0:$i,X1:$i,X2:($i > $i),X3:($i > $i),X4:$i]: ((((c_If_i @ (X4 = (c_Inj0 @ (c_Unj @ X4)))) @ (X2 @ (c_Unj @ X4))) @ (X3 @ (c_Unj @ X4))))))).
% 2.08/1.40 thf(ax73, axiom, (c_setsum = (^ [X0:$i,X1:$i]: (((c_binunion @ ((c_Repl @ X0) @ (^ [X2:$i]: ((c_Inj0 @ X2))))) @ ((c_Repl @ X1) @ (^ [X2:$i]: ((c_Inj1 @ X2))))))))).
% 2.08/1.40 thf(ax74, axiom, (c_proj0 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj0 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 2.08/1.40 thf(ax75, axiom, (c_proj1 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj1 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 2.08/1.40 thf(ax76, axiom, (c_binrep = (^ [X0:$i,X1:$i]: (((c_setsum @ X0) @ (c_Power @ X1)))))).
% 2.08/1.40 thf(ax77, axiom, (c_lam = (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: (((c_Repl @ (X1 @ X2)) @ (^ [X3:$i]: (((c_setsum @ X2) @ X3))))))))))).
% 2.08/1.40 thf(ax78, axiom, (c_setprod = (^ [X0:$i,X1:$i]: (((c_lam @ X0) @ (^ [X2:$i]: (X1))))))).
% 2.08/1.40 thf(ax79, axiom, (c_ap = (^ [X0:$i,X1:$i]: ((((c_ReplSep @ X0) @ (^ [X2:$i]: ((? [X3:$i]: ((X2 = ((c_setsum @ X1) @ X3))))))) @ (^ [X2:$i]: ((c_proj1 @ X2)))))))).
% 2.08/1.40 thf(ax80, axiom, (c_setsum_p = (^ [X0:$i]: ((((c_setsum @ ((c_ap @ X0) @ c_Empty)) @ ((c_ap @ X0) @ (c_ordsucc @ c_Empty))) = X0))))).
% 2.08/1.40 thf(ax81, axiom, (c_tuple_p = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X1) => (? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ (? [X4:$i]: ((X2 = ((c_setsum @ X3) @ X4)))))))))))))).
% 2.08/1.40 thf(ax82, axiom, (c_Pi = (^ [X0:$i,X1:($i > $i)]: (((c_Sep @ (c_Power @ ((c_lam @ X0) @ (^ [X2:$i]: ((c_Union @ (X1 @ X2))))))) @ (^ [X2:$i]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((c_ap @ X2) @ X3)) @ (X1 @ X3)))))))))))).
% 2.08/1.40 thf(ax83, axiom, (c_setexp = (^ [X0:$i,X1:$i]: (((c_Pi @ X1) @ (^ [X2:$i]: (X0))))))).
% 2.08/1.40 thf(ax84, axiom, (c_Sep2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $o))]: (((c_Sep @ ((c_lam @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: (((X2 @ ((c_ap @ X3) @ c_Empty)) @ ((c_ap @ X3) @ (c_ordsucc @ c_Empty)))))))))).
% 2.08/1.40 thf(ax85, axiom, (c_set_of_pairs = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => (? [X2:$i,X3:$i]: ((X1 = ((c_lam @ (c_ordsucc @ (c_ordsucc @ c_Empty))) @ (^ [X4:$i]: ((((c_If_i @ (X4 = c_Empty)) @ X2) @ X3)))))))))))))).
% 2.08/1.40 thf(ax86, axiom, (c_lam2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $i))]: (((c_lam @ X0) @ (^ [X3:$i]: (((c_lam @ (X1 @ X3)) @ (^ [X4:$i]: (((X2 @ X3) @ X4))))))))))).
% 2.08/1.40 thf(ax87, axiom, (c_PNoEq_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_iff @ (X1 @ X3)) @ (X2 @ X3))))))))).
% 2.08/1.40 thf(ax88, axiom, (c_PNoLt_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ ((c_and @ ((c_and @ (((c_PNoEq_ @ X3) @ X1) @ X2)) @ (c_not @ (X1 @ X3)))) @ (X2 @ X3))))))))).
% 2.08/1.40 thf(ax89, axiom, (c_PNoLt = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((c_or @ (((c_PNoLt_ @ ((c_binintersect @ X0) @ X2)) @ X1) @ X3)) @ ((c_and @ ((c_and @ ((c_In @ X0) @ X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))) @ (X3 @ X0)))) @ ((c_and @ ((c_and @ ((c_In @ X2) @ X0)) @ (((c_PNoEq_ @ X2) @ X1) @ X3))) @ (c_not @ (X1 @ X2)))))))).
% 2.08/1.40 thf(ax90, axiom, (c_PNoLe = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((((c_PNoLt @ X0) @ X1) @ X2) @ X3)) @ ((c_and @ (X0 = X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))))))).
% 2.08/1.40 thf(ax91, axiom, (c_PNo_downc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X1) @ X2) @ X3) @ X4))))))))))).
% 2.08/1.40 thf(ax92, axiom, (c_PNo_upc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X3) @ X4) @ X1) @ X2))))))))))).
% 2.08/1.40 thf(ax93, axiom, (c_SNoElts_ = (^ [X0:$i]: (((c_binunion @ X0) @ ((c_Repl @ X0) @ (^ [X1:$i]: (((^ [X2:$i]: (((c_SetAdjoin @ X2) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))).
% 2.08/1.40 thf(ax94, axiom, (c_SNo_ = (^ [X0:$i,X1:$i]: (((c_and @ ((c_Subq @ X1) @ (c_SNoElts_ @ X0))) @ (! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_exactly1of2 @ ((c_In @ ((^ [X3:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2)) @ X1)) @ ((c_In @ X2) @ X1)))))))))).
% 2.08/1.40 thf(ax95, axiom, (c_PSNo = (^ [X0:$i,X1:($i > $o)]: (((c_binunion @ ((c_Sep @ X0) @ (^ [X2:$i]: ((X1 @ X2))))) @ (((c_ReplSep @ X0) @ (^ [X2:$i]: ((c_not @ (X1 @ X2))))) @ (^ [X2:$i]: (((^ [X3:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2))))))))).
% 2.08/1.40 thf(ax96, axiom, (c_SNo = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0)))))))).
% 2.08/1.40 thf(ax97, axiom, (c_SNoLev = (^ [X0:$i]: ((c_Eps_i @ (^ [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0))))))))).
% 2.08/1.40 thf(ax98, axiom, (c_SNoEq_ = (^ [X0:$i,X1:$i,X2:$i]: ((((c_PNoEq_ @ X0) @ (^ [X3:$i]: (((c_In @ X3) @ X1)))) @ (^ [X3:$i]: (((c_In @ X3) @ X2)))))))).
% 2.08/1.40 thf(ax99, axiom, (c_SNoLt = (^ [X0:$i,X1:$i]: (((((c_PNoLt @ (c_SNoLev @ X0)) @ (^ [X2:$i]: (((c_In @ X2) @ X0)))) @ (c_SNoLev @ X1)) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax100, axiom, (c_SNoLe = (^ [X0:$i,X1:$i]: (((((c_PNoLe @ (c_SNoLev @ X0)) @ (^ [X2:$i]: (((c_In @ X2) @ X0)))) @ (c_SNoLev @ X1)) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.08/1.40 thf(ax101, axiom, (c_binop_on = (^ [X0:$i,X1:($i > ($i > $i))]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((X1 @ X2) @ X3)) @ X0))))))))))).
% 2.08/1.40 thf(ax102, axiom, (c_Loop = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i]: (((c_and @ ((c_and @ ((c_and @ ((c_and @ ((c_binop_on @ X0) @ X1)) @ ((c_binop_on @ X0) @ X2))) @ ((c_binop_on @ X0) @ X3))) @ (! [X5:$i]: ((((c_In @ X5) @ X0) => ((c_and @ (((X1 @ X4) @ X5) = X5)) @ (((X1 @ X5) @ X4) = X5))))))) @ (! [X5:$i]: ((((c_In @ X5) @ X0) => (! [X6:$i]: ((((c_In @ X6) @ X0) => ((c_and @ ((c_and @ ((c_and @ (((X2 @ X5) @ ((X1 @ X5) @ X6)) = X6)) @ (((X1 @ X5) @ ((X2 @ X5) @ X6)) = X6))) @ (((X3 @ ((X1 @ X5) @ X6)) @ X6) = X5))) @ (((X1 @ ((X3 @ X5) @ X6)) @ X6) = X5))))))))))))).
% 2.08/1.40 thf(ax103, axiom, (c_Loop_with_defs = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((c_and @ ((c_and @ ((c_and @ (((((c_Loop @ X0) @ X1) @ X2) @ X3) @ X4)) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (((X5 @ X14) @ X15) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X14) @ X15))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (! [X16:$i]: ((((c_In @ X16) @ X0) => ((((X6 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X14) @ ((X1 @ X15) @ X16))) @ ((X1 @ ((X1 @ X14) @ X15)) @ X16)))))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => ((c_and @ ((c_and @ ((c_and @ ((c_and @ (((X7 @ X14) @ X15) = ((X2 @ X14) @ ((X1 @ X15) @ X14)))) @ (((X10 @ X14) @ X15) = ((X1 @ X14) @ ((X1 @ X15) @ ((X2 @ X14) @ X4)))))) @ (((X11 @ X14) @ X15) = ((X1 @ ((X1 @ ((X3 @ X4) @ X14)) @ X15)) @ X14)))) @ (((X12 @ X14) @ X15) = ((X1 @ ((X2 @ X14) @ X15)) @ ((X2 @ ((X2 @ X14) @ X4)) @ X4))))) @ (((X13 @ X14) @ X15) = ((X1 @ ((X3 @ X4) @ ((X3 @ X4) @ X14))) @ ((X3 @ X15) @ X14)))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (! [X16:$i]: ((((c_In @ X16) @ X0) => ((c_and @ ((((X8 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X15) @ ((X1 @ X14) @ X16))))) @ ((((X9 @ X14) @ X15) @ X16) = ((X3 @ ((X1 @ ((X1 @ X16) @ X14)) @ X15)) @ ((X1 @ X14) @ X15)))))))))))))))))).
% 2.08/1.40 thf(ax104, axiom, (c_Loop_with_defs_cex1 = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((((((((((((((c_Loop_with_defs @ X0) @ X1) @ X2) @ X3) @ X4) @ X5) @ X6) @ X7) @ X8) @ X9) @ X10) @ X11) @ X12) @ X13)) @ (? [X14:$i]: (((c_and @ ((c_In @ X14) @ X0)) @ (? [X15:$i]: (((c_and @ ((c_In @ X15) @ X0)) @ (? [X16:$i]: (((c_and @ ((c_In @ X16) @ X0)) @ (? [X17:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (c_not @ (((X5 @ ((X1 @ ((X2 @ (((X8 @ X15) @ X16) @ X14)) @ X4)) @ X14)) @ X17) = X4))))))))))))))))))).
% 2.08/1.40 thf(ax105, axiom, (c_Loop_with_defs_cex2 = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((((((((((((((c_Loop_with_defs @ X0) @ X1) @ X2) @ X3) @ X4) @ X5) @ X6) @ X7) @ X8) @ X9) @ X10) @ X11) @ X12) @ X13)) @ (? [X14:$i]: (((c_and @ ((c_In @ X14) @ X0)) @ (? [X15:$i]: (((c_and @ ((c_In @ X15) @ X0)) @ (? [X16:$i]: (((c_and @ ((c_In @ X16) @ X0)) @ (? [X17:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (? [X18:$i]: (((c_and @ ((c_In @ X18) @ X0)) @ (c_not @ ((((X6 @ X18) @ ((X1 @ ((X3 @ X4) @ X14)) @ (((X9 @ X15) @ X16) @ X14))) @ X17) = X4)))))))))))))))))))))).
% 2.08/1.40 thf(ax106, axiom, (c_combinator = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ (c_Inj0 @ c_Empty)) => ((X1 @ (c_Inj0 @ (c_Power @ c_Empty))) => ((! [X2:$i,X3:$i]: (((X1 @ X2) => ((X1 @ X3) => (X1 @ (c_Inj1 @ ((c_setsum @ X2) @ X3))))))) => (X1 @ X0)))))))))).
% 2.08/1.40 thf(ax107, axiom, (c_combinator_equiv = (^ [X0:$i,X1:$i]: ((! [X2:($i > ($i > $o))]: (((((^ [X3:$i,X4:$i,X5:($i > ($i > $i))]: (((c_per_i @ X2) => ((! [X6:$i]: (((c_combinator @ X6) => ((X2 @ X6) @ X6)))) => ((! [X6:$i,X7:$i,X8:$i,X9:$i]: (((c_combinator @ X6) => ((c_combinator @ X7) => ((c_combinator @ X8) => ((c_combinator @ X9) => (((X2 @ X6) @ X8) => (((X2 @ X7) @ X9) => ((X2 @ ((X5 @ X6) @ X7)) @ ((X5 @ X8) @ X9)))))))))) => ((! [X6:$i,X7:$i]: (((X2 @ ((X5 @ ((X5 @ X3) @ X6)) @ X7)) @ X6))) => ((! [X6:$i,X7:$i,X8:$i]: (((X2 @ ((X5 @ ((X5 @ ((X5 @ X4) @ X6)) @ X7)) @ X8)) @ ((X5 @ ((X5 @ X6) @ X8)) @ ((X5 @ X7) @ X8))))) => ((X2 @ X0) @ X1)))))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ (c_Power @ c_Empty))) @ (^ [X3:$i,X4:$i]: ((c_Inj1 @ ((c_setsum @ X3) @ X4))))))))))).
% 2.08/1.40 thf(ax108, axiom, (c_equip_mod = (^ [X0:$i,X1:$i,X2:$i]: ((? [X3:$i,X4:$i]: (((c_or @ ((c_and @ ((c_equip @ ((c_setsum @ X0) @ X3)) @ X1)) @ ((c_equip @ ((c_setprod @ X4) @ X3)) @ X2))) @ ((c_and @ ((c_equip @ ((c_setsum @ X1) @ X3)) @ X0)) @ ((c_equip @ ((c_setprod @ X4) @ X3)) @ X2))))))))).
% 2.08/1.40 thf(conj, conjecture, (! [X0:(($i > ($i > ($i > $i))) > (($i > $i) > ((($i > ($i > $i)) > $i) > $i))),X1:(($i > $i) > ($i > $i)),X2:(((($i > ($i > ($i > $i))) > $i) > ($i > $i)) > ($i > $i)),X3:(($i > $i) > (($i > $i) > $i))]: (((! [X4:($i > ((($i > $i) > $i) > $i)),X5:(($i > $i) > $i),X6:((($i > ($i > $i)) > (($i > $i) > $i)) > $i),X7:$i]: ((((X3 @ (^ [X8:$i]: ((c_Inj1 @ c_Empty)))) @ (^ [X8:$i]: (((c_setsum @ c_Empty) @ c_Empty)))) = (c_Inj1 @ c_Empty)))) => ((! [X4:$i,X5:$i,X6:$i,X7:$i]: ((((X3 @ (^ [X8:$i]: (X6))) @ (^ [X8:$i]: (X7))) = ((c_setsum @ ((X2 @ (^ [X8:(($i > ($i > ($i > $i))) > $i),X9:$i]: (c_Empty))) @ (((X0 @ (^ [X8:$i,X9:$i,X10:$i]: (((X3 @ (^ [X11:$i]: (X10))) @ (^ [X11:$i]: (c_Empty)))))) @ (^ [X8:$i]: (c_Empty))) @ (^ [X8:($i > ($i > $i))]: (c_Empty))))) @ c_Empty)))) => ((! [X4:($i > $i),X5:($i > ($i > $i)),X6:($i > $i),X7:$i]: ((((X2 @ (^ [X8:(($i > ($i > ($i > $i))) > $i),X9:$i]: (X7))) @ c_Empty) = X7))) => ((! [X4:($i > (($i > ($i > $i)) > $i)),X5:($i > $i),X6:(((($i > $i) > $i) > $i) > $i),X7:($i > $i)]: ((((X2 @ (^ [X8:(($i > ($i > ($i > $i))) > $i),X9:$i]: ((X7 @ ((X2 @ (^ [X10:(($i > ($i > ($i > $i))) > $i),X11:$i]: ((((X0 @ (^ [X12:$i,X13:$i,X14:$i]: ((c_Inj1 @ c_Empty)))) @ (^ [X12:$i]: ((c_Inj0 @ c_Empty)))) @ (^ [X12:($i > ($i > $i))]: (((X3 @ (^ [X13:$i]: (c_Empty))) @ (^ [X13:$i]: (c_Empty))))))))) @ (c_Inj0 @ (((X0 @ (^ [X10:$i,X11:$i,X12:$i]: (c_Empty))) @ (^ [X10:$i]: (c_Empty))) @ (^ [X10:($i > ($i > $i))]: (c_Empty))))))))) @ ((X3 @ (^ [X8:$i]: (((c_setsum @ X8) @ c_Empty)))) @ (^ [X8:$i]: (c_Empty)))) = ((c_setsum @ (X7 @ (X5 @ (((X0 @ (^ [X8:$i,X9:$i,X10:$i]: ((c_Inj1 @ c_Empty)))) @ (^ [X8:$i]: ((((X0 @ (^ [X9:$i,X10:$i,X11:$i]: (c_Empty))) @ (^ [X9:$i]: (c_Empty))) @ (^ [X9:($i > ($i > $i))]: (c_Empty)))))) @ (^ [X8:($i > ($i > $i))]: (((c_setsum @ c_Empty) @ c_Empty))))))) @ ((X1 @ (^ [X8:$i]: ((X7 @ c_Empty)))) @ (X5 @ ((X4 @ ((X1 @ (^ [X8:$i]: (c_Empty))) @ c_Empty)) @ (^ [X8:$i,X9:$i]: (c_Empty))))))))) => ((! [X4:((($i > $i) > ($i > $i)) > $i),X5:$i,X6:$i,X7:$i]: ((((X1 @ (^ [X8:$i]: ((c_Inj1 @ ((X1 @ (^ [X9:$i]: ((c_Inj0 @ (((X0 @ (^ [X10:$i,X11:$i,X12:$i]: (c_Empty))) @ (^ [X10:$i]: (c_Empty))) @ (^ [X10:($i > ($i > $i))]: (c_Empty))))))) @ (c_Inj1 @ X7)))))) @ (c_Inj0 @ ((X2 @ (^ [X8:(($i > ($i > ($i > $i))) > $i),X9:$i]: (X9))) @ X5))) = (c_Inj0 @ ((X2 @ (^ [X8:(($i > ($i > ($i > $i))) > $i),X9:$i]: (X7))) @ ((c_setsum @ c_Empty) @ c_Empty)))))) => ((! [X4:((($i > $i) > $i) > $i),X5:($i > ($i > (($i > $i) > $i))),X6:$i,X7:(($i > $i) > (($i > $i) > $i))]: ((((X1 @ (^ [X8:$i]: (((X7 @ (^ [X9:$i]: (((c_setsum @ X9) @ X8)))) @ (^ [X9:$i]: (c_Empty)))))) @ c_Empty) = ((X7 @ (^ [X8:$i]: (((c_setsum @ ((X2 @ (^ [X9:(($i > ($i > ($i > $i))) > $i),X10:$i]: (c_Empty))) @ ((X3 @ (^ [X9:$i]: (((X2 @ (^ [X10:(($i > ($i > ($i > $i))) > $i),X11:$i]: (c_Empty))) @ c_Empty)))) @ (^ [X9:$i]: (((X1 @ (^ [X10:$i]: (c_Empty))) @ c_Empty)))))) @ ((X2 @ (^ [X9:(($i > ($i > ($i > $i))) > $i),X10:$i]: (c_Empty))) @ ((X2 @ (^ [X9:(($i > ($i > ($i > $i))) > $i),X10:$i]: (((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (^ [X9:(($i > ($i > ($i > $i))) > $i),X10:$i]: (c_Empty))) @ c_Empty))))))) @ (^ [X8:$i]: ((c_Inj1 @ ((X1 @ (^ [X9:$i]: (((X7 @ (^ [X10:$i]: (((X1 @ (^ [X11:$i]: (c_Empty))) @ c_Empty)))) @ (^ [X10:$i]: ((c_Inj1 @ c_Empty))))))) @ X6)))))))) => ((! [X4:($i > ((($i > $i) > ($i > $i)) > $i)),X5:$i,X6:$i,X7:$i]: (((((X0 @ (^ [X8:$i,X9:$i,X10:$i]: (X7))) @ (^ [X8:$i]: (X6))) @ (^ [X8:($i > ($i > $i))]: (c_Empty))) = X6))) => ((! [X4:$i,X5:$i,X6:($i > (($i > $i) > $i)),X7:($i > $i)]: (((((X0 @ (^ [X8:$i,X9:$i,X10:$i]: (((X1 @ (^ [X11:$i]: (((X2 @ (^ [X12:(($i > ($i > ($i > $i))) > $i),X13:$i]: (X10))) @ ((X2 @ (^ [X12:(($i > ($i > ($i > $i))) > $i),X13:$i]: (((c_setsum @ c_Empty) @ c_Empty)))) @ X11))))) @ (c_Inj1 @ c_Empty))))) @ (^ [X8:$i]: ((X7 @ c_Empty)))) @ (^ [X8:($i > ($i > $i))]: (c_Empty))) = (X7 @ X4)))) => c_False))))))))))).
% 2.08/1.40 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2DTF351.p
% 2.08/1.40 ------------------------
% 2.42/1.42 ---- Cleaned THF ---
% 2.42/1.42 thf(c_Eps_i_tp,type,
% 2.42/1.42 c_Eps_i: ( $i > $o ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_False_tp,type,
% 2.42/1.42 c_False: $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_True_tp,type,
% 2.42/1.42 c_True: $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_not_tp,type,
% 2.42/1.42 c_not: $o > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_and_tp,type,
% 2.42/1.42 c_and: $o > $o > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_or_tp,type,
% 2.42/1.42 c_or: $o > $o > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_iff_tp,type,
% 2.42/1.42 c_iff: $o > $o > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_In_tp,type,
% 2.42/1.42 c_In: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Subq_tp,type,
% 2.42/1.42 c_Subq: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Empty_tp,type,
% 2.42/1.42 c_Empty: $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Union_tp,type,
% 2.42/1.42 c_Union: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Power_tp,type,
% 2.42/1.42 c_Power: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Repl_tp,type,
% 2.42/1.42 c_Repl: $i > ( $i > $i ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_TransSet_tp,type,
% 2.42/1.42 c_TransSet: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_atleast2_tp,type,
% 2.42/1.42 c_atleast2: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_atleast3_tp,type,
% 2.42/1.42 c_atleast3: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_atleast4_tp,type,
% 2.42/1.42 c_atleast4: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_atleast5_tp,type,
% 2.42/1.42 c_atleast5: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_atleast6_tp,type,
% 2.42/1.42 c_atleast6: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_exactly2_tp,type,
% 2.42/1.42 c_exactly2: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_exactly3_tp,type,
% 2.42/1.42 c_exactly3: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_exactly4_tp,type,
% 2.42/1.42 c_exactly4: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_exactly5_tp,type,
% 2.42/1.42 c_exactly5: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_exu_i_tp,type,
% 2.42/1.42 c_exu_i: ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_reflexive_i_tp,type,
% 2.42/1.42 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_irreflexive_i_tp,type,
% 2.42/1.42 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_symmetric_i_tp,type,
% 2.42/1.42 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_antisymmetric_i_tp,type,
% 2.42/1.42 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_transitive_i_tp,type,
% 2.42/1.42 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_eqreln_i_tp,type,
% 2.42/1.42 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_per_i_tp,type,
% 2.42/1.42 c_per_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_linear_i_tp,type,
% 2.42/1.42 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_trichotomous_or_i_tp,type,
% 2.42/1.42 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_partialorder_i_tp,type,
% 2.42/1.42 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_totalorder_i_tp,type,
% 2.42/1.42 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_strictpartialorder_i_tp,type,
% 2.42/1.42 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_stricttotalorder_i_tp,type,
% 2.42/1.42 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_If_i_tp,type,
% 2.42/1.42 c_If_i: $o > $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_exactly1of2_tp,type,
% 2.42/1.42 c_exactly1of2: $o > $o > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_exactly1of3_tp,type,
% 2.42/1.42 c_exactly1of3: $o > $o > $o > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_nIn_tp,type,
% 2.42/1.42 c_nIn: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_nSubq_tp,type,
% 2.42/1.42 c_nSubq: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_UPair_tp,type,
% 2.42/1.42 c_UPair: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Sing_tp,type,
% 2.42/1.42 c_Sing: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_binunion_tp,type,
% 2.42/1.42 c_binunion: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_SetAdjoin_tp,type,
% 2.42/1.42 c_SetAdjoin: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_famunion_tp,type,
% 2.42/1.42 c_famunion: $i > ( $i > $i ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Sep_tp,type,
% 2.42/1.42 c_Sep: $i > ( $i > $o ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_ReplSep_tp,type,
% 2.42/1.42 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_binintersect_tp,type,
% 2.42/1.42 c_binintersect: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_setminus_tp,type,
% 2.42/1.42 c_setminus: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_inj_tp,type,
% 2.42/1.42 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_bij_tp,type,
% 2.42/1.42 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_atleastp_tp,type,
% 2.42/1.42 c_atleastp: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_equip_tp,type,
% 2.42/1.42 c_equip: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_In_rec_poly_G_i_tp,type,
% 2.42/1.42 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_In_rec_poly_i_tp,type,
% 2.42/1.42 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_ordsucc_tp,type,
% 2.42/1.42 c_ordsucc: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_nat_p_tp,type,
% 2.42/1.42 c_nat_p: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_nat_primrec_tp,type,
% 2.42/1.42 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_add_nat_tp,type,
% 2.42/1.42 c_add_nat: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_mul_nat_tp,type,
% 2.42/1.42 c_mul_nat: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_ordinal_tp,type,
% 2.42/1.42 c_ordinal: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_V__tp,type,
% 2.42/1.42 c_V_: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Inj1_tp,type,
% 2.42/1.42 c_Inj1: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Inj0_tp,type,
% 2.42/1.42 c_Inj0: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Unj_tp,type,
% 2.42/1.42 c_Unj: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_combine_funcs_tp,type,
% 2.42/1.42 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_setsum_tp,type,
% 2.42/1.42 c_setsum: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_proj0_tp,type,
% 2.42/1.42 c_proj0: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_proj1_tp,type,
% 2.42/1.42 c_proj1: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_binrep_tp,type,
% 2.42/1.42 c_binrep: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_lam_tp,type,
% 2.42/1.42 c_lam: $i > ( $i > $i ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_setprod_tp,type,
% 2.42/1.42 c_setprod: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_ap_tp,type,
% 2.42/1.42 c_ap: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_setsum_p_tp,type,
% 2.42/1.42 c_setsum_p: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_tuple_p_tp,type,
% 2.42/1.42 c_tuple_p: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Pi_tp,type,
% 2.42/1.42 c_Pi: $i > ( $i > $i ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_setexp_tp,type,
% 2.42/1.42 c_setexp: $i > $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_Sep2_tp,type,
% 2.42/1.42 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_set_of_pairs_tp,type,
% 2.42/1.42 c_set_of_pairs: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_lam2_tp,type,
% 2.42/1.42 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_PNoEq__tp,type,
% 2.42/1.42 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_PNoLt__tp,type,
% 2.42/1.42 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_PNoLt_tp,type,
% 2.42/1.42 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_PNoLe_tp,type,
% 2.42/1.42 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_PNo_downc_tp,type,
% 2.42/1.42 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_PNo_upc_tp,type,
% 2.42/1.42 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNoElts__tp,type,
% 2.42/1.42 c_SNoElts_: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNo__tp,type,
% 2.42/1.42 c_SNo_: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_PSNo_tp,type,
% 2.42/1.42 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNo_tp,type,
% 2.42/1.42 c_SNo: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNoLev_tp,type,
% 2.42/1.42 c_SNoLev: $i > $i ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNoEq__tp,type,
% 2.42/1.42 c_SNoEq_: $i > $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNoLt_tp,type,
% 2.42/1.42 c_SNoLt: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_SNoLe_tp,type,
% 2.42/1.42 c_SNoLe: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_binop_on_tp,type,
% 2.42/1.42 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Loop_tp,type,
% 2.42/1.42 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Loop_with_defs_tp,type,
% 2.42/1.42 c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Loop_with_defs_cex1_tp,type,
% 2.42/1.42 c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_Loop_with_defs_cex2_tp,type,
% 2.42/1.42 c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_combinator_tp,type,
% 2.42/1.42 c_combinator: $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_combinator_equiv_tp,type,
% 2.42/1.42 c_combinator_equiv: $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(c_equip_mod_tp,type,
% 2.42/1.42 c_equip_mod: $i > $i > $i > $o ).
% 2.42/1.42
% 2.42/1.42 thf(ax1,axiom,
% 2.42/1.42 ! [X0: $i > $o,X1: $i] :
% 2.42/1.42 ( ( X0 @ X1 )
% 2.42/1.42 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax2,axiom,
% 2.42/1.42 ! [X0: $o] :
% 2.42/1.42 ( ( c_not @ ( c_not @ X0 ) )
% 2.42/1.42 => X0 ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax3,axiom,
% 2.42/1.42 ! [X0: $o,X1: $o] :
% 2.42/1.42 ( ( c_iff @ X0 @ X1 )
% 2.42/1.42 => ( X0 = X1 ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax4,axiom,
% 2.42/1.42 ! [X0: $i,X1: $i] :
% 2.42/1.42 ( ( c_Subq @ X0 @ X1 )
% 2.42/1.42 => ( ( c_Subq @ X1 @ X0 )
% 2.42/1.42 => ( X0 = X1 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax5,axiom,
% 2.42/1.42 ( c_not
% 2.42/1.42 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax6,axiom,
% 2.42/1.42 ! [X0: $i,X1: $i] :
% 2.42/1.42 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.42/1.42 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax7,axiom,
% 2.42/1.42 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax8,axiom,
% 2.42/1.42 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.42/1.42 ( c_iff
% 2.42/1.42 @ ( c_In @ X2
% 2.42/1.42 @ ( c_Repl @ X0
% 2.42/1.42 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.42/1.42 @ ? [X3: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X3 @ X0 )
% 2.42/1.42 @ ( X2
% 2.42/1.42 = ( X1 @ X3 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax9,axiom,
% 2.42/1.42 ! [X0: $i > $o] :
% 2.42/1.42 ( ! [X1: $i] :
% 2.42/1.42 ( ( X0 @ X1 )
% 2.42/1.42 => ! [X2: $i] :
% 2.42/1.42 ( ( c_In @ X2 @ X1 )
% 2.42/1.42 => ( X0 @ X2 ) ) )
% 2.42/1.42 => ( ( X0 @ c_Empty )
% 2.42/1.42 => ( ! [X1: $i] :
% 2.42/1.42 ( ( X0 @ X1 )
% 2.42/1.42 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.42/1.42 => ( ! [X1: $i] :
% 2.42/1.42 ( ( X0 @ X1 )
% 2.42/1.42 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.42/1.42 => ( ! [X1: $i] :
% 2.42/1.42 ( ( X0 @ X1 )
% 2.42/1.42 => ! [X2: $i > $i] :
% 2.42/1.42 ( ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X1 )
% 2.42/1.42 => ( X0 @ ( X2 @ X3 ) ) )
% 2.42/1.42 => ( X0
% 2.42/1.42 @ ( c_Repl @ X1
% 2.42/1.42 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.42/1.42 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax10,axiom,
% 2.42/1.42 ! [X0: $i > $o] :
% 2.42/1.42 ( ! [X1: $i] :
% 2.42/1.42 ( ! [X2: $i] :
% 2.42/1.42 ( ( c_In @ X2 @ X1 )
% 2.42/1.42 => ( X0 @ X2 ) )
% 2.42/1.42 => ( X0 @ X1 ) )
% 2.42/1.42 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax11,axiom,
% 2.42/1.42 ( c_False
% 2.42/1.42 = ( ! [X0: $o] : X0 ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax12,axiom,
% 2.42/1.42 ( c_True
% 2.42/1.42 = ( ! [X0: $o] :
% 2.42/1.42 ( X0
% 2.42/1.42 => X0 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax13,axiom,
% 2.42/1.42 ( c_not
% 2.42/1.42 = ( ^ [X0: $o] :
% 2.42/1.42 ( X0
% 2.42/1.42 => c_False ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax14,axiom,
% 2.42/1.42 ( c_and
% 2.42/1.42 = ( ^ [X0: $o,X1: $o] :
% 2.42/1.42 ! [X2: $o] :
% 2.42/1.42 ( ( X0
% 2.42/1.42 => ( X1
% 2.42/1.42 => X2 ) )
% 2.42/1.42 => X2 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax15,axiom,
% 2.42/1.42 ( c_or
% 2.42/1.42 = ( ^ [X0: $o,X1: $o] :
% 2.42/1.42 ! [X2: $o] :
% 2.42/1.42 ( ( X0
% 2.42/1.42 => X2 )
% 2.42/1.42 => ( ( X1
% 2.42/1.42 => X2 )
% 2.42/1.42 => X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax16,axiom,
% 2.42/1.42 ( c_iff
% 2.42/1.42 = ( ^ [X0: $o,X1: $o] :
% 2.42/1.42 ( c_and
% 2.42/1.42 @ ( X0
% 2.42/1.42 => X1 )
% 2.42/1.42 @ ( X1
% 2.42/1.42 => X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax17,axiom,
% 2.42/1.42 ( c_Subq
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ! [X2: $i] :
% 2.42/1.42 ( ( c_In @ X2 @ X0 )
% 2.42/1.42 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax18,axiom,
% 2.42/1.42 ( c_TransSet
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ! [X1: $i] :
% 2.42/1.42 ( ( c_In @ X1 @ X0 )
% 2.42/1.42 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax19,axiom,
% 2.42/1.42 ( c_atleast2
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax20,axiom,
% 2.42/1.42 ( c_atleast3
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax21,axiom,
% 2.42/1.42 ( c_atleast4
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax22,axiom,
% 2.42/1.42 ( c_atleast5
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax23,axiom,
% 2.42/1.42 ( c_atleast6
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax24,axiom,
% 2.42/1.42 ( c_exactly2
% 2.42/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax25,axiom,
% 2.42/1.42 ( c_exactly3
% 2.42/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax26,axiom,
% 2.42/1.42 ( c_exactly4
% 2.42/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax27,axiom,
% 2.42/1.42 ( c_exactly5
% 2.42/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax28,axiom,
% 2.42/1.42 ( c_exu_i
% 2.42/1.42 = ( ^ [X0: $i > $o] :
% 2.42/1.42 ( c_and
% 2.42/1.42 @ ? [X1: $i] : ( X0 @ X1 )
% 2.42/1.42 @ ! [X1: $i,X2: $i] :
% 2.42/1.42 ( ( X0 @ X1 )
% 2.42/1.42 => ( ( X0 @ X2 )
% 2.42/1.42 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax29,axiom,
% 2.42/1.42 ( c_reflexive_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax30,axiom,
% 2.42/1.42 ( c_irreflexive_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax31,axiom,
% 2.42/1.42 ( c_symmetric_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i,X2: $i] :
% 2.42/1.42 ( ( X0 @ X1 @ X2 )
% 2.42/1.42 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax32,axiom,
% 2.42/1.42 ( c_antisymmetric_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i,X2: $i] :
% 2.42/1.42 ( ( X0 @ X1 @ X2 )
% 2.42/1.42 => ( ( X0 @ X2 @ X1 )
% 2.42/1.42 => ( X1 = X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax33,axiom,
% 2.42/1.42 ( c_transitive_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i,X2: $i,X3: $i] :
% 2.42/1.42 ( ( X0 @ X1 @ X2 )
% 2.42/1.42 => ( ( X0 @ X2 @ X3 )
% 2.42/1.42 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax34,axiom,
% 2.42/1.42 ( c_eqreln_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax35,axiom,
% 2.42/1.42 ( c_per_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax36,axiom,
% 2.42/1.42 ( c_linear_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax37,axiom,
% 2.42/1.42 ( c_trichotomous_or_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.42/1.42 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax38,axiom,
% 2.42/1.42 ( c_partialorder_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax39,axiom,
% 2.42/1.42 ( c_totalorder_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax40,axiom,
% 2.42/1.42 ( c_strictpartialorder_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax41,axiom,
% 2.42/1.42 ( c_stricttotalorder_i
% 2.42/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax42,axiom,
% 2.42/1.42 ( c_If_i
% 2.42/1.42 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.42/1.42 ( c_Eps_i
% 2.42/1.42 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax43,axiom,
% 2.42/1.42 ( c_exactly1of2
% 2.42/1.42 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax44,axiom,
% 2.42/1.42 ( c_exactly1of3
% 2.42/1.42 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax45,axiom,
% 2.42/1.42 ( c_nIn
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax46,axiom,
% 2.42/1.42 ( c_nSubq
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax47,axiom,
% 2.42/1.42 ( c_UPair
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.42/1.42 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax48,axiom,
% 2.42/1.42 ( c_Sing
% 2.42/1.42 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax49,axiom,
% 2.42/1.42 ( c_binunion
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax50,axiom,
% 2.42/1.42 ( c_SetAdjoin
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax51,axiom,
% 2.42/1.42 ( c_famunion
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i] :
% 2.42/1.42 ( c_Union
% 2.42/1.42 @ ( c_Repl @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax52,axiom,
% 2.42/1.42 ( c_Sep
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o] :
% 2.42/1.42 ( c_If_i
% 2.42/1.42 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.42/1.42 @ ( c_Repl @ X0
% 2.42/1.42 @ ^ [X2: $i] :
% 2.42/1.42 ( ^ [X3: $i] :
% 2.42/1.42 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.42/1.42 @ ( c_Eps_i
% 2.42/1.42 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.42/1.42 @ X2 ) )
% 2.42/1.42 @ c_Empty ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax53,axiom,
% 2.42/1.42 ( c_ReplSep
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.42/1.42 ( c_Repl
% 2.42/1.42 @ ( c_Sep @ X0
% 2.42/1.42 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.42/1.42 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax54,axiom,
% 2.42/1.42 ( c_binintersect
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_Sep @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax55,axiom,
% 2.42/1.42 ( c_setminus
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_Sep @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax56,axiom,
% 2.42/1.42 ( c_inj
% 2.42/1.42 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.42/1.42 ( c_and
% 2.42/1.42 @ ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X0 )
% 2.42/1.42 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.42/1.42 @ ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X0 )
% 2.42/1.42 => ! [X4: $i] :
% 2.42/1.42 ( ( c_In @ X4 @ X0 )
% 2.42/1.42 => ( ( ( X2 @ X3 )
% 2.42/1.42 = ( X2 @ X4 ) )
% 2.42/1.42 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax57,axiom,
% 2.42/1.42 ( c_bij
% 2.42/1.42 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.42/1.42 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.42/1.42 @ ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X1 )
% 2.42/1.42 => ? [X4: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X4 @ X0 )
% 2.42/1.42 @ ( ( X2 @ X4 )
% 2.42/1.42 = X3 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax58,axiom,
% 2.42/1.42 ( c_atleastp
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax59,axiom,
% 2.42/1.42 ( c_equip
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax60,axiom,
% 2.42/1.42 ( c_In_rec_poly_G_i
% 2.42/1.42 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.42/1.42 ! [X3: $i > $i > $o] :
% 2.42/1.42 ( ! [X4: $i,X5: $i > $i] :
% 2.42/1.42 ( ! [X6: $i] :
% 2.42/1.42 ( ( c_In @ X6 @ X4 )
% 2.42/1.42 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.42/1.42 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.42/1.42 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax61,axiom,
% 2.42/1.42 ( c_In_rec_poly_i
% 2.42/1.42 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.42/1.42 ( c_Eps_i
% 2.42/1.42 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax62,axiom,
% 2.42/1.42 ( c_ordsucc
% 2.42/1.42 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax63,axiom,
% 2.42/1.42 ( c_nat_p
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ! [X1: $i > $o] :
% 2.42/1.42 ( ( X1 @ c_Empty )
% 2.42/1.42 => ( ! [X2: $i] :
% 2.42/1.42 ( ( X1 @ X2 )
% 2.42/1.42 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.42/1.42 => ( X1 @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax64,axiom,
% 2.42/1.42 ( c_nat_primrec
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.42/1.42 ( c_In_rec_poly_i
% 2.42/1.42 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax65,axiom,
% 2.42/1.42 ( c_add_nat
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_nat_primrec @ X0
% 2.42/1.42 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.42/1.42 @ X1 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax66,axiom,
% 2.42/1.42 ( c_mul_nat
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_nat_primrec @ c_Empty
% 2.42/1.42 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.42/1.42 @ X1 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax67,axiom,
% 2.42/1.42 ( c_ordinal
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( c_and @ ( c_TransSet @ X0 )
% 2.42/1.42 @ ! [X1: $i] :
% 2.42/1.42 ( ( c_In @ X1 @ X0 )
% 2.42/1.42 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax68,axiom,
% 2.42/1.42 ( c_V_
% 2.42/1.42 = ( c_In_rec_poly_i
% 2.42/1.42 @ ^ [X0: $i,X1: $i > $i] :
% 2.42/1.42 ( c_famunion @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax69,axiom,
% 2.42/1.42 ( c_Inj1
% 2.42/1.42 = ( c_In_rec_poly_i
% 2.42/1.42 @ ^ [X0: $i,X1: $i > $i] :
% 2.42/1.42 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.42/1.42 @ ( c_Repl @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax70,axiom,
% 2.42/1.42 ( c_Inj0
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( c_Repl @ X0
% 2.42/1.42 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax71,axiom,
% 2.42/1.42 ( c_Unj
% 2.42/1.42 = ( c_In_rec_poly_i
% 2.42/1.42 @ ^ [X0: $i,X1: $i > $i] :
% 2.42/1.42 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.42/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax72,axiom,
% 2.42/1.42 ( c_combine_funcs
% 2.42/1.42 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.42/1.42 ( c_If_i
% 2.42/1.42 @ ( X4
% 2.42/1.42 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.42/1.42 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.42/1.42 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax73,axiom,
% 2.42/1.42 ( c_setsum
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_binunion
% 2.42/1.42 @ ( c_Repl @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.42/1.42 @ ( c_Repl @ X1
% 2.42/1.42 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax74,axiom,
% 2.42/1.42 ( c_proj0
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( c_ReplSep @ X0
% 2.42/1.42 @ ^ [X1: $i] :
% 2.42/1.42 ? [X2: $i] :
% 2.42/1.42 ( ( c_Inj0 @ X2 )
% 2.42/1.42 = X1 )
% 2.42/1.42 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax75,axiom,
% 2.42/1.42 ( c_proj1
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( c_ReplSep @ X0
% 2.42/1.42 @ ^ [X1: $i] :
% 2.42/1.42 ? [X2: $i] :
% 2.42/1.42 ( ( c_Inj1 @ X2 )
% 2.42/1.42 = X1 )
% 2.42/1.42 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax76,axiom,
% 2.42/1.42 ( c_binrep
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax77,axiom,
% 2.42/1.42 ( c_lam
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i] :
% 2.42/1.42 ( c_famunion @ X0
% 2.42/1.42 @ ^ [X2: $i] :
% 2.42/1.42 ( c_Repl @ ( X1 @ X2 )
% 2.42/1.42 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax78,axiom,
% 2.42/1.42 ( c_setprod
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_lam @ X0
% 2.42/1.42 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax79,axiom,
% 2.42/1.42 ( c_ap
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_ReplSep @ X0
% 2.42/1.42 @ ^ [X2: $i] :
% 2.42/1.42 ? [X3: $i] :
% 2.42/1.42 ( X2
% 2.42/1.42 = ( c_setsum @ X1 @ X3 ) )
% 2.42/1.42 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax80,axiom,
% 2.42/1.42 ( c_setsum_p
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.42/1.42 = X0 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax81,axiom,
% 2.42/1.42 ( c_tuple_p
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ! [X2: $i] :
% 2.42/1.42 ( ( c_In @ X2 @ X1 )
% 2.42/1.42 => ? [X3: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X3 @ X0 )
% 2.42/1.42 @ ? [X4: $i] :
% 2.42/1.42 ( X2
% 2.42/1.42 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax82,axiom,
% 2.42/1.42 ( c_Pi
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i] :
% 2.42/1.42 ( c_Sep
% 2.42/1.42 @ ( c_Power
% 2.42/1.42 @ ( c_lam @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.42/1.42 @ ^ [X2: $i] :
% 2.42/1.42 ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X0 )
% 2.42/1.42 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax83,axiom,
% 2.42/1.42 ( c_setexp
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_Pi @ X1
% 2.42/1.42 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax84,axiom,
% 2.42/1.42 ( c_Sep2
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.42/1.42 ( c_Sep
% 2.42/1.42 @ ( c_lam @ X0
% 2.42/1.42 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.42/1.42 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax85,axiom,
% 2.42/1.42 ( c_set_of_pairs
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ! [X1: $i] :
% 2.42/1.42 ( ( c_In @ X1 @ X0 )
% 2.42/1.42 => ? [X2: $i,X3: $i] :
% 2.42/1.42 ( X1
% 2.42/1.42 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.42/1.42 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax86,axiom,
% 2.42/1.42 ( c_lam2
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.42/1.42 ( c_lam @ X0
% 2.42/1.42 @ ^ [X3: $i] :
% 2.42/1.42 ( c_lam @ ( X1 @ X3 )
% 2.42/1.42 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax87,axiom,
% 2.42/1.42 ( c_PNoEq_
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.42/1.42 ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X0 )
% 2.42/1.42 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax88,axiom,
% 2.42/1.42 ( c_PNoLt_
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.42/1.42 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax89,axiom,
% 2.42/1.42 ( c_PNoLt
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax90,axiom,
% 2.42/1.42 ( c_PNoLe
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax91,axiom,
% 2.42/1.42 ( c_PNo_downc
% 2.42/1.42 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.42/1.42 ? [X3: $i] :
% 2.42/1.42 ( c_and @ ( c_ordinal @ X3 )
% 2.42/1.42 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax92,axiom,
% 2.42/1.42 ( c_PNo_upc
% 2.42/1.42 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.42/1.42 ? [X3: $i] :
% 2.42/1.42 ( c_and @ ( c_ordinal @ X3 )
% 2.42/1.42 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax93,axiom,
% 2.42/1.42 ( c_SNoElts_
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( c_binunion @ X0
% 2.42/1.42 @ ( c_Repl @ X0
% 2.42/1.42 @ ^ [X1: $i] :
% 2.42/1.42 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.42/1.42 @ X1 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax94,axiom,
% 2.42/1.42 ( c_SNo_
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.42/1.42 @ ! [X2: $i] :
% 2.42/1.42 ( ( c_In @ X2 @ X0 )
% 2.42/1.42 => ( c_exactly1of2
% 2.42/1.42 @ ( c_In
% 2.42/1.42 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.42/1.42 @ X2 )
% 2.42/1.42 @ X1 )
% 2.42/1.42 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax95,axiom,
% 2.42/1.42 ( c_PSNo
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $o] :
% 2.42/1.42 ( c_binunion
% 2.42/1.42 @ ( c_Sep @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.42/1.42 @ ( c_ReplSep @ X0
% 2.42/1.42 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.42/1.42 @ ^ [X2: $i] :
% 2.42/1.42 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.42/1.42 @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax96,axiom,
% 2.42/1.42 ( c_SNo
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax97,axiom,
% 2.42/1.42 ( c_SNoLev
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ( c_Eps_i
% 2.42/1.42 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax98,axiom,
% 2.42/1.42 ( c_SNoEq_
% 2.42/1.42 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.42/1.42 ( c_PNoEq_ @ X0
% 2.42/1.42 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.42/1.42 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax99,axiom,
% 2.42/1.42 ( c_SNoLt
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.42/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.42/1.42 @ ( c_SNoLev @ X1 )
% 2.42/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax100,axiom,
% 2.42/1.42 ( c_SNoLe
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.42/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.42/1.42 @ ( c_SNoLev @ X1 )
% 2.42/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax101,axiom,
% 2.42/1.42 ( c_binop_on
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.42/1.42 ! [X2: $i] :
% 2.42/1.42 ( ( c_In @ X2 @ X0 )
% 2.42/1.42 => ! [X3: $i] :
% 2.42/1.42 ( ( c_In @ X3 @ X0 )
% 2.42/1.42 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax102,axiom,
% 2.42/1.42 ( c_Loop
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.42/1.42 ( c_and
% 2.42/1.42 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.42/1.42 @ ! [X5: $i] :
% 2.42/1.42 ( ( c_In @ X5 @ X0 )
% 2.42/1.42 => ( c_and
% 2.42/1.42 @ ( ( X1 @ X4 @ X5 )
% 2.42/1.42 = X5 )
% 2.42/1.42 @ ( ( X1 @ X5 @ X4 )
% 2.42/1.42 = X5 ) ) ) )
% 2.42/1.42 @ ! [X5: $i] :
% 2.42/1.42 ( ( c_In @ X5 @ X0 )
% 2.42/1.42 => ! [X6: $i] :
% 2.42/1.42 ( ( c_In @ X6 @ X0 )
% 2.42/1.42 => ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.42/1.42 = X6 )
% 2.42/1.42 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.42/1.42 = X6 ) )
% 2.42/1.42 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.42/1.42 = X5 ) )
% 2.42/1.42 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.42/1.42 = X5 ) ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax103,axiom,
% 2.42/1.42 ( c_Loop_with_defs
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.42/1.42 ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.42/1.42 @ ! [X14: $i] :
% 2.42/1.42 ( ( c_In @ X14 @ X0 )
% 2.42/1.42 => ! [X15: $i] :
% 2.42/1.42 ( ( c_In @ X15 @ X0 )
% 2.42/1.42 => ( ( X5 @ X14 @ X15 )
% 2.42/1.42 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.42/1.42 @ ! [X14: $i] :
% 2.42/1.42 ( ( c_In @ X14 @ X0 )
% 2.42/1.42 => ! [X15: $i] :
% 2.42/1.42 ( ( c_In @ X15 @ X0 )
% 2.42/1.42 => ! [X16: $i] :
% 2.42/1.42 ( ( c_In @ X16 @ X0 )
% 2.42/1.42 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.42/1.42 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.42/1.42 @ ! [X14: $i] :
% 2.42/1.42 ( ( c_In @ X14 @ X0 )
% 2.42/1.42 => ! [X15: $i] :
% 2.42/1.42 ( ( c_In @ X15 @ X0 )
% 2.42/1.42 => ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( c_and
% 2.42/1.42 @ ( ( X7 @ X14 @ X15 )
% 2.42/1.42 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.42/1.42 @ ( ( X10 @ X14 @ X15 )
% 2.42/1.42 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.42/1.42 @ ( ( X11 @ X14 @ X15 )
% 2.42/1.42 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.42/1.42 @ ( ( X12 @ X14 @ X15 )
% 2.42/1.42 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.42/1.42 @ ( ( X13 @ X14 @ X15 )
% 2.42/1.42 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.42/1.42 @ ! [X14: $i] :
% 2.42/1.42 ( ( c_In @ X14 @ X0 )
% 2.42/1.42 => ! [X15: $i] :
% 2.42/1.42 ( ( c_In @ X15 @ X0 )
% 2.42/1.42 => ! [X16: $i] :
% 2.42/1.42 ( ( c_In @ X16 @ X0 )
% 2.42/1.42 => ( c_and
% 2.42/1.42 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.42/1.42 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.42/1.42 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.42/1.42 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax104,axiom,
% 2.42/1.42 ( c_Loop_with_defs_cex1
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.42/1.42 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.42/1.42 @ ? [X14: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X14 @ X0 )
% 2.42/1.42 @ ? [X15: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X15 @ X0 )
% 2.42/1.42 @ ? [X16: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X16 @ X0 )
% 2.42/1.42 @ ? [X17: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X17 @ X0 )
% 2.42/1.42 @ ( c_not
% 2.42/1.42 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.42/1.42 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax105,axiom,
% 2.42/1.42 ( c_Loop_with_defs_cex2
% 2.42/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.42/1.42 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.42/1.42 @ ? [X14: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X14 @ X0 )
% 2.42/1.42 @ ? [X15: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X15 @ X0 )
% 2.42/1.42 @ ? [X16: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X16 @ X0 )
% 2.42/1.42 @ ? [X17: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X17 @ X0 )
% 2.42/1.42 @ ? [X18: $i] :
% 2.42/1.42 ( c_and @ ( c_In @ X18 @ X0 )
% 2.42/1.42 @ ( c_not
% 2.42/1.42 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.42/1.42 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax106,axiom,
% 2.42/1.42 ( c_combinator
% 2.42/1.42 = ( ^ [X0: $i] :
% 2.42/1.42 ! [X1: $i > $o] :
% 2.42/1.42 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.42/1.42 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.42/1.42 => ( ! [X2: $i,X3: $i] :
% 2.42/1.42 ( ( X1 @ X2 )
% 2.42/1.42 => ( ( X1 @ X3 )
% 2.42/1.42 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.42/1.42 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax107,axiom,
% 2.42/1.42 ( c_combinator_equiv
% 2.42/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.42/1.42 ! [X2: $i > $i > $o] :
% 2.42/1.42 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.42/1.42 ( ( c_per_i @ X2 )
% 2.42/1.42 => ( ! [X6: $i] :
% 2.42/1.42 ( ( c_combinator @ X6 )
% 2.42/1.42 => ( X2 @ X6 @ X6 ) )
% 2.42/1.42 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.42/1.42 ( ( c_combinator @ X6 )
% 2.42/1.42 => ( ( c_combinator @ X7 )
% 2.42/1.42 => ( ( c_combinator @ X8 )
% 2.42/1.42 => ( ( c_combinator @ X9 )
% 2.42/1.42 => ( ( X2 @ X6 @ X8 )
% 2.42/1.42 => ( ( X2 @ X7 @ X9 )
% 2.42/1.42 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.42/1.42 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.42/1.42 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.42/1.42 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.42/1.42 @ ( c_Inj0 @ c_Empty )
% 2.42/1.42 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.42/1.42 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(ax108,axiom,
% 2.42/1.42 ( c_equip_mod
% 2.42/1.42 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.42/1.42 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 2.42/1.42
% 2.42/1.42 thf(conj,conjecture,
% 2.42/1.42 ! [X0: ( $i > $i > $i > $i ) > ( $i > $i ) > ( ( $i > $i > $i ) > $i ) > $i,X1: ( $i > $i ) > $i > $i,X2: ( ( ( $i > $i > $i > $i ) > $i ) > $i > $i ) > $i > $i,X3: ( $i > $i ) > ( $i > $i ) > $i] :
% 2.42/1.42 ( ! [X4: $i > ( ( $i > $i ) > $i ) > $i,X5: ( $i > $i ) > $i,X6: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i,X7: $i] :
% 2.42/1.42 ( ( X3
% 2.42/1.42 @ ^ [X8: $i] : ( c_Inj1 @ c_Empty )
% 2.42/1.42 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ c_Empty ) )
% 2.42/1.42 = ( c_Inj1 @ c_Empty ) )
% 2.42/1.42 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 2.42/1.42 ( ( X3
% 2.42/1.42 @ ^ [X8: $i] : X6
% 2.42/1.42 @ ^ [X8: $i] : X7 )
% 2.42/1.42 = ( c_setsum
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : c_Empty
% 2.42/1.42 @ ( X0
% 2.42/1.42 @ ^ [X8: $i,X9: $i,X10: $i] :
% 2.42/1.42 ( X3
% 2.42/1.42 @ ^ [X11: $i] : X10
% 2.42/1.42 @ ^ [X11: $i] : c_Empty )
% 2.42/1.42 @ ^ [X8: $i] : c_Empty
% 2.42/1.42 @ ^ [X8: $i > $i > $i] : c_Empty ) )
% 2.42/1.42 @ c_Empty ) )
% 2.42/1.42 => ( ! [X4: $i > $i,X5: $i > $i > $i,X6: $i > $i,X7: $i] :
% 2.42/1.42 ( ( X2
% 2.42/1.42 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : X7
% 2.42/1.42 @ c_Empty )
% 2.42/1.42 = X7 )
% 2.42/1.42 => ( ! [X4: $i > ( $i > $i > $i ) > $i,X5: $i > $i,X6: ( ( ( $i > $i ) > $i ) > $i ) > $i,X7: $i > $i] :
% 2.42/1.42 ( ( X2
% 2.42/1.42 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] :
% 2.42/1.42 ( X7
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X10: ( $i > $i > $i > $i ) > $i,X11: $i] :
% 2.42/1.42 ( X0
% 2.42/1.42 @ ^ [X12: $i,X13: $i,X14: $i] : ( c_Inj1 @ c_Empty )
% 2.42/1.42 @ ^ [X12: $i] : ( c_Inj0 @ c_Empty )
% 2.42/1.42 @ ^ [X12: $i > $i > $i] :
% 2.42/1.42 ( X3
% 2.42/1.42 @ ^ [X13: $i] : c_Empty
% 2.42/1.42 @ ^ [X13: $i] : c_Empty ) )
% 2.42/1.42 @ ( c_Inj0
% 2.42/1.42 @ ( X0
% 2.42/1.42 @ ^ [X10: $i,X11: $i,X12: $i] : c_Empty
% 2.42/1.42 @ ^ [X10: $i] : c_Empty
% 2.42/1.42 @ ^ [X10: $i > $i > $i] : c_Empty ) ) ) )
% 2.42/1.42 @ ( X3
% 2.42/1.42 @ ^ [X8: $i] : ( c_setsum @ X8 @ c_Empty )
% 2.42/1.42 @ ^ [X8: $i] : c_Empty ) )
% 2.42/1.42 = ( c_setsum
% 2.42/1.42 @ ( X7
% 2.42/1.42 @ ( X5
% 2.42/1.42 @ ( X0
% 2.42/1.42 @ ^ [X8: $i,X9: $i,X10: $i] : ( c_Inj1 @ c_Empty )
% 2.42/1.42 @ ^ [X8: $i] :
% 2.42/1.42 ( X0
% 2.42/1.42 @ ^ [X9: $i,X10: $i,X11: $i] : c_Empty
% 2.42/1.42 @ ^ [X9: $i] : c_Empty
% 2.42/1.42 @ ^ [X9: $i > $i > $i] : c_Empty )
% 2.42/1.42 @ ^ [X8: $i > $i > $i] : ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 2.42/1.42 @ ( X1
% 2.42/1.42 @ ^ [X8: $i] : ( X7 @ c_Empty )
% 2.42/1.42 @ ( X5
% 2.42/1.42 @ ( X4
% 2.42/1.42 @ ( X1
% 2.42/1.42 @ ^ [X8: $i] : c_Empty
% 2.42/1.42 @ c_Empty )
% 2.42/1.42 @ ^ [X8: $i,X9: $i] : c_Empty ) ) ) ) )
% 2.42/1.42 => ( ! [X4: ( ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i,X7: $i] :
% 2.42/1.42 ( ( X1
% 2.42/1.42 @ ^ [X8: $i] :
% 2.42/1.42 ( c_Inj1
% 2.42/1.42 @ ( X1
% 2.42/1.42 @ ^ [X9: $i] :
% 2.42/1.42 ( c_Inj0
% 2.42/1.42 @ ( X0
% 2.42/1.42 @ ^ [X10: $i,X11: $i,X12: $i] : c_Empty
% 2.42/1.42 @ ^ [X10: $i] : c_Empty
% 2.42/1.42 @ ^ [X10: $i > $i > $i] : c_Empty ) )
% 2.42/1.42 @ ( c_Inj1 @ X7 ) ) )
% 2.42/1.42 @ ( c_Inj0
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : X9
% 2.42/1.42 @ X5 ) ) )
% 2.42/1.42 = ( c_Inj0
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X8: ( $i > $i > $i > $i ) > $i,X9: $i] : X7
% 2.42/1.42 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 2.42/1.42 => ( ! [X4: ( ( $i > $i ) > $i ) > $i,X5: $i > $i > ( $i > $i ) > $i,X6: $i,X7: ( $i > $i ) > ( $i > $i ) > $i] :
% 2.42/1.42 ( ( X1
% 2.42/1.42 @ ^ [X8: $i] :
% 2.42/1.42 ( X7
% 2.42/1.42 @ ^ [X9: $i] : ( c_setsum @ X9 @ X8 )
% 2.42/1.42 @ ^ [X9: $i] : c_Empty )
% 2.42/1.42 @ c_Empty )
% 2.42/1.42 = ( X7
% 2.42/1.42 @ ^ [X8: $i] :
% 2.42/1.42 ( c_setsum
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : c_Empty
% 2.42/1.42 @ ( X3
% 2.42/1.42 @ ^ [X9: $i] :
% 2.42/1.42 ( X2
% 2.42/1.42 @ ^ [X10: ( $i > $i > $i > $i ) > $i,X11: $i] : c_Empty
% 2.42/1.42 @ c_Empty )
% 2.42/1.42 @ ^ [X9: $i] :
% 2.42/1.42 ( X1
% 2.42/1.42 @ ^ [X10: $i] : c_Empty
% 2.42/1.42 @ c_Empty ) ) )
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : c_Empty
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : ( c_setsum @ c_Empty @ c_Empty )
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X9: ( $i > $i > $i > $i ) > $i,X10: $i] : c_Empty
% 2.42/1.42 @ c_Empty ) ) ) )
% 2.42/1.42 @ ^ [X8: $i] :
% 2.42/1.42 ( c_Inj1
% 2.42/1.42 @ ( X1
% 2.42/1.42 @ ^ [X9: $i] :
% 2.42/1.42 ( X7
% 2.42/1.42 @ ^ [X10: $i] :
% 2.42/1.42 ( X1
% 2.42/1.42 @ ^ [X11: $i] : c_Empty
% 2.42/1.42 @ c_Empty )
% 2.42/1.42 @ ^ [X10: $i] : ( c_Inj1 @ c_Empty ) )
% 2.42/1.42 @ X6 ) ) ) )
% 2.42/1.42 => ( ! [X4: $i > ( ( $i > $i ) > $i > $i ) > $i,X5: $i,X6: $i,X7: $i] :
% 2.42/1.42 ( ( X0
% 2.42/1.42 @ ^ [X8: $i,X9: $i,X10: $i] : X7
% 2.42/1.42 @ ^ [X8: $i] : X6
% 2.42/1.42 @ ^ [X8: $i > $i > $i] : c_Empty )
% 2.42/1.42 = X6 )
% 2.42/1.42 => ( ! [X4: $i,X5: $i,X6: $i > ( $i > $i ) > $i,X7: $i > $i] :
% 2.42/1.42 ( ( X0
% 2.42/1.42 @ ^ [X8: $i,X9: $i,X10: $i] :
% 2.42/1.42 ( X1
% 2.42/1.42 @ ^ [X11: $i] :
% 2.42/1.42 ( X2
% 2.42/1.42 @ ^ [X12: ( $i > $i > $i > $i ) > $i,X13: $i] : X10
% 2.42/1.42 @ ( X2
% 2.42/1.42 @ ^ [X12: ( $i > $i > $i > $i ) > $i,X13: $i] : ( c_setsum @ c_Empty @ c_Empty )
% 2.42/1.42 @ X11 ) )
% 2.42/1.42 @ ( c_Inj1 @ c_Empty ) )
% 2.42/1.42 @ ^ [X8: $i] : ( X7 @ c_Empty )
% 2.42/1.42 @ ^ [X8: $i > $i > $i] : c_Empty )
% 2.42/1.42 = ( X7 @ X4 ) )
% 2.42/1.42 => c_False ) ) ) ) ) ) ) ) ).
% 2.42/1.42 ------------------------
% 2.42/1.44 % (459)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/4Mi)
% 2.42/1.44 % (458)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/183Mi)
% 2.42/1.44 % (465)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/18Mi)
% 2.42/1.44 % (459)Instruction limit reached!
% 2.42/1.44 % (459)------------------------------
% 2.42/1.44 % (459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (459)Termination reason: Unknown
% 2.42/1.44 % (459)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (459)Memory used [KB]: 1279
% 2.42/1.44 % (459)Time elapsed: 0.003 s
% 2.42/1.44 % (459)Instructions burned: 6 (million)
% 2.42/1.44 % (459)------------------------------
% 2.42/1.44 % (459)------------------------------
% 2.42/1.44 % (465)Instruction limit reached!
% 2.42/1.44 % (465)------------------------------
% 2.42/1.44 % (465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (465)Termination reason: Unknown
% 2.42/1.44 % (465)Termination phase: Property scanning
% 2.42/1.44
% 2.42/1.44 % (465)Memory used [KB]: 1535
% 2.42/1.44 % (465)Time elapsed: 0.007 s
% 2.42/1.44 % (465)Instructions burned: 20 (million)
% 2.42/1.44 % (465)------------------------------
% 2.42/1.44 % (465)------------------------------
% 2.42/1.44 % (460)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/27Mi)
% 2.42/1.44 % (461)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/2Mi)
% 2.42/1.44 % (462)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/2Mi)
% 2.42/1.44 % (464)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/275Mi)
% 2.42/1.44 % (461)Instruction limit reached!
% 2.42/1.44 % (461)------------------------------
% 2.42/1.44 % (461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (461)Termination reason: Unknown
% 2.42/1.44 % (462)Instruction limit reached!
% 2.42/1.44 % (462)------------------------------
% 2.42/1.44 % (462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.44 % (462)Termination reason: Unknown
% 2.42/1.44 % (462)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (462)Memory used [KB]: 1151
% 2.42/1.44 % (462)Time elapsed: 0.003 s
% 2.42/1.44 % (462)Instructions burned: 2 (million)
% 2.42/1.44 % (462)------------------------------
% 2.42/1.44 % (462)------------------------------
% 2.42/1.44 % (461)Termination phase: shuffling
% 2.42/1.44
% 2.42/1.44 % (461)Memory used [KB]: 1151
% 2.42/1.44 % (461)Time elapsed: 0.003 s
% 2.42/1.44 % (461)Instructions burned: 2 (million)
% 2.42/1.44 % (461)------------------------------
% 2.42/1.44 % (461)------------------------------
% 2.42/1.45 % (466)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/3Mi)
% 2.42/1.45 % (466)Instruction limit reached!
% 2.42/1.45 % (466)------------------------------
% 2.42/1.45 % (466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.45 % (466)Termination reason: Unknown
% 2.42/1.45 % (466)Termination phase: shuffling
% 2.42/1.45
% 2.42/1.45 % (466)Memory used [KB]: 1279
% 2.42/1.45 % (466)Time elapsed: 0.002 s
% 2.42/1.45 % (466)Instructions burned: 4 (million)
% 2.42/1.45 % (466)------------------------------
% 2.42/1.45 % (466)------------------------------
% 2.42/1.45 % (467)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/37Mi)
% 2.42/1.46 % (470)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/1041Mi)
% 2.42/1.46 % (460)Instruction limit reached!
% 2.42/1.46 % (460)------------------------------
% 2.42/1.46 % (460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.46 % (460)Termination reason: Unknown
% 2.42/1.46 % (460)Termination phase: Property scanning
% 2.42/1.46
% 2.42/1.46 % (460)Memory used [KB]: 1535
% 2.42/1.46 % (460)Time elapsed: 0.016 s
% 2.42/1.46 % (460)Instructions burned: 28 (million)
% 2.42/1.46 % (460)------------------------------
% 2.42/1.46 % (460)------------------------------
% 2.42/1.46 % (469)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/3Mi)
% 2.42/1.46 % (468)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/15Mi)
% 2.42/1.46 % (467)Instruction limit reached!
% 2.42/1.46 % (467)------------------------------
% 2.42/1.46 % (467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.46 % (467)Termination reason: Unknown
% 2.42/1.46 % (467)Termination phase: Property scanning
% 2.42/1.46
% 2.42/1.46 % (467)Memory used [KB]: 1535
% 2.42/1.46 % (467)Time elapsed: 0.012 s
% 2.42/1.46 % (467)Instructions burned: 37 (million)
% 2.42/1.46 % (467)------------------------------
% 2.42/1.46 % (467)------------------------------
% 2.42/1.46 % (469)Instruction limit reached!
% 2.42/1.46 % (469)------------------------------
% 2.42/1.46 % (469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.46 % (469)Termination reason: Unknown
% 2.42/1.46 % (469)Termination phase: shuffling
% 2.42/1.46
% 2.42/1.46 % (469)Memory used [KB]: 1279
% 2.42/1.46 % (469)Time elapsed: 0.003 s
% 2.42/1.46 % (469)Instructions burned: 3 (million)
% 2.42/1.46 % (469)------------------------------
% 2.42/1.46 % (469)------------------------------
% 2.42/1.47 % (468)Instruction limit reached!
% 2.42/1.47 % (468)------------------------------
% 2.42/1.47 % (468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.47 % (468)Termination reason: Unknown
% 2.42/1.47 % (468)Termination phase: shuffling
% 2.42/1.47
% 2.42/1.47 % (468)Memory used [KB]: 1535
% 2.42/1.47 % (468)Time elapsed: 0.010 s
% 2.42/1.47 % (468)Instructions burned: 16 (million)
% 2.42/1.47 % (468)------------------------------
% 2.42/1.47 % (468)------------------------------
% 2.42/1.47 % (471)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/7Mi)
% 2.42/1.47 % (472)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/16Mi)
% 2.42/1.47 % (473)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/3Mi)
% 2.42/1.47 % (473)Instruction limit reached!
% 2.42/1.47 % (473)------------------------------
% 2.42/1.47 % (473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.47 % (473)Termination reason: Unknown
% 2.42/1.47 % (473)Termination phase: shuffling
% 2.42/1.47
% 2.42/1.47 % (473)Memory used [KB]: 1279
% 2.42/1.47 % (473)Time elapsed: 0.002 s
% 2.42/1.47 % (473)Instructions burned: 3 (million)
% 2.42/1.47 % (473)------------------------------
% 2.42/1.47 % (473)------------------------------
% 2.42/1.48 % (471)Instruction limit reached!
% 2.42/1.48 % (471)------------------------------
% 2.42/1.48 % (471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.48 % (471)Termination reason: Unknown
% 2.42/1.48 % (471)Termination phase: shuffling
% 2.42/1.48
% 2.42/1.48 % (471)Memory used [KB]: 1407
% 2.42/1.48 % (471)Time elapsed: 0.005 s
% 2.42/1.48 % (471)Instructions burned: 9 (million)
% 2.42/1.48 % (471)------------------------------
% 2.42/1.48 % (471)------------------------------
% 2.42/1.48 % (472)Instruction limit reached!
% 2.42/1.48 % (472)------------------------------
% 2.42/1.48 % (472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.48 % (472)Termination reason: Unknown
% 2.42/1.48 % (472)Termination phase: shuffling
% 2.42/1.48
% 2.42/1.48 % (472)Memory used [KB]: 1535
% 2.42/1.48 % (472)Time elapsed: 0.007 s
% 2.42/1.48 % (472)Instructions burned: 18 (million)
% 2.42/1.48 % (472)------------------------------
% 2.42/1.48 % (472)------------------------------
% 2.42/1.48 % (458)Instruction limit reached!
% 2.42/1.48 % (458)------------------------------
% 2.42/1.48 % (458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.48 % (458)Termination reason: Unknown
% 2.42/1.48 % (458)Termination phase: Saturation
% 2.42/1.48
% 2.42/1.48 % (458)Memory used [KB]: 6524
% 2.42/1.48 % (458)Time elapsed: 0.045 s
% 2.42/1.48 % (458)Instructions burned: 185 (million)
% 2.42/1.48 % (458)------------------------------
% 2.42/1.48 % (458)------------------------------
% 2.42/1.48 % (475)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/7Mi)
% 2.42/1.49 % (476)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/3Mi)
% 2.42/1.49 % (476)Instruction limit reached!
% 2.42/1.49 % (476)------------------------------
% 2.42/1.49 % (476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (476)Termination reason: Unknown
% 2.42/1.49 % (476)Termination phase: shuffling
% 2.42/1.49
% 2.42/1.49 % (476)Memory used [KB]: 1279
% 2.42/1.49 % (476)Time elapsed: 0.003 s
% 2.42/1.49 % (476)Instructions burned: 4 (million)
% 2.42/1.49 % (476)------------------------------
% 2.42/1.49 % (476)------------------------------
% 2.42/1.49 % (475)Instruction limit reached!
% 2.42/1.49 % (475)------------------------------
% 2.42/1.49 % (475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (475)Termination reason: Unknown
% 2.42/1.49 % (475)Termination phase: shuffling
% 2.42/1.49
% 2.42/1.49 % (475)Memory used [KB]: 1279
% 2.42/1.49 % (475)Time elapsed: 0.004 s
% 2.42/1.49 % (475)Instructions burned: 8 (million)
% 2.42/1.49 % (475)------------------------------
% 2.42/1.49 % (475)------------------------------
% 2.42/1.49 % (474)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/3Mi)
% 2.42/1.49 % (477)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/4Mi)
% 2.42/1.49 % (478)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/18Mi)
% 2.42/1.49 % (474)Instruction limit reached!
% 2.42/1.49 % (474)------------------------------
% 2.42/1.49 % (474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (474)Termination reason: Unknown
% 2.42/1.49 % (474)Termination phase: shuffling
% 2.42/1.49
% 2.42/1.49 % (474)Memory used [KB]: 1279
% 2.42/1.49 % (474)Time elapsed: 0.004 s
% 2.42/1.49 % (474)Instructions burned: 4 (million)
% 2.42/1.49 % (474)------------------------------
% 2.42/1.49 % (474)------------------------------
% 2.42/1.49 % (477)Instruction limit reached!
% 2.42/1.49 % (477)------------------------------
% 2.42/1.49 % (477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (477)Termination reason: Unknown
% 2.42/1.49 % (477)Termination phase: shuffling
% 2.42/1.49
% 2.42/1.49 % (477)Memory used [KB]: 1279
% 2.42/1.49 % (477)Time elapsed: 0.003 s
% 2.42/1.49 % (477)Instructions burned: 4 (million)
% 2.42/1.49 % (477)------------------------------
% 2.42/1.49 % (477)------------------------------
% 2.42/1.49 % (478)Instruction limit reached!
% 2.42/1.49 % (478)------------------------------
% 2.42/1.49 % (478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.49 % (478)Termination reason: Unknown
% 2.42/1.49 % (478)Termination phase: shuffling
% 2.42/1.49
% 2.42/1.49 % (478)Memory used [KB]: 1535
% 2.42/1.49 % (478)Time elapsed: 0.006 s
% 2.42/1.49 % (478)Instructions burned: 19 (million)
% 2.42/1.49 % (478)------------------------------
% 2.42/1.49 % (478)------------------------------
% 2.45/1.50 % (479)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/710Mi)
% 2.45/1.50 % (480)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/6Mi)
% 2.45/1.50 % (480)Instruction limit reached!
% 2.45/1.50 % (480)------------------------------
% 2.45/1.50 % (480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (480)Termination reason: Unknown
% 2.45/1.50 % (480)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (480)Memory used [KB]: 1279
% 2.45/1.50 % (480)Time elapsed: 0.004 s
% 2.45/1.50 % (480)Instructions burned: 8 (million)
% 2.45/1.50 % (480)------------------------------
% 2.45/1.50 % (480)------------------------------
% 2.45/1.50 % (481)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/902Mi)
% 2.45/1.50 % (483)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/5Mi)
% 2.45/1.51 % (483)Instruction limit reached!
% 2.45/1.51 % (483)------------------------------
% 2.45/1.51 % (483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.51 % (483)Termination reason: Unknown
% 2.45/1.51 % (483)Termination phase: shuffling
% 2.45/1.51
% 2.45/1.51 % (483)Memory used [KB]: 1279
% 2.45/1.51 % (483)Time elapsed: 0.003 s
% 2.45/1.51 % (483)Instructions burned: 8 (million)
% 2.45/1.51 % (483)------------------------------
% 2.45/1.51 % (483)------------------------------
% 2.45/1.51 % (482)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/21Mi)
% 2.45/1.51 % (484)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/6Mi)
% 2.45/1.51 % (484)Instruction limit reached!
% 2.45/1.51 % (484)------------------------------
% 2.45/1.51 % (484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.51 % (484)Termination reason: Unknown
% 2.45/1.51 % (484)Termination phase: shuffling
% 2.45/1.51
% 2.45/1.51 % (484)Memory used [KB]: 1279
% 2.45/1.51 % (484)Time elapsed: 0.004 s
% 2.45/1.51 % (484)Instructions burned: 7 (million)
% 2.45/1.51 % (484)------------------------------
% 2.45/1.51 % (484)------------------------------
% 2.45/1.51 % (485)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/377Mi)
% 2.45/1.52 % (482)Instruction limit reached!
% 2.45/1.52 % (482)------------------------------
% 2.45/1.52 % (482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.52 % (482)Termination reason: Unknown
% 2.45/1.52 % (482)Termination phase: Property scanning
% 2.45/1.52
% 2.45/1.52 % (482)Memory used [KB]: 1535
% 2.45/1.52 % (482)Time elapsed: 0.013 s
% 2.45/1.52 % (482)Instructions burned: 22 (million)
% 2.45/1.52 % (482)------------------------------
% 2.45/1.52 % (482)------------------------------
% 2.45/1.52 % (486)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/779Mi)
% 2.45/1.54 % (488)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_351 for (2999ds/19Mi)
% 2.45/1.55 % (488)Instruction limit reached!
% 2.45/1.55 % (488)------------------------------
% 2.45/1.55 % (488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.55 % (488)Termination reason: Unknown
% 2.45/1.55 % (488)Termination phase: Property scanning
% 2.45/1.55
% 2.45/1.55 % (488)Memory used [KB]: 1535
% 2.45/1.55 % (488)Time elapsed: 0.011 s
% 2.45/1.55 % (488)Instructions burned: 21 (million)
% 2.45/1.55 % (488)------------------------------
% 2.45/1.55 % (488)------------------------------
% 2.45/1.56 % (489)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_351 for (2998ds/879Mi)
% 2.45/1.56 % (464)Instruction limit reached!
% 2.45/1.56 % (464)------------------------------
% 2.45/1.56 % (464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.56 % (464)Termination reason: Unknown
% 2.45/1.56 % (464)Termination phase: Saturation
% 2.45/1.56
% 2.45/1.56 % (464)Memory used [KB]: 6524
% 2.45/1.56 % (464)Time elapsed: 0.117 s
% 2.45/1.56 % (464)Instructions burned: 276 (million)
% 2.45/1.56 % (464)------------------------------
% 2.45/1.56 % (464)------------------------------
% 2.45/1.57 % (490)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_351 for (2998ds/17Mi)
% 2.45/1.57 % (490)Instruction limit reached!
% 2.45/1.57 % (490)------------------------------
% 2.45/1.57 % (490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.57 % (490)Termination reason: Unknown
% 2.45/1.57 % (490)Termination phase: shuffling
% 2.45/1.57
% 2.45/1.57 % (490)Memory used [KB]: 1535
% 2.45/1.57 % (490)Time elapsed: 0.006 s
% 2.45/1.57 % (490)Instructions burned: 17 (million)
% 2.45/1.57 % (490)------------------------------
% 2.45/1.57 % (490)------------------------------
% 2.45/1.58 % (491)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2998ds/3Mi)
% 2.45/1.59 % (491)Instruction limit reached!
% 2.45/1.59 % (491)------------------------------
% 2.45/1.59 % (491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.59 % (491)Termination reason: Unknown
% 2.45/1.59 % (491)Termination phase: shuffling
% 2.45/1.59
% 2.45/1.59 % (491)Memory used [KB]: 1279
% 2.45/1.59 % (491)Time elapsed: 0.003 s
% 2.45/1.59 % (491)Instructions burned: 4 (million)
% 2.45/1.59 % (491)------------------------------
% 2.45/1.59 % (491)------------------------------
% 2.45/1.60 % (492)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_351 for (2998ds/30Mi)
% 2.45/1.60 % (492)Instruction limit reached!
% 2.45/1.60 % (492)------------------------------
% 2.45/1.60 % (492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.60 % (492)Termination reason: Unknown
% 2.45/1.60 % (492)Termination phase: Preprocessing 3
% 2.45/1.60
% 2.45/1.60 % (492)Memory used [KB]: 1663
% 2.45/1.60 % (492)Time elapsed: 0.011 s
% 2.45/1.60 % (492)Instructions burned: 31 (million)
% 2.45/1.60 % (492)------------------------------
% 2.45/1.60 % (492)------------------------------
% 2.45/1.61 % (485)Instruction limit reached!
% 2.45/1.61 % (485)------------------------------
% 2.45/1.61 % (485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.61 % (485)Termination reason: Unknown
% 2.45/1.61 % (485)Termination phase: Saturation
% 2.45/1.61
% 2.45/1.61 % (485)Memory used [KB]: 6652
% 2.45/1.61 % (485)Time elapsed: 0.094 s
% 2.45/1.61 % (485)Instructions burned: 377 (million)
% 2.45/1.61 % (485)------------------------------
% 2.45/1.61 % (485)------------------------------
% 2.45/1.62 % (493)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_351 for (2998ds/127Mi)
% 2.45/1.62 % (502)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_351 for (2998ds/100Mi)
% 2.45/1.64 % (502)Instruction limit reached!
% 2.45/1.64 % (502)------------------------------
% 2.45/1.64 % (502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.64 % (502)Termination reason: Unknown
% 2.45/1.64 % (502)Termination phase: Property scanning
% 2.45/1.64
% 2.45/1.64 % (502)Memory used [KB]: 1791
% 2.45/1.64 % (502)Time elapsed: 0.025 s
% 2.45/1.64 % (502)Instructions burned: 102 (million)
% 2.45/1.64 % (502)------------------------------
% 2.45/1.64 % (502)------------------------------
% 2.45/1.65 % (493)Instruction limit reached!
% 2.45/1.65 % (493)------------------------------
% 2.45/1.65 % (493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.65 % (493)Termination reason: Unknown
% 2.45/1.65 % (493)Termination phase: Saturation
% 2.45/1.65
% 2.45/1.65 % (493)Memory used [KB]: 6396
% 2.45/1.65 % (493)Time elapsed: 0.035 s
% 2.45/1.65 % (493)Instructions burned: 128 (million)
% 2.45/1.65 % (493)------------------------------
% 2.45/1.65 % (493)------------------------------
% 2.45/1.65 % (507)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/3Mi)
% 2.45/1.65 % (507)Instruction limit reached!
% 2.45/1.65 % (507)------------------------------
% 2.45/1.65 % (507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.65 % (507)Termination reason: Unknown
% 2.45/1.65 % (507)Termination phase: shuffling
% 2.45/1.65
% 2.45/1.65 % (507)Memory used [KB]: 1279
% 2.45/1.65 % (507)Time elapsed: 0.002 s
% 2.45/1.65 % (507)Instructions burned: 4 (million)
% 2.45/1.65 % (507)------------------------------
% 2.45/1.65 % (507)------------------------------
% 2.45/1.66 % (508)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/20Mi)
% 2.45/1.66 % (509)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/86Mi)
% 2.45/1.66 % (508)Instruction limit reached!
% 2.45/1.66 % (508)------------------------------
% 2.45/1.66 % (508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.66 % (508)Termination reason: Unknown
% 2.45/1.66 % (508)Termination phase: Property scanning
% 2.45/1.66
% 2.45/1.66 % (508)Memory used [KB]: 1535
% 2.45/1.66 % (508)Time elapsed: 0.008 s
% 2.45/1.66 % (508)Instructions burned: 21 (million)
% 2.45/1.66 % (508)------------------------------
% 2.45/1.66 % (508)------------------------------
% 2.45/1.67 % (510)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/107Mi)
% 2.45/1.68 % (509)Instruction limit reached!
% 2.45/1.68 % (509)------------------------------
% 2.45/1.68 % (509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.68 % (509)Termination reason: Unknown
% 2.45/1.68 % (509)Termination phase: Property scanning
% 2.45/1.68
% 2.45/1.68 % (509)Memory used [KB]: 1918
% 2.45/1.68 % (509)Time elapsed: 0.022 s
% 2.45/1.68 % (509)Instructions burned: 89 (million)
% 2.45/1.68 % (509)------------------------------
% 2.45/1.68 % (509)------------------------------
% 2.45/1.69 % (511)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/39Mi)
% 2.45/1.70 % (511)Instruction limit reached!
% 2.45/1.70 % (511)------------------------------
% 2.45/1.70 % (511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.70 % (511)Termination reason: Unknown
% 2.45/1.70 % (511)Termination phase: Property scanning
% 2.45/1.70
% 2.45/1.70 % (511)Memory used [KB]: 1535
% 2.45/1.70 % (511)Time elapsed: 0.011 s
% 2.45/1.70 % (511)Instructions burned: 40 (million)
% 2.45/1.70 % (511)------------------------------
% 2.45/1.70 % (511)------------------------------
% 2.45/1.70 % (470)Instruction limit reached!
% 2.45/1.70 % (470)------------------------------
% 2.45/1.70 % (470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.70 % (510)Instruction limit reached!
% 2.45/1.70 % (510)------------------------------
% 2.45/1.70 % (510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.70 % (510)Termination reason: Unknown
% 2.45/1.70 % (510)Termination phase: Saturation
% 2.45/1.70
% 2.45/1.70 % (510)Memory used [KB]: 6396
% 2.45/1.70 % (510)Time elapsed: 0.031 s
% 2.45/1.70 % (510)Instructions burned: 109 (million)
% 2.45/1.70 % (510)------------------------------
% 2.45/1.70 % (510)------------------------------
% 2.45/1.70 % (470)Termination reason: Unknown
% 2.45/1.70 % (470)Termination phase: Saturation
% 2.45/1.70
% 2.45/1.70 % (470)Memory used [KB]: 7291
% 2.45/1.70 % (470)Time elapsed: 0.248 s
% 2.45/1.70 % (470)Instructions burned: 1044 (million)
% 2.45/1.70 % (470)------------------------------
% 2.45/1.70 % (470)------------------------------
% 2.45/1.71 % (479)Instruction limit reached!
% 2.45/1.71 % (479)------------------------------
% 2.45/1.71 % (479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.71 % (479)Termination reason: Unknown
% 2.45/1.71 % (479)Termination phase: Saturation
% 2.45/1.71
% 2.45/1.71 % (479)Memory used [KB]: 7291
% 2.45/1.71 % (479)Time elapsed: 0.215 s
% 2.45/1.71 % (479)Instructions burned: 711 (million)
% 2.45/1.71 % (479)------------------------------
% 2.45/1.71 % (479)------------------------------
% 2.45/1.71 % (512)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/448Mi)
% 2.45/1.71 % (517)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/98Mi)
% 2.45/1.71 % (516)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/46Mi)
% 2.45/1.72 % (518)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_351 for (2997ds/507Mi)
% 2.45/1.73 % (516)Instruction limit reached!
% 2.45/1.73 % (516)------------------------------
% 2.45/1.73 % (516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.73 % (516)Termination reason: Unknown
% 2.45/1.73 % (516)Termination phase: Property scanning
% 2.45/1.73
% 2.45/1.73 % (516)Memory used [KB]: 1663
% 2.45/1.73 % (516)Time elapsed: 0.015 s
% 2.45/1.73 % (516)Instructions burned: 47 (million)
% 2.45/1.73 % (516)------------------------------
% 2.45/1.73 % (516)------------------------------
% 2.45/1.74 % (517)Instruction limit reached!
% 2.45/1.74 % (517)------------------------------
% 2.45/1.74 % (517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.74 % (517)Termination reason: Unknown
% 2.45/1.74 % (517)Termination phase: Property scanning
% 2.45/1.74
% 2.45/1.74 % (517)Memory used [KB]: 1791
% 2.45/1.74 % (517)Time elapsed: 0.024 s
% 2.45/1.74 % (517)Instructions burned: 100 (million)
% 2.45/1.74 % (517)------------------------------
% 2.45/1.74 % (517)------------------------------
% 2.45/1.74 % (519)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/149Mi)
% 2.45/1.75 % (520)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/39Mi)
% 2.45/1.75 % (481)Instruction limit reached!
% 2.45/1.75 % (481)------------------------------
% 2.45/1.75 % (481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.75 % (481)Termination reason: Unknown
% 2.45/1.75 % (481)Termination phase: Saturation
% 2.45/1.75
% 2.45/1.75 % (481)Memory used [KB]: 6780
% 2.45/1.75 % (481)Time elapsed: 0.255 s
% 2.45/1.75 % (481)Instructions burned: 902 (million)
% 2.45/1.75 % (481)------------------------------
% 2.45/1.75 % (481)------------------------------
% 2.45/1.76 % (520)Instruction limit reached!
% 2.45/1.76 % (520)------------------------------
% 2.45/1.76 % (520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (520)Termination reason: Unknown
% 2.45/1.76 % (520)Termination phase: Function definition elimination
% 2.45/1.76
% 2.45/1.76 % (520)Memory used [KB]: 1663
% 2.45/1.76 % (520)Time elapsed: 0.012 s
% 2.45/1.76 % (520)Instructions burned: 42 (million)
% 2.45/1.76 % (520)------------------------------
% 2.45/1.76 % (520)------------------------------
% 2.45/1.76 % (486)Instruction limit reached!
% 2.45/1.76 % (486)------------------------------
% 2.45/1.76 % (486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (486)Termination reason: Unknown
% 2.45/1.76 % (486)Termination phase: Saturation
% 2.45/1.76
% 2.45/1.76 % (486)Memory used [KB]: 7675
% 2.45/1.76 % (486)Time elapsed: 0.239 s
% 2.45/1.76 % (486)Instructions burned: 780 (million)
% 2.45/1.76 % (486)------------------------------
% 2.45/1.76 % (486)------------------------------
% 2.45/1.76 % (521)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/6Mi)
% 2.45/1.76 % (521)Instruction limit reached!
% 2.45/1.76 % (521)------------------------------
% 2.45/1.76 % (521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (521)Termination reason: Unknown
% 2.45/1.76 % (521)Termination phase: shuffling
% 2.45/1.76
% 2.45/1.76 % (521)Memory used [KB]: 1279
% 2.45/1.76 % (521)Time elapsed: 0.003 s
% 2.45/1.76 % (521)Instructions burned: 7 (million)
% 2.45/1.76 % (521)------------------------------
% 2.45/1.76 % (521)------------------------------
% 2.45/1.77 % (522)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/1087Mi)
% 2.45/1.77 % (523)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/47Mi)
% 2.45/1.77 % (524)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/44Mi)
% 2.45/1.78 % (519)Instruction limit reached!
% 2.45/1.78 % (519)------------------------------
% 2.45/1.78 % (519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.78 % (519)Termination reason: Unknown
% 2.45/1.78 % (519)Termination phase: Saturation
% 2.45/1.78
% 2.45/1.78 % (519)Memory used [KB]: 6652
% 2.45/1.78 % (519)Time elapsed: 0.045 s
% 2.45/1.78 % (519)Instructions burned: 151 (million)
% 2.45/1.78 % (519)------------------------------
% 2.45/1.78 % (519)------------------------------
% 2.45/1.78 % (523)Instruction limit reached!
% 2.45/1.78 % (523)------------------------------
% 2.45/1.78 % (523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.78 % (523)Termination reason: Unknown
% 2.45/1.78 % (523)Termination phase: Function definition elimination
% 2.45/1.78
% 2.45/1.78 % (523)Memory used [KB]: 1663
% 2.45/1.78 % (523)Time elapsed: 0.015 s
% 2.45/1.78 % (523)Instructions burned: 47 (million)
% 2.45/1.78 % (523)------------------------------
% 2.45/1.78 % (523)------------------------------
% 2.45/1.79 % (524)Instruction limit reached!
% 2.45/1.79 % (524)------------------------------
% 2.45/1.79 % (524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.79 % (524)Termination reason: Unknown
% 2.45/1.79 % (524)Termination phase: Property scanning
% 2.45/1.79
% 2.45/1.79 % (524)Memory used [KB]: 1535
% 2.45/1.79 % (524)Time elapsed: 0.012 s
% 2.45/1.79 % (524)Instructions burned: 44 (million)
% 2.45/1.79 % (524)------------------------------
% 2.45/1.79 % (524)------------------------------
% 2.45/1.79 % (525)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/432Mi)
% 2.45/1.79 % (526)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/62Mi)
% 2.45/1.79 % (527)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/31Mi)
% 2.45/1.80 % (527)Instruction limit reached!
% 2.45/1.80 % (527)------------------------------
% 2.45/1.80 % (527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.80 % (527)Termination reason: Unknown
% 2.45/1.80 % (527)Termination phase: Property scanning
% 2.45/1.80
% 2.45/1.80 % (527)Memory used [KB]: 1663
% 2.45/1.80 % (527)Time elapsed: 0.010 s
% 2.45/1.80 % (527)Instructions burned: 34 (million)
% 2.45/1.80 % (527)------------------------------
% 2.45/1.80 % (527)------------------------------
% 2.45/1.81 % (526)Instruction limit reached!
% 2.45/1.81 % (526)------------------------------
% 2.45/1.81 % (526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.81 % (526)Termination reason: Unknown
% 2.45/1.81 % (526)Termination phase: Function definition elimination
% 2.45/1.81
% 2.45/1.81 % (526)Memory used [KB]: 1791
% 2.45/1.81 % (526)Time elapsed: 0.018 s
% 2.45/1.81 % (526)Instructions burned: 64 (million)
% 2.45/1.81 % (526)------------------------------
% 2.45/1.81 % (526)------------------------------
% 2.45/1.81 % (528)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/96Mi)
% 2.45/1.82 % (529)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/453Mi)
% 2.45/1.82 % (489)Instruction limit reached!
% 2.45/1.82 % (489)------------------------------
% 2.45/1.82 % (489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.82 % (489)Termination reason: Unknown
% 2.45/1.82 % (489)Termination phase: Saturation
% 2.45/1.82
% 2.45/1.82 % (489)Memory used [KB]: 7164
% 2.45/1.82 % (489)Time elapsed: 0.269 s
% 2.45/1.82 % (489)Instructions burned: 880 (million)
% 2.45/1.82 % (489)------------------------------
% 2.45/1.82 % (489)------------------------------
% 2.45/1.83 % (533)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_351 for (2996ds/71Mi)
% 2.45/1.84 % (528)Instruction limit reached!
% 2.45/1.84 % (528)------------------------------
% 2.45/1.84 % (528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.84 % (528)Termination reason: Unknown
% 2.45/1.84 % (528)Termination phase: Property scanning
% 2.45/1.84
% 2.45/1.84 % (528)Memory used [KB]: 1918
% 2.45/1.84 % (528)Time elapsed: 0.024 s
% 2.45/1.84 % (528)Instructions burned: 98 (million)
% 2.45/1.84 % (528)------------------------------
% 2.45/1.84 % (528)------------------------------
% 2.45/1.84 % (512)Instruction limit reached!
% 2.45/1.84 % (512)------------------------------
% 2.45/1.84 % (512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.84 % (512)Termination reason: Unknown
% 2.45/1.84 % (512)Termination phase: Saturation
% 2.45/1.84
% 2.45/1.84 % (512)Memory used [KB]: 7419
% 2.45/1.84 % (512)Time elapsed: 0.156 s
% 2.45/1.84 % (512)Instructions burned: 449 (million)
% 2.45/1.84 % (512)------------------------------
% 2.45/1.84 % (512)------------------------------
% 2.45/1.85 % (536)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/83Mi)
% 2.45/1.85 % (539)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/11Mi)
% 2.45/1.85 % (533)Instruction limit reached!
% 2.45/1.85 % (533)------------------------------
% 2.45/1.85 % (533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.85 % (533)Termination reason: Unknown
% 2.45/1.85 % (533)Termination phase: Function definition elimination
% 2.45/1.85
% 2.45/1.85 % (533)Memory used [KB]: 1918
% 2.45/1.85 % (533)Time elapsed: 0.020 s
% 2.45/1.85 % (533)Instructions burned: 73 (million)
% 2.45/1.85 % (533)------------------------------
% 2.45/1.85 % (533)------------------------------
% 2.45/1.85 % (539)Instruction limit reached!
% 2.45/1.85 % (539)------------------------------
% 2.45/1.85 % (539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.85 % (539)Termination reason: Unknown
% 2.45/1.85 % (539)Termination phase: shuffling
% 2.45/1.85
% 2.45/1.85 % (539)Memory used [KB]: 1407
% 2.45/1.85 % (539)Time elapsed: 0.004 s
% 2.45/1.85 % (539)Instructions burned: 11 (million)
% 2.45/1.85 % (539)------------------------------
% 2.45/1.85 % (539)------------------------------
% 2.45/1.85 % (518)Instruction limit reached!
% 2.45/1.85 % (518)------------------------------
% 2.45/1.85 % (518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.85 % (518)Termination reason: Unknown
% 2.45/1.85 % (518)Termination phase: Saturation
% 2.45/1.85
% 2.45/1.85 % (518)Memory used [KB]: 6652
% 2.45/1.85 % (518)Time elapsed: 0.135 s
% 2.45/1.85 % (518)Instructions burned: 509 (million)
% 2.45/1.85 % (518)------------------------------
% 2.45/1.85 % (518)------------------------------
% 2.45/1.86 % (547)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/41Mi)
% 2.45/1.86 % (549)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/6Mi)
% 2.45/1.86 % (550)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/150Mi)
% 2.45/1.87 % (549)Instruction limit reached!
% 2.45/1.87 % (549)------------------------------
% 2.45/1.87 % (549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.87 % (549)Termination reason: Unknown
% 2.45/1.87 % (549)Termination phase: shuffling
% 2.45/1.87
% 2.45/1.87 % (549)Memory used [KB]: 1279
% 2.45/1.87 % (549)Time elapsed: 0.003 s
% 2.45/1.87 % (549)Instructions burned: 8 (million)
% 2.45/1.87 % (549)------------------------------
% 2.45/1.87 % (549)------------------------------
% 2.45/1.87 % (536)Instruction limit reached!
% 2.45/1.87 % (536)------------------------------
% 2.45/1.87 % (536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.87 % (536)Termination reason: Unknown
% 2.45/1.87 % (536)Termination phase: Saturation
% 2.45/1.87
% 2.45/1.87 % (536)Memory used [KB]: 6396
% 2.45/1.87 % (536)Time elapsed: 0.024 s
% 2.45/1.87 % (536)Instructions burned: 83 (million)
% 2.45/1.87 % (536)------------------------------
% 2.45/1.87 % (536)------------------------------
% 2.45/1.87 % (547)Instruction limit reached!
% 2.45/1.87 % (547)------------------------------
% 2.45/1.87 % (547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.87 % (547)Termination reason: Unknown
% 2.45/1.87 % (547)Termination phase: Function definition elimination
% 2.45/1.87
% 2.45/1.87 % (547)Memory used [KB]: 1535
% 2.45/1.87 % (547)Time elapsed: 0.013 s
% 2.45/1.87 % (547)Instructions burned: 41 (million)
% 2.45/1.87 % (547)------------------------------
% 2.45/1.87 % (547)------------------------------
% 2.45/1.87 % (552)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/343Mi)
% 2.45/1.88 % (553)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/109Mi)
% 2.45/1.88 % (554)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/253Mi)
% 2.45/1.90 % (550)Instruction limit reached!
% 2.45/1.90 % (550)------------------------------
% 2.45/1.90 % (550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.90 % (550)Termination reason: Unknown
% 2.45/1.90 % (550)Termination phase: Saturation
% 2.45/1.90
% 2.45/1.90 % (550)Memory used [KB]: 6396
% 2.45/1.90 % (550)Time elapsed: 0.037 s
% 2.45/1.90 % (550)Instructions burned: 151 (million)
% 2.45/1.90 % (550)------------------------------
% 2.45/1.90 % (550)------------------------------
% 2.45/1.90 % (553)Instruction limit reached!
% 2.45/1.90 % (553)------------------------------
% 2.45/1.90 % (553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.90 % (553)Termination reason: Unknown
% 2.45/1.90 % (553)Termination phase: Property scanning
% 2.45/1.90
% 2.45/1.90 % (553)Memory used [KB]: 1918
% 2.45/1.90 % (553)Time elapsed: 0.027 s
% 2.45/1.90 % (553)Instructions burned: 110 (million)
% 2.45/1.90 % (553)------------------------------
% 2.45/1.90 % (553)------------------------------
% 2.45/1.91 % (525)Instruction limit reached!
% 2.45/1.91 % (525)------------------------------
% 2.45/1.91 % (525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.91 % (525)Termination reason: Unknown
% 2.45/1.91 % (525)Termination phase: Saturation
% 2.45/1.91
% 2.45/1.91 % (525)Memory used [KB]: 3454
% 2.45/1.91 % (525)Time elapsed: 0.117 s
% 2.45/1.91 % (525)Instructions burned: 434 (million)
% 2.45/1.91 % (525)------------------------------
% 2.45/1.91 % (525)------------------------------
% 2.45/1.91 % (555)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/140Mi)
% 2.45/1.91 % (556)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/614Mi)
% 2.45/1.92 % (557)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/202Mi)
% 2.45/1.92 % (529)Instruction limit reached!
% 2.45/1.92 % (529)------------------------------
% 2.45/1.92 % (529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.92 % (529)Termination reason: Unknown
% 2.45/1.92 % (529)Termination phase: Saturation
% 2.45/1.92
% 2.45/1.92 % (529)Memory used [KB]: 6524
% 2.45/1.92 % (529)Time elapsed: 0.107 s
% 2.45/1.92 % (529)Instructions burned: 453 (million)
% 2.45/1.92 % (529)------------------------------
% 2.45/1.92 % (529)------------------------------
% 2.45/1.93 % (558)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_351 for (2995ds/339Mi)
% 2.45/1.95 % (555)Instruction limit reached!
% 2.45/1.95 % (555)------------------------------
% 2.45/1.95 % (555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.95 % (555)Termination reason: Unknown
% 2.45/1.95 % (555)Termination phase: Saturation
% 2.45/1.95
% 2.45/1.95 % (555)Memory used [KB]: 6652
% 2.45/1.95 % (555)Time elapsed: 0.042 s
% 2.45/1.95 % (555)Instructions burned: 142 (million)
% 2.45/1.95 % (555)------------------------------
% 2.45/1.95 % (555)------------------------------
% 2.45/1.96 % (554)Instruction limit reached!
% 2.45/1.96 % (554)------------------------------
% 2.45/1.96 % (554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.96 % (554)Termination reason: Unknown
% 2.45/1.96 % (554)Termination phase: Saturation
% 2.45/1.96
% 2.45/1.96 % (554)Memory used [KB]: 6524
% 2.45/1.96 % (554)Time elapsed: 0.075 s
% 2.45/1.96 % (554)Instructions burned: 253 (million)
% 2.45/1.96 % (554)------------------------------
% 2.45/1.96 % (554)------------------------------
% 2.45/1.96 % (559)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/283Mi)
% 2.45/1.97 % (560)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/134Mi)
% 2.45/1.97 % (552)Instruction limit reached!
% 2.45/1.97 % (552)------------------------------
% 2.45/1.97 % (552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.97 % (552)Termination reason: Unknown
% 2.45/1.97 % (552)Termination phase: Saturation
% 2.45/1.97
% 2.45/1.97 % (552)Memory used [KB]: 6652
% 2.45/1.97 % (552)Time elapsed: 0.097 s
% 2.45/1.97 % (552)Instructions burned: 344 (million)
% 2.45/1.97 % (552)------------------------------
% 2.45/1.97 % (552)------------------------------
% 2.45/1.98 % (557)Instruction limit reached!
% 2.45/1.98 % (557)------------------------------
% 2.45/1.98 % (557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.98 % (557)Termination reason: Unknown
% 2.45/1.98 % (557)Termination phase: Saturation
% 2.45/1.98
% 2.45/1.98 % (557)Memory used [KB]: 6524
% 2.45/1.98 % (557)Time elapsed: 0.059 s
% 2.45/1.98 % (557)Instructions burned: 202 (million)
% 2.45/1.98 % (557)------------------------------
% 2.45/1.98 % (557)------------------------------
% 2.45/1.98 % (561)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/298Mi)
% 2.45/1.98 % (562)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/192Mi)
% 2.45/2.00 % (560)Instruction limit reached!
% 2.45/2.00 % (560)------------------------------
% 2.45/2.00 % (560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/2.00 % (560)Termination reason: Unknown
% 2.45/2.00 % (560)Termination phase: Saturation
% 2.45/2.00
% 2.45/2.00 % (560)Memory used [KB]: 6396
% 2.45/2.00 % (560)Time elapsed: 0.034 s
% 2.45/2.00 % (560)Instructions burned: 137 (million)
% 2.45/2.00 % (560)------------------------------
% 2.45/2.00 % (560)------------------------------
% 2.45/2.01 % (563)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/258Mi)
% 6.42/2.03 % (558)Instruction limit reached!
% 6.42/2.03 % (558)------------------------------
% 6.42/2.03 % (558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.03 % (558)Termination reason: Unknown
% 6.42/2.03 % (558)Termination phase: Saturation
% 6.42/2.03
% 6.42/2.03 % (558)Memory used [KB]: 7419
% 6.42/2.03 % (558)Time elapsed: 0.095 s
% 6.42/2.03 % (558)Instructions burned: 340 (million)
% 6.42/2.03 % (558)------------------------------
% 6.42/2.03 % (558)------------------------------
% 6.42/2.03 % (562)Instruction limit reached!
% 6.42/2.03 % (562)------------------------------
% 6.42/2.03 % (562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.03 % (562)Termination reason: Unknown
% 6.42/2.03 % (562)Termination phase: Saturation
% 6.42/2.03
% 6.42/2.03 % (562)Memory used [KB]: 6524
% 6.42/2.03 % (562)Time elapsed: 0.047 s
% 6.42/2.03 % (562)Instructions burned: 192 (million)
% 6.42/2.03 % (562)------------------------------
% 6.42/2.03 % (562)------------------------------
% 6.42/2.04 % (564)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/90Mi)
% 6.42/2.04 % (565)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_351 for (2994ds/231Mi)
% 6.42/2.04 % (559)Instruction limit reached!
% 6.42/2.04 % (559)------------------------------
% 6.42/2.04 % (559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.04 % (559)Termination reason: Unknown
% 6.42/2.04 % (559)Termination phase: Saturation
% 6.42/2.04
% 6.42/2.04 % (559)Memory used [KB]: 6780
% 6.42/2.04 % (559)Time elapsed: 0.102 s
% 6.42/2.04 % (559)Instructions burned: 283 (million)
% 6.42/2.04 % (559)------------------------------
% 6.42/2.04 % (559)------------------------------
% 6.42/2.05 % (561)Instruction limit reached!
% 6.42/2.05 % (561)------------------------------
% 6.42/2.05 % (561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.05 % (561)Termination reason: Unknown
% 6.42/2.05 % (561)Termination phase: Saturation
% 6.42/2.05
% 6.42/2.05 % (561)Memory used [KB]: 6908
% 6.42/2.05 % (561)Time elapsed: 0.072 s
% 6.42/2.05 % (561)Instructions burned: 301 (million)
% 6.42/2.05 % (561)------------------------------
% 6.42/2.05 % (561)------------------------------
% 6.42/2.05 % (567)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/458Mi)
% 6.42/2.06 % (564)Instruction limit reached!
% 6.42/2.06 % (564)------------------------------
% 6.42/2.06 % (564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.06 % (564)Termination reason: Unknown
% 6.42/2.06 % (564)Termination phase: Twee Goal Transformation
% 6.42/2.06
% 6.42/2.06 % (564)Memory used [KB]: 1918
% 6.42/2.06 % (564)Time elapsed: 0.023 s
% 6.42/2.06 % (564)Instructions burned: 90 (million)
% 6.42/2.06 % (564)------------------------------
% 6.42/2.06 % (564)------------------------------
% 6.42/2.06 % (568)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/31Mi)
% 6.42/2.07 % (556)Instruction limit reached!
% 6.42/2.07 % (556)------------------------------
% 6.42/2.07 % (556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.07 % (556)Termination reason: Unknown
% 6.42/2.07 % (556)Termination phase: Saturation
% 6.42/2.07
% 6.42/2.07 % (556)Memory used [KB]: 7547
% 6.42/2.07 % (556)Time elapsed: 0.156 s
% 6.42/2.07 % (556)Instructions burned: 614 (million)
% 6.42/2.07 % (556)------------------------------
% 6.42/2.07 % (556)------------------------------
% 6.42/2.07 % (568)Instruction limit reached!
% 6.42/2.07 % (568)------------------------------
% 6.42/2.07 % (568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.07 % (568)Termination reason: Unknown
% 6.42/2.07 % (568)Termination phase: Preprocessing 3
% 6.42/2.07
% 6.42/2.07 % (568)Memory used [KB]: 1535
% 6.42/2.07 % (568)Time elapsed: 0.009 s
% 6.42/2.07 % (568)Instructions burned: 31 (million)
% 6.42/2.07 % (568)------------------------------
% 6.42/2.07 % (568)------------------------------
% 6.42/2.07 % (569)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/297Mi)
% 6.42/2.07 % (563)Instruction limit reached!
% 6.42/2.07 % (563)------------------------------
% 6.42/2.07 % (563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.07 % (563)Termination reason: Unknown
% 6.42/2.07 % (563)Termination phase: Saturation
% 6.42/2.07
% 6.42/2.07 % (563)Memory used [KB]: 6524
% 6.42/2.07 % (563)Time elapsed: 0.063 s
% 6.42/2.07 % (563)Instructions burned: 259 (million)
% 6.42/2.07 % (563)------------------------------
% 6.42/2.07 % (563)------------------------------
% 6.42/2.08 % (570)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/987Mi)
% 6.42/2.08 % (571)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/182Mi)
% 6.42/2.08 % (572)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/182Mi)
% 6.42/2.08 % (522)Instruction limit reached!
% 6.42/2.08 % (522)------------------------------
% 6.42/2.08 % (522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.08 % (522)Termination reason: Unknown
% 6.42/2.08 % (522)Termination phase: Saturation
% 6.42/2.08
% 6.42/2.08 % (522)Memory used [KB]: 7547
% 6.42/2.08 % (522)Time elapsed: 0.315 s
% 6.42/2.08 % (522)Instructions burned: 1090 (million)
% 6.42/2.08 % (522)------------------------------
% 6.42/2.08 % (522)------------------------------
% 6.42/2.09 % (573)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/154Mi)
% 6.42/2.11 % (565)Instruction limit reached!
% 6.42/2.11 % (565)------------------------------
% 6.42/2.11 % (565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.11 % (565)Termination reason: Unknown
% 6.42/2.11 % (565)Termination phase: Saturation
% 6.42/2.11
% 6.42/2.11 % (565)Memory used [KB]: 7291
% 6.42/2.11 % (565)Time elapsed: 0.087 s
% 6.42/2.11 % (565)Instructions burned: 233 (million)
% 6.42/2.11 % (565)------------------------------
% 6.42/2.11 % (565)------------------------------
% 6.93/2.11 % (574)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/79Mi)
% 6.93/2.12 % (571)Instruction limit reached!
% 6.93/2.12 % (571)------------------------------
% 6.93/2.12 % (571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.12 % (571)Termination reason: Unknown
% 6.93/2.12 % (571)Termination phase: Saturation
% 6.93/2.12
% 6.93/2.12 % (571)Memory used [KB]: 6396
% 6.93/2.12 % (571)Time elapsed: 0.044 s
% 6.93/2.12 % (571)Instructions burned: 183 (million)
% 6.93/2.12 % (571)------------------------------
% 6.93/2.12 % (571)------------------------------
% 6.93/2.13 % (573)Instruction limit reached!
% 6.93/2.13 % (573)------------------------------
% 6.93/2.13 % (573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.13 % (573)Termination reason: Unknown
% 6.93/2.13 % (573)Termination phase: Saturation
% 6.93/2.13
% 6.93/2.13 % (573)Memory used [KB]: 6396
% 6.93/2.13 % (573)Time elapsed: 0.038 s
% 6.93/2.13 % (573)Instructions burned: 156 (million)
% 6.93/2.13 % (573)------------------------------
% 6.93/2.13 % (573)------------------------------
% 6.93/2.13 % (575)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_351 for (2993ds/216Mi)
% 6.93/2.13 % (572)Instruction limit reached!
% 6.93/2.13 % (572)------------------------------
% 6.93/2.13 % (572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.13 % (572)Termination reason: Unknown
% 6.93/2.13 % (572)Termination phase: Saturation
% 6.93/2.13
% 6.93/2.13 % (572)Memory used [KB]: 6524
% 6.93/2.13 % (572)Time elapsed: 0.073 s
% 6.93/2.13 % (572)Instructions burned: 184 (million)
% 6.93/2.13 % (572)------------------------------
% 6.93/2.13 % (572)------------------------------
% 6.93/2.13 % (574)Instruction limit reached!
% 6.93/2.13 % (574)------------------------------
% 6.93/2.13 % (574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.13 % (574)Termination reason: Unknown
% 6.93/2.13 % (574)Termination phase: Property scanning
% 6.93/2.13
% 6.93/2.13 % (574)Memory used [KB]: 1918
% 6.93/2.13 % (574)Time elapsed: 0.020 s
% 6.93/2.13 % (574)Instructions burned: 79 (million)
% 6.93/2.13 % (574)------------------------------
% 6.93/2.13 % (574)------------------------------
% 6.93/2.14 % (576)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/114Mi)
% 6.93/2.14 % (577)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/922Mi)
% 6.93/2.14 % (578)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/182Mi)
% 6.93/2.15 % (569)Instruction limit reached!
% 6.93/2.15 % (569)------------------------------
% 6.93/2.15 % (569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.15 % (569)Termination reason: Unknown
% 6.93/2.15 % (569)Termination phase: Saturation
% 6.93/2.15
% 6.93/2.15 % (569)Memory used [KB]: 6524
% 6.93/2.15 % (569)Time elapsed: 0.102 s
% 6.93/2.15 % (569)Instructions burned: 299 (million)
% 6.93/2.15 % (569)------------------------------
% 6.93/2.15 % (569)------------------------------
% 6.93/2.16 % (579)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/164Mi)
% 6.93/2.16 % (576)Instruction limit reached!
% 6.93/2.16 % (576)------------------------------
% 6.93/2.16 % (576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.16 % (576)Termination reason: Unknown
% 6.93/2.16 % (576)Termination phase: Saturation
% 6.93/2.16
% 6.93/2.16 % (576)Memory used [KB]: 6396
% 6.93/2.16 % (576)Time elapsed: 0.028 s
% 6.93/2.16 % (576)Instructions burned: 115 (million)
% 6.93/2.16 % (576)------------------------------
% 6.93/2.16 % (576)------------------------------
% 6.93/2.17 % (567)Instruction limit reached!
% 6.93/2.17 % (567)------------------------------
% 6.93/2.17 % (567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.17 % (567)Termination reason: Unknown
% 6.93/2.17 % (567)Termination phase: Saturation
% 6.93/2.17
% 6.93/2.17 % (567)Memory used [KB]: 6780
% 6.93/2.17 % (567)Time elapsed: 0.116 s
% 6.93/2.17 % (567)Instructions burned: 459 (million)
% 6.93/2.17 % (567)------------------------------
% 6.93/2.17 % (567)------------------------------
% 6.93/2.17 % (580)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/50Mi)
% 6.93/2.18 % (581)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/368Mi)
% 6.93/2.19 % (578)Instruction limit reached!
% 6.93/2.19 % (578)------------------------------
% 6.93/2.19 % (578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.19 % (578)Termination reason: Unknown
% 6.93/2.19 % (580)Instruction limit reached!
% 6.93/2.19 % (580)------------------------------
% 6.93/2.19 % (580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.19 % (580)Termination reason: Unknown
% 6.93/2.19 % (580)Termination phase: Function definition elimination
% 6.93/2.19
% 6.93/2.19 % (580)Memory used [KB]: 1663
% 6.93/2.19 % (580)Time elapsed: 0.014 s
% 6.93/2.19 % (580)Instructions burned: 54 (million)
% 6.93/2.19 % (580)------------------------------
% 6.93/2.19 % (580)------------------------------
% 6.93/2.19 % (578)Termination phase: Saturation
% 6.93/2.19
% 6.93/2.19 % (578)Memory used [KB]: 6396
% 6.93/2.19 % (578)Time elapsed: 0.044 s
% 6.93/2.19 % (578)Instructions burned: 183 (million)
% 6.93/2.19 % (578)------------------------------
% 6.93/2.19 % (578)------------------------------
% 6.93/2.19 % (575)Instruction limit reached!
% 6.93/2.19 % (575)------------------------------
% 6.93/2.19 % (575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.19 % (575)Termination reason: Unknown
% 6.93/2.19 % (575)Termination phase: Saturation
% 6.93/2.19
% 6.93/2.19 % (575)Memory used [KB]: 6396
% 6.93/2.19 % (575)Time elapsed: 0.082 s
% 6.93/2.19 % (575)Instructions burned: 218 (million)
% 6.93/2.19 % (575)------------------------------
% 6.93/2.19 % (575)------------------------------
% 6.93/2.20 % (582)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/1021Mi)
% 6.93/2.20 % (583)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/267Mi)
% 7.51/2.20 % (584)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/204Mi)
% 7.51/2.21 % (579)Instruction limit reached!
% 7.51/2.21 % (579)------------------------------
% 7.51/2.21 % (579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.21 % (579)Termination reason: Unknown
% 7.51/2.21 % (579)Termination phase: Saturation
% 7.51/2.21
% 7.51/2.21 % (579)Memory used [KB]: 2046
% 7.51/2.21 % (579)Time elapsed: 0.049 s
% 7.51/2.21 % (579)Instructions burned: 167 (million)
% 7.51/2.21 % (579)------------------------------
% 7.51/2.21 % (579)------------------------------
% 7.51/2.22 % (585)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_351 for (2992ds/26Mi)
% 7.51/2.22 % (585)Instruction limit reached!
% 7.51/2.22 % (585)------------------------------
% 7.51/2.22 % (585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.22 % (585)Termination reason: Unknown
% 7.51/2.22 % (585)Termination phase: Property scanning
% 7.51/2.22
% 7.51/2.22 % (585)Memory used [KB]: 1535
% 7.51/2.22 % (585)Time elapsed: 0.008 s
% 7.51/2.22 % (585)Instructions burned: 27 (million)
% 7.51/2.22 % (585)------------------------------
% 7.51/2.22 % (585)------------------------------
% 7.51/2.23 % (586)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_351 for (2991ds/53Mi)
% 7.51/2.25 % (584)Instruction limit reached!
% 7.51/2.25 % (584)------------------------------
% 7.51/2.25 % (584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.25 % (584)Termination reason: Unknown
% 7.51/2.25 % (584)Termination phase: Saturation
% 7.51/2.25
% 7.51/2.25 % (584)Memory used [KB]: 6524
% 7.51/2.25 % (584)Time elapsed: 0.050 s
% 7.51/2.25 % (584)Instructions burned: 206 (million)
% 7.51/2.25 % (584)------------------------------
% 7.51/2.25 % (584)------------------------------
% 7.51/2.25 % (586)Instruction limit reached!
% 7.51/2.25 % (586)------------------------------
% 7.51/2.25 % (586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.25 % (586)Termination reason: Unknown
% 7.51/2.25 % (586)Termination phase: Function definition elimination
% 7.51/2.25
% 7.51/2.25 % (586)Memory used [KB]: 1663
% 7.51/2.25 % (586)Time elapsed: 0.014 s
% 7.51/2.25 % (586)Instructions burned: 53 (million)
% 7.51/2.25 % (586)------------------------------
% 7.51/2.25 % (586)------------------------------
% 7.51/2.25 % (587)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_351 for (2991ds/4436Mi)
% 7.51/2.26 % (588)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_351 for (2991ds/1539Mi)
% 7.51/2.26 % (583)Instruction limit reached!
% 7.51/2.26 % (583)------------------------------
% 7.51/2.26 % (583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.26 % (583)Termination reason: Unknown
% 7.51/2.26 % (583)Termination phase: Saturation
% 7.51/2.26
% 7.51/2.26 % (583)Memory used [KB]: 6524
% 7.51/2.26 % (583)Time elapsed: 0.064 s
% 7.51/2.26 % (583)Instructions burned: 269 (million)
% 7.51/2.26 % (583)------------------------------
% 7.51/2.26 % (583)------------------------------
% 7.51/2.27 % (589)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_351 for (2991ds/408Mi)
% 7.51/2.27 % (581)Instruction limit reached!
% 7.51/2.27 % (581)------------------------------
% 7.51/2.27 % (581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.27 % (581)Termination reason: Unknown
% 7.51/2.27 % (581)Termination phase: Saturation
% 7.51/2.27
% 7.51/2.27 % (581)Memory used [KB]: 7419
% 7.51/2.27 % (581)Time elapsed: 0.098 s
% 7.51/2.28 % (581)Instructions burned: 370 (million)
% 7.51/2.28 % (581)------------------------------
% 7.51/2.28 % (581)------------------------------
% 7.51/2.28 % (590)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_351 for (2991ds/5205Mi)
% 7.84/2.32 % (570)Instruction limit reached!
% 7.84/2.32 % (570)------------------------------
% 7.84/2.32 % (570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.32 % (570)Termination reason: Unknown
% 7.84/2.32 % (570)Termination phase: Saturation
% 7.84/2.32
% 7.84/2.32 % (570)Memory used [KB]: 7419
% 7.84/2.32 % (570)Time elapsed: 0.267 s
% 7.84/2.32 % (570)Instructions burned: 989 (million)
% 7.84/2.32 % (570)------------------------------
% 7.84/2.32 % (570)------------------------------
% 7.84/2.33 % (591)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_351 for (2991ds/1913Mi)
% 7.84/2.38 % (577)Instruction limit reached!
% 7.84/2.38 % (577)------------------------------
% 7.84/2.38 % (577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.38 % (577)Termination reason: Unknown
% 7.84/2.38 % (577)Termination phase: Saturation
% 7.84/2.38
% 7.84/2.38 % (577)Memory used [KB]: 7419
% 7.84/2.38 % (577)Time elapsed: 0.237 s
% 7.84/2.38 % (577)Instructions burned: 924 (million)
% 7.84/2.38 % (577)------------------------------
% 7.84/2.38 % (577)------------------------------
% 7.84/2.38 % (589)Instruction limit reached!
% 7.84/2.38 % (589)------------------------------
% 7.84/2.38 % (589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.84/2.38 % (589)Termination reason: Unknown
% 7.84/2.38 % (589)Termination phase: Saturation
% 7.84/2.39
% 7.84/2.39 % (589)Memory used [KB]: 7419
% 7.84/2.39 % (589)Time elapsed: 0.118 s
% 7.84/2.39 % (589)Instructions burned: 411 (million)
% 7.84/2.39 % (589)------------------------------
% 7.84/2.39 % (589)------------------------------
% 7.84/2.39 % (592)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_351 for (2990ds/4350Mi)
% 7.84/2.39 % (593)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_351 for (2990ds/68Mi)
% 8.46/2.41 % (593)Instruction limit reached!
% 8.46/2.41 % (593)------------------------------
% 8.46/2.41 % (593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.41 % (593)Termination reason: Unknown
% 8.46/2.41 % (593)Termination phase: Function definition elimination
% 8.46/2.41
% 8.46/2.41 % (593)Memory used [KB]: 1663
% 8.46/2.41 % (593)Time elapsed: 0.018 s
% 8.46/2.41 % (593)Instructions burned: 68 (million)
% 8.46/2.41 % (593)------------------------------
% 8.46/2.41 % (593)------------------------------
% 8.46/2.42 % (594)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_351 for (2990ds/358Mi)
% 8.46/2.45 % (582)Instruction limit reached!
% 8.46/2.45 % (582)------------------------------
% 8.46/2.45 % (582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.45 % (582)Termination reason: Unknown
% 8.46/2.45 % (582)Termination phase: Saturation
% 8.46/2.45
% 8.46/2.45 % (582)Memory used [KB]: 7036
% 8.46/2.45 % (582)Time elapsed: 0.254 s
% 8.46/2.45 % (582)Instructions burned: 1022 (million)
% 8.46/2.45 % (582)------------------------------
% 8.46/2.45 % (582)------------------------------
% 8.46/2.46 % (595)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_351 for (2989ds/31Mi)
% 8.46/2.47 % (595)Instruction limit reached!
% 8.46/2.47 % (595)------------------------------
% 8.46/2.47 % (595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.47 % (595)Termination reason: Unknown
% 8.46/2.47 % (595)Termination phase: Clausification
% 8.46/2.47
% 8.46/2.47 % (595)Memory used [KB]: 1663
% 8.46/2.47 % (595)Time elapsed: 0.010 s
% 8.46/2.47 % (595)Instructions burned: 33 (million)
% 8.46/2.47 % (595)------------------------------
% 8.46/2.47 % (595)------------------------------
% 8.46/2.48 % (596)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_351 for (2989ds/279Mi)
% 8.77/2.52 % (594)Instruction limit reached!
% 8.77/2.52 % (594)------------------------------
% 8.77/2.52 % (594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.52 % (594)Termination reason: Unknown
% 8.77/2.52 % (594)Termination phase: Saturation
% 8.77/2.52
% 8.77/2.52 % (594)Memory used [KB]: 6524
% 8.77/2.52 % (594)Time elapsed: 0.099 s
% 8.77/2.52 % (594)Instructions burned: 358 (million)
% 8.77/2.52 % (594)------------------------------
% 8.77/2.52 % (594)------------------------------
% 8.77/2.53 % (597)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_351 for (2989ds/258Mi)
% 8.77/2.55 % (596)Instruction limit reached!
% 8.77/2.55 % (596)------------------------------
% 8.77/2.55 % (596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.55 % (596)Termination reason: Unknown
% 8.77/2.55 % (596)Termination phase: Saturation
% 8.77/2.55
% 8.77/2.55 % (596)Memory used [KB]: 7036
% 8.77/2.55 % (596)Time elapsed: 0.079 s
% 8.77/2.55 % (596)Instructions burned: 281 (million)
% 8.77/2.55 % (596)------------------------------
% 8.77/2.55 % (596)------------------------------
% 8.77/2.56 % (598)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_351 for (2988ds/26Mi)
% 8.77/2.57 % (598)Instruction limit reached!
% 8.77/2.57 % (598)------------------------------
% 8.77/2.57 % (598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.77/2.57 % (598)Termination reason: Unknown
% 8.77/2.57 % (598)Termination phase: Property scanning
% 8.77/2.57
% 8.77/2.57 % (598)Memory used [KB]: 1535
% 8.77/2.57 % (598)Time elapsed: 0.008 s
% 8.77/2.57 % (598)Instructions burned: 27 (million)
% 8.77/2.57 % (598)------------------------------
% 8.77/2.57 % (598)------------------------------
% 8.77/2.58 % (599)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_351 for (2988ds/995Mi)
% 8.98/2.61 % (597)Instruction limit reached!
% 8.98/2.61 % (597)------------------------------
% 8.98/2.61 % (597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.98/2.61 % (597)Termination reason: Unknown
% 8.98/2.61 % (597)Termination phase: Saturation
% 8.98/2.61
% 8.98/2.61 % (597)Memory used [KB]: 6780
% 8.98/2.61 % (597)Time elapsed: 0.077 s
% 8.98/2.61 % (597)Instructions burned: 260 (million)
% 8.98/2.61 % (597)------------------------------
% 8.98/2.61 % (597)------------------------------
% 8.98/2.62 % (600)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_351 for (2988ds/373Mi)
% 8.98/2.64 % (588)Instruction limit reached!
% 8.98/2.64 % (588)------------------------------
% 8.98/2.64 % (588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.98/2.64 % (588)Termination reason: Unknown
% 8.98/2.64 % (588)Termination phase: Saturation
% 8.98/2.64
% 8.98/2.64 % (588)Memory used [KB]: 7547
% 8.98/2.64 % (588)Time elapsed: 0.381 s
% 8.98/2.64 % (588)Instructions burned: 1542 (million)
% 8.98/2.64 % (588)------------------------------
% 8.98/2.64 % (588)------------------------------
% 8.98/2.64 % (601)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_351 for (2987ds/253Mi)
% 9.46/2.70 % (601)Instruction limit reached!
% 9.46/2.70 % (601)------------------------------
% 9.46/2.70 % (601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.70 % (601)Termination reason: Unknown
% 9.46/2.70 % (601)Termination phase: Saturation
% 9.46/2.70
% 9.46/2.70 % (601)Memory used [KB]: 6396
% 9.46/2.70 % (601)Time elapsed: 0.060 s
% 9.46/2.70 % (601)Instructions burned: 253 (million)
% 9.46/2.70 % (601)------------------------------
% 9.46/2.70 % (601)------------------------------
% 9.46/2.71 % (600)Instruction limit reached!
% 9.46/2.71 % (600)------------------------------
% 9.46/2.71 % (600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.71 % (600)Termination reason: Unknown
% 9.46/2.71 % (600)Termination phase: Saturation
% 9.46/2.71
% 9.46/2.71 % (600)Memory used [KB]: 7036
% 9.46/2.71 % (600)Time elapsed: 0.095 s
% 9.46/2.71 % (600)Instructions burned: 374 (million)
% 9.46/2.71 % (600)------------------------------
% 9.46/2.71 % (600)------------------------------
% 9.46/2.71 % (602)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_351 for (2987ds/832Mi)
% 9.46/2.72 % (603)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_351 for (2987ds/668Mi)
% 9.46/2.76 % (591)First to succeed.
% 9.46/2.78 % (591)Refutation found. Thanks to Tanya!
% 9.46/2.78 % SZS status Theorem for DTF2THF_351
% 9.46/2.78 % SZS output start Proof for DTF2THF_351
% 9.46/2.78 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_3, type, c_not: $o > $o).
% 9.46/2.78 thf(func_def_4, type, c_and: $o > $o > $o).
% 9.46/2.78 thf(func_def_5, type, c_or: $o > $o > $o).
% 9.46/2.78 thf(func_def_6, type, c_iff: $o > $o > $o).
% 9.46/2.78 thf(func_def_7, type, c_In: $i > $i > $o).
% 9.46/2.78 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 9.46/2.78 thf(func_def_10, type, c_Union: $i > $i).
% 9.46/2.78 thf(func_def_11, type, c_Power: $i > $i).
% 9.46/2.78 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 9.46/2.78 thf(func_def_13, type, c_TransSet: $i > $o).
% 9.46/2.78 thf(func_def_14, type, c_atleast2: $i > $o).
% 9.46/2.78 thf(func_def_15, type, c_atleast3: $i > $o).
% 9.46/2.78 thf(func_def_16, type, c_atleast4: $i > $o).
% 9.46/2.78 thf(func_def_17, type, c_atleast5: $i > $o).
% 9.46/2.78 thf(func_def_18, type, c_atleast6: $i > $o).
% 9.46/2.78 thf(func_def_19, type, c_exactly2: $i > $o).
% 9.46/2.78 thf(func_def_20, type, c_exactly3: $i > $o).
% 9.46/2.78 thf(func_def_21, type, c_exactly4: $i > $o).
% 9.46/2.78 thf(func_def_22, type, c_exactly5: $i > $o).
% 9.46/2.78 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 9.46/2.78 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 9.46/2.78 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 9.46/2.78 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 9.46/2.78 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 9.46/2.78 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 9.46/2.78 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 9.46/2.78 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 9.46/2.78 thf(func_def_43, type, c_Sing: $i > $i).
% 9.46/2.78 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 9.46/2.78 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 9.46/2.78 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 9.46/2.78 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 9.46/2.78 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 9.46/2.78 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 9.46/2.78 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 9.46/2.78 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 9.46/2.78 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 9.46/2.78 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 9.46/2.78 thf(func_def_54, type, c_equip: $i > $i > $o).
% 9.46/2.78 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 9.46/2.78 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 9.46/2.78 thf(func_def_57, type, c_ordsucc: $i > $i).
% 9.46/2.78 thf(func_def_58, type, c_nat_p: $i > $o).
% 9.46/2.78 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 9.46/2.78 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 9.46/2.78 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 9.46/2.78 thf(func_def_62, type, c_ordinal: $i > $o).
% 9.46/2.78 thf(func_def_63, type, c_V_: $i > $i).
% 9.46/2.78 thf(func_def_64, type, c_Inj1: $i > $i).
% 9.46/2.78 thf(func_def_65, type, c_Inj0: $i > $i).
% 9.46/2.78 thf(func_def_66, type, c_Unj: $i > $i).
% 9.46/2.78 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 9.46/2.78 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 9.46/2.78 thf(func_def_69, type, c_proj0: $i > $i).
% 9.46/2.78 thf(func_def_70, type, c_proj1: $i > $i).
% 9.46/2.78 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 9.46/2.78 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 9.46/2.78 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 9.46/2.78 thf(func_def_74, type, c_ap: $i > $i > $i).
% 9.46/2.78 thf(func_def_75, type, c_setsum_p: $i > $o).
% 9.46/2.78 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 9.46/2.78 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 9.46/2.78 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 9.46/2.78 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 9.46/2.78 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 9.46/2.78 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 9.46/2.78 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 9.46/2.78 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 9.46/2.78 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 9.46/2.78 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 9.46/2.78 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 9.46/2.78 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 9.46/2.78 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 9.46/2.78 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 9.46/2.78 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 9.46/2.78 thf(func_def_91, type, c_SNo: $i > $o).
% 9.46/2.78 thf(func_def_92, type, c_SNoLev: $i > $i).
% 9.46/2.78 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 9.46/2.78 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 9.46/2.78 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 9.46/2.78 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 9.46/2.78 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 9.46/2.78 thf(func_def_98, type, c_Loop_with_defs: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o).
% 9.46/2.78 thf(func_def_99, type, c_Loop_with_defs_cex1: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o).
% 9.46/2.78 thf(func_def_100, type, c_Loop_with_defs_cex2: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o).
% 9.46/2.78 thf(func_def_101, type, c_combinator: $i > $o).
% 9.46/2.78 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 9.46/2.78 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 9.46/2.78 thf(func_def_131, type, sP0: ($i > $o) > $o).
% 9.46/2.78 thf(func_def_132, type, sP1: ($i > $o) > $o).
% 9.46/2.78 thf(func_def_133, type, sK2: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_134, type, sK3: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_135, type, sK4: ($i > $o) > $i > $i).
% 9.46/2.78 thf(func_def_136, type, sK5: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_137, type, sK6: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_138, type, sK7: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_139, type, sK8: ($i > $o) > $i).
% 9.46/2.78 thf(func_def_140, type, sK9: ($i > $i) > $i > $i).
% 9.46/2.78 thf(func_def_141, type, sK10: ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i).
% 9.46/2.78 thf(func_def_142, type, sK11: ($i > $i) > ($i > $i) > $i).
% 9.46/2.78 thf(func_def_143, type, sK12: ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i).
% 9.46/2.78 thf(func_def_145, type, sK14: $i > $i > $i).
% 9.46/2.78 thf(func_def_146, type, sK15: $i > $i > $i).
% 9.46/2.78 thf(func_def_147, type, sK16: $i > $i > $i > $o).
% 9.46/2.78 thf(func_def_149, type, sK18: $i > ($i > $i) > $i > $i).
% 9.46/2.78 thf(func_def_150, type, sK19: $i > $i > ($i > $i) > $i > $o).
% 9.46/2.78 thf(func_def_151, type, sK20: $o > $o > $o).
% 9.46/2.78 thf(func_def_152, type, sK21: $i > $i > $i).
% 9.46/2.78 thf(func_def_153, type, sK22: $i > $i > $i).
% 9.46/2.78 thf(func_def_154, type, ph23: !>[X0: $tType]:(X0)).
% 9.46/2.78 thf(f1734,plain,(
% 9.46/2.78 $false),
% 9.46/2.78 inference(trivial_inequality_removal,[status(thm)],[f1709])).
% 9.46/2.78 thf(f1709,plain,(
% 9.46/2.78 ($true = $false)),
% 9.46/2.78 inference(superposition,[status(thm)],[f472,f1650])).
% 9.46/2.78 thf(f1650,plain,(
% 9.46/2.78 ( ! [X0 : $o] : (($true = X0)) )),
% 9.46/2.78 inference(trivial_inequality_removal,[status(thm)],[f1605])).
% 9.46/2.78 thf(f1605,plain,(
% 9.46/2.78 ( ! [X0 : $o] : (($true = $false) | ($true = X0)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f472,f1569])).
% 9.46/2.78 thf(f1569,plain,(
% 9.46/2.78 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true = X0)) )),
% 9.46/2.78 inference(trivial_inequality_removal,[status(thm)],[f1556])).
% 9.46/2.78 thf(f1556,plain,(
% 9.46/2.78 ( ! [X0 : $o,X1 : $o] : (($true = X0) | ($true = $false) | ($true = X1)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f1548,f595])).
% 9.46/2.78 thf(f595,plain,(
% 9.46/2.78 ( ! [X2 : $o,X1 : $i] : (((c_In @ X1 @ c_Empty) = $false) | ($true = X2)) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f594])).
% 9.46/2.78 thf(f594,plain,(
% 9.46/2.78 ( ! [X2 : $o,X1 : $i] : (((c_In @ X1 @ c_Empty) = $false) | ($true = ((^[Y0 : $o]: (Y0)) @ X2))) )),
% 9.46/2.78 inference(pi_clausification,[status(thm)],[f593])).
% 9.46/2.78 thf(f593,plain,(
% 9.46/2.78 ( ! [X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: (Y0)))) | ((c_In @ X1 @ c_Empty) = $false)) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f592])).
% 9.46/2.78 thf(f592,plain,(
% 9.46/2.78 ( ! [X1 : $i] : ((((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X1) = $false) | ($true = (!! @ $o @ (^[Y0 : $o]: (Y0))))) )),
% 9.46/2.78 inference(pi_clausification,[status(thm)],[f591])).
% 9.46/2.78 thf(f591,plain,(
% 9.46/2.78 ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false) | ($true = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 9.46/2.78 inference(binary_proxy_clausification,[status(thm)],[f590])).
% 9.46/2.78 thf(f590,plain,(
% 9.46/2.78 ($true = ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f469])).
% 9.46/2.78 thf(f469,plain,(
% 9.46/2.78 ($true = ((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f391,f407])).
% 9.46/2.78 thf(f407,plain,(
% 9.46/2.78 (c_not = (^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f399,f363])).
% 9.46/2.78 thf(f363,plain,(
% 9.46/2.78 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f243])).
% 9.46/2.78 thf(f243,plain,(
% 9.46/2.78 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f242])).
% 9.46/2.78 thf(f242,plain,(
% 9.46/2.78 (! [X0 : $o] : X0 = c_False)),
% 9.46/2.78 inference(rectify,[status(thm)],[f11])).
% 9.46/2.78 thf(f11,axiom,(
% 9.46/2.78 (! [X0 : $o] : X0 = c_False)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax11)).
% 9.46/2.78 thf(f399,plain,(
% 9.46/2.78 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f113])).
% 9.46/2.78 thf(f113,plain,(
% 9.46/2.78 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f112])).
% 9.46/2.78 thf(f112,plain,(
% 9.46/2.78 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 9.46/2.78 inference(rectify,[status(thm)],[f13])).
% 9.46/2.78 thf(f13,axiom,(
% 9.46/2.78 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax13)).
% 9.46/2.78 thf(f391,plain,(
% 9.46/2.78 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f248])).
% 9.46/2.78 thf(f248,plain,(
% 9.46/2.78 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f247])).
% 9.46/2.78 thf(f247,plain,(
% 9.46/2.78 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 9.46/2.78 inference(rectify,[status(thm)],[f5])).
% 9.46/2.78 thf(f5,axiom,(
% 9.46/2.78 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax5)).
% 9.46/2.78 thf(f1548,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i] : (((c_In @ (c_Union @ c_Empty) @ X0) = $true) | ($true = X2)) )),
% 9.46/2.78 inference(forward_demodulation,[status(thm)],[f1547,f1220])).
% 9.46/2.78 thf(f1220,plain,(
% 9.46/2.78 ( ! [X0 : $i] : (((c_Union @ c_Empty) = X0)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f1149,f665])).
% 9.46/2.78 thf(f665,plain,(
% 9.46/2.78 ( ! [X0 : $i,X1 : $i] : (((sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X0)))) @ X1) = X0)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f660,f384])).
% 9.46/2.78 thf(f384,plain,(
% 9.46/2.78 ( ! [X11 : $i] : (((sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ c_Empty) = X11)) )),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f320])).
% 9.46/2.78 thf(f320,plain,(
% 9.46/2.78 ! [X4 : $i,X5 : $i > $i] : ((X5 @ X4) = (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) & ! [X6 : $i > $i,X7 : $i > $i,X8 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X6 @ (X7 @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK10 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK9 @ (^[Y0 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (sK9 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6 @ (sK12 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK11 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK11 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) & ((c_Inj1 @ c_Empty) = (sK11 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & ! [X9 : ($i > $i) > ($i > $i) > $i,X10 : $i] : ((X9 @ (^[Y0 : $i]: (c_setsum @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK11 @ (^[Y1 : $i]: (sK12 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (sK9 @ (^[Y1 : $i]: (X9 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X10)))) = (sK9 @ (^[Y0 : $i]: (X9 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) & ! [X11 : $i] : ((sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ c_Empty) = X11) & (c_False != $true) & ! [X12 : $i,X13 : $i] : ((sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X12)))))) @ (^[Y0 : $i]: (X13)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X13) & ! [X14 : $i,X15 : $i] : ((sK9 @ (^[Y0 : $i]: (c_Inj1 @ (sK9 @ (^[Y1 : $i]: (c_Inj0 @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X14)))) @ (c_Inj0 @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X15))) = (c_Inj0 @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X14)))) @ (c_setsum @ c_Empty @ c_Empty)))) & ! [X16 : $i,X17 : $i] : ((c_setsum @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK11 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (sK11 @ (^[Y0 : $i]: (X17)) @ (^[Y0 : $i]: (X16))))),
% 9.46/2.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f318,f319])).
% 9.46/2.78 thf(f319,plain,(
% 9.46/2.78 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (! [X4 : $i,X5 : $i > $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X5 @ X4)) & ! [X6 : $i > $i,X7 : $i > $i,X8 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X6 @ (X7 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6 @ (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X2 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X2 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) & ((c_Inj1 @ c_Empty) = (X2 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & ! [X9 : ($i > $i) > ($i > $i) > $i,X10 : $i] : ((X9 @ (^[Y0 : $i]: (c_setsum @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : $i]: (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X9 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X10)))) = (X0 @ (^[Y0 : $i]: (X9 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) & ! [X11 : $i] : ((X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ c_Empty) = X11) & (c_False != $true) & ! [X12 : $i,X13 : $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X12)))))) @ (^[Y0 : $i]: (X13)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X13) & ! [X14 : $i,X15 : $i] : ((c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X14)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X14)))) @ (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X15)))) & ! [X16 : $i,X17 : $i] : ((c_setsum @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X2 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (X2 @ (^[Y0 : $i]: (X17)) @ (^[Y0 : $i]: (X16))))) => (! [X5 : $i > $i,X4 : $i] : ((X5 @ X4) = (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) & ! [X8 : $i > ($i > $i > $i) > $i,X7 : $i > $i,X6 : $i > $i] : ((c_setsum @ (X6 @ (X7 @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK10 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK9 @ (^[Y0 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (sK9 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6 @ (sK12 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK11 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK11 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) & ((c_Inj1 @ c_Empty) = (sK11 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & ! [X10 : $i,X9 : ($i > $i) > ($i > $i) > $i] : ((X9 @ (^[Y0 : $i]: (c_setsum @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK11 @ (^[Y1 : $i]: (sK12 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (sK9 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (sK12 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (sK9 @ (^[Y1 : $i]: (X9 @ (^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X10)))) = (sK9 @ (^[Y0 : $i]: (X9 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) & ! [X11 : $i] : ((sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ c_Empty) = X11) & (c_False != $true) & ! [X13 : $i,X12 : $i] : ((sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X12)))))) @ (^[Y0 : $i]: (X13)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X13) & ! [X15 : $i,X14 : $i] : ((sK9 @ (^[Y0 : $i]: (c_Inj1 @ (sK9 @ (^[Y1 : $i]: (c_Inj0 @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X14)))) @ (c_Inj0 @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X15))) = (c_Inj0 @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X14)))) @ (c_setsum @ c_Empty @ c_Empty)))) & ! [X17 : $i,X16 : $i] : ((c_setsum @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK11 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (sK11 @ (^[Y0 : $i]: (X17)) @ (^[Y0 : $i]: (X16)))))),
% 9.46/2.78 introduced(definition,[],[choice_axiom])).
% 9.46/2.78 thf(f318,plain,(
% 9.46/2.78 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (! [X4 : $i,X5 : $i > $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X5 @ X4)) & ! [X6 : $i > $i,X7 : $i > $i,X8 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X6 @ (X7 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6 @ (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X2 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X2 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) & ((c_Inj1 @ c_Empty) = (X2 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & ! [X9 : ($i > $i) > ($i > $i) > $i,X10 : $i] : ((X9 @ (^[Y0 : $i]: (c_setsum @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : $i]: (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X9 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X10)))) = (X0 @ (^[Y0 : $i]: (X9 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) & ! [X11 : $i] : ((X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ c_Empty) = X11) & (c_False != $true) & ! [X12 : $i,X13 : $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X12)))))) @ (^[Y0 : $i]: (X13)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X13) & ! [X14 : $i,X15 : $i] : ((c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X14)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X14)))) @ (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X15)))) & ! [X16 : $i,X17 : $i] : ((c_setsum @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X2 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (X2 @ (^[Y0 : $i]: (X17)) @ (^[Y0 : $i]: (X16)))))),
% 9.46/2.78 inference(rectify,[status(thm)],[f293])).
% 9.46/2.78 thf(f293,plain,(
% 9.46/2.78 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (! [X16 : $i,X17 : $i > $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X17 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X17 @ X16)) & ! [X7 : $i > $i,X8 : $i > $i,X9 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X7 @ (X8 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X7 @ c_Empty)) @ (X8 @ (X9 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X7 @ (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X2 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X2 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) & ((c_Inj1 @ c_Empty) = (X2 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) & ! [X12 : ($i > $i) > ($i > $i) > $i,X13 : $i] : ((X0 @ (^[Y0 : $i]: (X12 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X12 @ (^[Y0 : $i]: (c_setsum @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : $i]: (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X12 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X13))))) & ! [X6 : $i] : ((X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty) = X6) & (c_False != $true) & ! [X14 : $i,X15 : $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X14)))))) @ (^[Y0 : $i]: (X15)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X15) & ! [X10 : $i,X11 : $i] : ((c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X10)))) @ (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X11)))) & ! [X4 : $i,X5 : $i] : ((c_setsum @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X2 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (X2 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4)))))),
% 9.46/2.78 inference(flattening,[status(thm)],[f292])).
% 9.46/2.78 thf(f292,plain,(
% 9.46/2.78 ? [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (((((((((c_False != $true) & ! [X16 : $i,X17 : $i > $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X17 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X17 @ X16))) & ! [X14 : $i,X15 : $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X14)))))) @ (^[Y0 : $i]: (X15)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X15)) & ! [X12 : ($i > $i) > ($i > $i) > $i,X13 : $i] : ((X0 @ (^[Y0 : $i]: (X12 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X12 @ (^[Y0 : $i]: (c_setsum @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : $i]: (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X12 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X13)))))) & ! [X10 : $i,X11 : $i] : ((c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X10)))) @ (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X11))))) & ! [X7 : $i > $i,X8 : $i > $i,X9 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X7 @ (X8 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X7 @ c_Empty)) @ (X8 @ (X9 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X7 @ (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X2 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X2 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) & ! [X6 : $i] : ((X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty) = X6)) & ! [X4 : $i,X5 : $i] : ((c_setsum @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X2 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (X2 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4))))) & ((c_Inj1 @ c_Empty) = (X2 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))))),
% 9.46/2.78 inference(ennf_transformation,[status(thm)],[f288])).
% 9.46/2.78 thf(f288,plain,(
% 9.46/2.78 ~! [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (((c_Inj1 @ c_Empty) = (X2 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) => (! [X4 : $i,X5 : $i] : ((c_setsum @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X2 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty) = (X2 @ (^[Y0 : $i]: (X5)) @ (^[Y0 : $i]: (X4)))) => (! [X6 : $i] : ((X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty) = X6) => (! [X7 : $i > $i,X8 : $i > $i,X9 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X7 @ (X8 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X7 @ c_Empty)) @ (X8 @ (X9 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X7 @ (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X2 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X2 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) => (! [X10 : $i,X11 : $i] : ((c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X10)))) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X10)))) @ (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X11)))) => (! [X12 : ($i > $i) > ($i > $i) > $i,X13 : $i] : ((X0 @ (^[Y0 : $i]: (X12 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty) = (X12 @ (^[Y0 : $i]: (c_setsum @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : $i]: (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X12 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X13))))) => (! [X14 : $i,X15 : $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X14)))))) @ (^[Y0 : $i]: (X15)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X15) => (! [X16 : $i,X17 : $i > $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X17 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X17 @ X16)) => (c_False = $true)))))))))),
% 9.46/2.78 inference(rectify,[status(thm)],[f252])).
% 9.46/2.78 thf(f252,plain,(
% 9.46/2.78 ~! [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (((c_Inj1 @ c_Empty) = (X2 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))) => (! [X10 : $i,X12 : $i] : ((X2 @ (^[Y0 : $i]: (X12)) @ (^[Y0 : $i]: (X10))) = (c_setsum @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X2 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) => (! [X27 : $i] : ((X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X27)))) @ c_Empty) = X27) => (! [X31 : $i > $i,X32 : $i > $i,X33 : $i > ($i > $i > $i) > $i] : ((c_setsum @ (X31 @ (X32 @ (X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X1 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[Y0 : $i]: (X31 @ c_Empty)) @ (X32 @ (X33 @ (X0 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X31 @ (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X1 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X2 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X2 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) => (! [X69 : $i,X70 : $i] : ((X0 @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (c_Inj0 @ (X1 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X69)))) @ (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X70))) = (c_Inj0 @ (X3 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X69)))) @ (c_setsum @ c_Empty @ c_Empty)))) => (! [X82 : ($i > $i) > ($i > $i) > $i,X83 : $i] : ((X82 @ (^[Y0 : $i]: (c_setsum @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : $i]: (X3 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X0 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X3 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X0 @ (^[Y1 : $i]: (X82 @ (^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X83)))) = (X0 @ (^[Y0 : $i]: (X82 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) => (! [X108 : $i,X109 : $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X108)))))) @ (^[Y0 : $i]: (X109)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X109) => (! [X119 : $i,X120 : $i > $i] : ((X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X0 @ (^[Y3 : $i]: (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X3 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X120 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X120 @ X119)) => (c_False = $true)))))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f251])).
% 9.46/2.78 thf(f251,plain,(
% 9.46/2.78 ~! [X0 : ($i > $i) > $i > $i,X1 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X2 : ($i > $i) > ($i > $i) > $i,X3 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (((c_Inj1 @ c_Empty) = (X2 @ (^[X8 : $i] : (c_Inj1 @ c_Empty)) @ (^[X9 : $i] : (c_setsum @ c_Empty @ c_Empty)))) => (! [X10 : $i,X12 : $i] : ((c_setsum @ (X3 @ (^[X14 : ($i > $i > $i > $i) > $i, X15 : $i] : (c_Empty)) @ (X1 @ (^[X16 : $i, X17 : $i, X18 : $i] : (X2 @ (^[X19 : $i] : (X18)) @ (^[X20 : $i] : (c_Empty)))) @ (^[X21 : $i] : (c_Empty)) @ (^[X22 : $i > $i > $i] : (c_Empty)))) @ c_Empty) = (X2 @ (^[X23 : $i] : (X12)) @ (^[X24 : $i] : (X10)))) => (! [X27 : $i] : (X27 = (X3 @ (^[X29 : ($i > $i > $i > $i) > $i, X30 : $i] : (X27)) @ c_Empty)) => (! [X31 : $i > $i,X32 : $i > $i,X33 : $i > ($i > $i > $i) > $i] : ((X3 @ (^[X35 : ($i > $i > $i > $i) > $i, X36 : $i] : (X31 @ (X3 @ (^[X37 : ($i > $i > $i > $i) > $i, X38 : $i] : (X1 @ (^[X39 : $i, X40 : $i, X41 : $i] : (c_Inj1 @ c_Empty)) @ (^[X42 : $i] : (c_Inj0 @ c_Empty)) @ (^[X43 : $i > $i > $i] : (X2 @ (^[X44 : $i] : (c_Empty)) @ (^[X45 : $i] : (c_Empty)))))) @ (c_Inj0 @ (X1 @ (^[X46 : $i, X47 : $i, X48 : $i] : (c_Empty)) @ (^[X49 : $i] : (c_Empty)) @ (^[X50 : $i > $i > $i] : (c_Empty))))))) @ (X2 @ (^[X51 : $i] : (c_setsum @ X51 @ c_Empty)) @ (^[X52 : $i] : (c_Empty)))) = (c_setsum @ (X31 @ (X32 @ (X1 @ (^[X53 : $i, X54 : $i, X55 : $i] : (c_Inj1 @ c_Empty)) @ (^[X56 : $i] : (X1 @ (^[X57 : $i, X58 : $i, X59 : $i] : (c_Empty)) @ (^[X60 : $i] : (c_Empty)) @ (^[X61 : $i > $i > $i] : (c_Empty)))) @ (^[X62 : $i > $i > $i] : (c_setsum @ c_Empty @ c_Empty))))) @ (X0 @ (^[X63 : $i] : (X31 @ c_Empty)) @ (X32 @ (X33 @ (X0 @ (^[X64 : $i] : (c_Empty)) @ c_Empty) @ (^[X65 : $i, X66 : $i] : (c_Empty))))))) => (! [X69 : $i,X70 : $i] : ((c_Inj0 @ (X3 @ (^[X71 : ($i > $i > $i > $i) > $i, X72 : $i] : (X69)) @ (c_setsum @ c_Empty @ c_Empty))) = (X0 @ (^[X73 : $i] : (c_Inj1 @ (X0 @ (^[X74 : $i] : (c_Inj0 @ (X1 @ (^[X75 : $i, X76 : $i, X77 : $i] : (c_Empty)) @ (^[X78 : $i] : (c_Empty)) @ (^[X79 : $i > $i > $i] : (c_Empty))))) @ (c_Inj1 @ X69)))) @ (c_Inj0 @ (X3 @ (^[X80 : ($i > $i > $i > $i) > $i, X81 : $i] : (X81)) @ X70)))) => (! [X82 : ($i > $i) > ($i > $i) > $i,X83 : $i] : ((X0 @ (^[X86 : $i] : (X82 @ (^[X87 : $i] : (c_setsum @ X87 @ X86)) @ (^[X88 : $i] : (c_Empty)))) @ c_Empty) = (X82 @ (^[X89 : $i] : (c_setsum @ (X3 @ (^[X90 : ($i > $i > $i > $i) > $i, X91 : $i] : (c_Empty)) @ (X2 @ (^[X92 : $i] : (X3 @ (^[X93 : ($i > $i > $i > $i) > $i, X94 : $i] : (c_Empty)) @ c_Empty)) @ (^[X95 : $i] : (X0 @ (^[X96 : $i] : (c_Empty)) @ c_Empty)))) @ (X3 @ (^[X97 : ($i > $i > $i > $i) > $i, X98 : $i] : (c_Empty)) @ (X3 @ (^[X99 : ($i > $i > $i > $i) > $i, X100 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ (X3 @ (^[X101 : ($i > $i > $i > $i) > $i, X102 : $i] : (c_Empty)) @ c_Empty))))) @ (^[X103 : $i] : (c_Inj1 @ (X0 @ (^[X104 : $i] : (X82 @ (^[X105 : $i] : (X0 @ (^[X106 : $i] : (c_Empty)) @ c_Empty)) @ (^[X107 : $i] : (c_Inj1 @ c_Empty)))) @ X83))))) => (! [X108 : $i,X109 : $i] : (X109 = (X1 @ (^[X112 : $i, X113 : $i, X114 : $i] : (X108)) @ (^[X115 : $i] : (X109)) @ (^[X116 : $i > $i > $i] : (c_Empty)))) => (! [X119 : $i,X120 : $i > $i] : ((X1 @ (^[X121 : $i, X122 : $i, X123 : $i] : (X0 @ (^[X124 : $i] : (X3 @ (^[X125 : ($i > $i > $i > $i) > $i, X126 : $i] : (X123)) @ (X3 @ (^[X127 : ($i > $i > $i > $i) > $i, X128 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ X124))) @ (c_Inj1 @ c_Empty))) @ (^[X129 : $i] : (X120 @ c_Empty)) @ (^[X130 : $i > $i > $i] : (c_Empty))) = (X120 @ X119)) => c_False))))))))),
% 9.46/2.78 inference(rectify,[status(thm)],[f110])).
% 9.46/2.78 thf(f110,negated_conjecture,(
% 9.46/2.78 ~! [X1 : ($i > $i) > $i > $i,X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X3 : ($i > $i) > ($i > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (! [X7 : $i,X4 : $i > (($i > $i) > $i) > $i,X6 : (($i > $i > $i) > ($i > $i) > $i) > $i,X5 : ($i > $i) > $i] : ((c_Inj1 @ c_Empty) = (X3 @ (^[X8 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (c_setsum @ c_Empty @ c_Empty)))) => (! [X7 : $i,X5 : $i,X6 : $i,X4 : $i] : ((c_setsum @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (c_Empty)) @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X3 @ (^[X11 : $i] : (X10)) @ (^[X11 : $i] : (c_Empty)))) @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) @ c_Empty) = (X3 @ (^[X8 : $i] : (X6)) @ (^[X8 : $i] : (X7)))) => (! [X4 : $i > $i,X6 : $i > $i,X7 : $i,X5 : $i > $i > $i] : (X7 = (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ c_Empty)) => (! [X7 : $i > $i,X5 : $i > $i,X4 : $i > ($i > $i > $i) > $i,X6 : ((($i > $i) > $i) > $i) > $i] : ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7 @ (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : (c_Inj1 @ c_Empty)) @ (^[X12 : $i] : (c_Inj0 @ c_Empty)) @ (^[X12 : $i > $i > $i] : (X3 @ (^[X13 : $i] : (c_Empty)) @ (^[X13 : $i] : (c_Empty)))))) @ (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))))) @ (X3 @ (^[X8 : $i] : (c_setsum @ X8 @ c_Empty)) @ (^[X8 : $i] : (c_Empty)))) = (c_setsum @ (X7 @ (X5 @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty)) @ (^[X9 : $i] : (c_Empty)) @ (^[X9 : $i > $i > $i] : (c_Empty)))) @ (^[X8 : $i > $i > $i] : (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[X8 : $i] : (X7 @ c_Empty)) @ (X5 @ (X4 @ (X1 @ (^[X8 : $i] : (c_Empty)) @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty))))))) => (! [X4 : (($i > $i) > $i > $i) > $i,X6 : $i,X7 : $i,X5 : $i] : ((c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ (c_setsum @ c_Empty @ c_Empty))) = (X1 @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))) @ (c_Inj1 @ X7)))) @ (c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X9)) @ X5)))) => (! [X7 : ($i > $i) > ($i > $i) > $i,X6 : $i,X5 : $i > $i > ($i > $i) > $i,X4 : (($i > $i) > $i) > $i] : ((X1 @ (^[X8 : $i] : (X7 @ (^[X9 : $i] : (c_setsum @ X9 @ X8)) @ (^[X9 : $i] : (c_Empty)))) @ c_Empty) = (X7 @ (^[X8 : $i] : (c_setsum @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X3 @ (^[X9 : $i] : (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X9 : $i] : (X1 @ (^[X10 : $i] : (c_Empty)) @ c_Empty)))) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ c_Empty))))) @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (X7 @ (^[X10 : $i] : (X1 @ (^[X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X10 : $i] : (c_Inj1 @ c_Empty)))) @ X6))))) => (! [X7 : $i,X6 : $i,X4 : $i > (($i > $i) > $i > $i) > $i,X5 : $i] : (X6 = (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7)) @ (^[X8 : $i] : (X6)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) => (! [X6 : $i > ($i > $i) > $i,X5 : $i,X4 : $i,X7 : $i > $i] : ((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X1 @ (^[X11 : $i] : (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (X10)) @ (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ X11))) @ (c_Inj1 @ c_Empty))) @ (^[X8 : $i] : (X7 @ c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty))) = (X7 @ X4)) => c_False))))))))),
% 9.46/2.78 inference(negated_conjecture,[status(cth)],[f109])).
% 9.46/2.78 thf(f109,conjecture,(
% 9.46/2.78 ! [X1 : ($i > $i) > $i > $i,X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X3 : ($i > $i) > ($i > $i) > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i] : (! [X7 : $i,X4 : $i > (($i > $i) > $i) > $i,X6 : (($i > $i > $i) > ($i > $i) > $i) > $i,X5 : ($i > $i) > $i] : ((c_Inj1 @ c_Empty) = (X3 @ (^[X8 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (c_setsum @ c_Empty @ c_Empty)))) => (! [X7 : $i,X5 : $i,X6 : $i,X4 : $i] : ((c_setsum @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (c_Empty)) @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X3 @ (^[X11 : $i] : (X10)) @ (^[X11 : $i] : (c_Empty)))) @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) @ c_Empty) = (X3 @ (^[X8 : $i] : (X6)) @ (^[X8 : $i] : (X7)))) => (! [X4 : $i > $i,X6 : $i > $i,X7 : $i,X5 : $i > $i > $i] : (X7 = (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ c_Empty)) => (! [X7 : $i > $i,X5 : $i > $i,X4 : $i > ($i > $i > $i) > $i,X6 : ((($i > $i) > $i) > $i) > $i] : ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7 @ (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : (c_Inj1 @ c_Empty)) @ (^[X12 : $i] : (c_Inj0 @ c_Empty)) @ (^[X12 : $i > $i > $i] : (X3 @ (^[X13 : $i] : (c_Empty)) @ (^[X13 : $i] : (c_Empty)))))) @ (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))))) @ (X3 @ (^[X8 : $i] : (c_setsum @ X8 @ c_Empty)) @ (^[X8 : $i] : (c_Empty)))) = (c_setsum @ (X7 @ (X5 @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (c_Inj1 @ c_Empty)) @ (^[X8 : $i] : (X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty)) @ (^[X9 : $i] : (c_Empty)) @ (^[X9 : $i > $i > $i] : (c_Empty)))) @ (^[X8 : $i > $i > $i] : (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[X8 : $i] : (X7 @ c_Empty)) @ (X5 @ (X4 @ (X1 @ (^[X8 : $i] : (c_Empty)) @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty))))))) => (! [X4 : (($i > $i) > $i > $i) > $i,X6 : $i,X7 : $i,X5 : $i] : ((c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7)) @ (c_setsum @ c_Empty @ c_Empty))) = (X1 @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : $i > $i > $i] : (c_Empty))))) @ (c_Inj1 @ X7)))) @ (c_Inj0 @ (X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X9)) @ X5)))) => (! [X7 : ($i > $i) > ($i > $i) > $i,X6 : $i,X5 : $i > $i > ($i > $i) > $i,X4 : (($i > $i) > $i) > $i] : ((X1 @ (^[X8 : $i] : (X7 @ (^[X9 : $i] : (c_setsum @ X9 @ X8)) @ (^[X9 : $i] : (c_Empty)))) @ c_Empty) = (X7 @ (^[X8 : $i] : (c_setsum @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X3 @ (^[X9 : $i] : (X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X9 : $i] : (X1 @ (^[X10 : $i] : (c_Empty)) @ c_Empty)))) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ (X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty)) @ c_Empty))))) @ (^[X8 : $i] : (c_Inj1 @ (X1 @ (^[X9 : $i] : (X7 @ (^[X10 : $i] : (X1 @ (^[X11 : $i] : (c_Empty)) @ c_Empty)) @ (^[X10 : $i] : (c_Inj1 @ c_Empty)))) @ X6))))) => (! [X7 : $i,X6 : $i,X4 : $i > (($i > $i) > $i > $i) > $i,X5 : $i] : (X6 = (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7)) @ (^[X8 : $i] : (X6)) @ (^[X8 : $i > $i > $i] : (c_Empty)))) => (! [X6 : $i > ($i > $i) > $i,X5 : $i,X4 : $i,X7 : $i > $i] : ((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X1 @ (^[X11 : $i] : (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (X10)) @ (X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (c_setsum @ c_Empty @ c_Empty)) @ X11))) @ (c_Inj1 @ c_Empty))) @ (^[X8 : $i] : (X7 @ c_Empty)) @ (^[X8 : $i > $i > $i] : (c_Empty))) = (X7 @ X4)) => c_False))))))))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',conj)).
% 9.46/2.78 thf(f660,plain,(
% 9.46/2.78 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2))) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f493,f493])).
% 9.46/2.78 thf(f493,plain,(
% 9.46/2.78 ( ! [X4 : $i,X5 : $i > $i] : (((sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y12 : $i]: ((^[Y13 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => (!! @ $o @ (^[Y22 : $o]: (Y22)))) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => (!! @ $o @ (^[Y18 : $o]: (Y18)))) => (((c_Repl @ Y12 @ Y13) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))))))) @ Y11)))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty)))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = (X5 @ X4))) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f462])).
% 9.46/2.78 thf(f462,plain,(
% 9.46/2.78 ( ! [X4 : $i,X5 : $i > $i] : (((X5 @ X4) = (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ (c_Repl @ Y6 @ (^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: ((^[Y11 : $i > ($i > $i) > $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (c_In_rec_poly_G_i @ Y11 @ Y12 @ Y13)))))) @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Union @ ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $i]: ((^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => Y24) => ((Y23 => Y24) => Y24))))))) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ Y18 @ (Y19 = Y21)) @ ((^[Y22 : $o]: ((^[Y23 : $o]: (!! @ $o @ (^[Y24 : $o]: ((Y22 => (Y23 => Y24)) => Y24)))))) @ ((^[Y22 : $o]: (Y22 => (!! @ $o @ (^[Y23 : $o]: (Y23))))) @ Y18) @ (Y20 = Y21)))))))))) @ (c_In @ c_Empty @ Y17) @ Y15 @ Y16)))))) @ Y13 @ Y14))))) @ ((^[Y13 : $i]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $i]: ((^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => Y23) => ((Y22 => Y23) => Y23))))))) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ Y17 @ (Y18 = Y20)) @ ((^[Y21 : $o]: ((^[Y22 : $o]: (!! @ $o @ (^[Y23 : $o]: ((Y21 => (Y22 => Y23)) => Y23)))))) @ ((^[Y21 : $o]: (Y21 => (!! @ $o @ (^[Y22 : $o]: (Y22))))) @ Y17) @ (Y19 = Y20)))))))))) @ (c_In @ c_Empty @ Y16) @ Y14 @ Y15)))))) @ Y13 @ Y13)) @ c_Empty) @ (c_Repl @ Y11 @ (^[Y13 : $i]: (Y12 @ Y13))))))) @ Y10)))) @ Y8))) @ (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i > ($i > $i) > $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (c_In_rec_poly_G_i @ Y9 @ Y10 @ Y11)))))) @ (^[Y9 : $i]: ((^[Y10 : $i > $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Union @ ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $i]: ((^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: ((^[Y20 : $o]: ((^[Y21 : $o]: (!! 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% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f388,f437,f433])).
% 9.46/2.78 thf(f433,plain,(
% 9.46/2.78 (c_Inj1 = ((^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => (!! @ $o @ (^[Y12 : $o]: (Y12))))) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => (!! @ $o @ (^[Y11 : $o]: (Y11))))) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y2 @ Y2)) @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f358,f324,f423,f422])).
% 9.46/2.78 thf(f422,plain,(
% 9.46/2.78 (c_Sing = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => (!! @ $o @ (^[Y9 : $o]: (Y9))))) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f321,f421])).
% 9.46/2.78 thf(f421,plain,(
% 9.46/2.78 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => Y9) => ((Y8 => Y9) => Y9))))))) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ Y3 @ (Y4 = Y6)) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => (!! @ $o @ (^[Y8 : $o]: (Y8))))) @ Y3) @ (Y5 = Y6)))))))))) @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f332,f419])).
% 9.46/2.78 thf(f419,plain,(
% 9.46/2.78 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => Y6) => ((Y5 => Y6) => Y6))))))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ Y0 @ (Y1 = Y3)) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $o]: (Y4 => (!! @ $o @ (^[Y5 : $o]: (Y5))))) @ Y0) @ (Y2 = Y3)))))))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f389,f354,f350,f350,f407])).
% 9.46/2.78 thf(f350,plain,(
% 9.46/2.78 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f146])).
% 9.46/2.78 thf(f146,plain,(
% 9.46/2.78 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f145])).
% 9.46/2.78 thf(f145,plain,(
% 9.46/2.78 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 9.46/2.78 inference(rectify,[status(thm)],[f14])).
% 9.46/2.78 thf(f14,axiom,(
% 9.46/2.78 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax14)).
% 9.46/2.78 thf(f354,plain,(
% 9.46/2.78 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f273])).
% 9.46/2.78 thf(f273,plain,(
% 9.46/2.78 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f272])).
% 9.46/2.78 thf(f272,plain,(
% 9.46/2.78 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))) = c_or)),
% 9.46/2.78 inference(rectify,[status(thm)],[f15])).
% 9.46/2.78 thf(f15,axiom,(
% 9.46/2.78 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))) = c_or)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax15)).
% 9.46/2.78 thf(f389,plain,(
% 9.46/2.78 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f200])).
% 9.46/2.78 thf(f200,plain,(
% 9.46/2.78 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f42])).
% 9.46/2.78 thf(f42,axiom,(
% 9.46/2.78 ((^[X0 : $o, X1 : $i, X2 : $i] : (c_Eps_i @ (^[X3 : $i] : (c_or @ (c_and @ X0 @ (X1 = X3)) @ (c_and @ (c_not @ X0) @ (X2 = X3)))))) = c_If_i)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax42)).
% 9.46/2.78 thf(f332,plain,(
% 9.46/2.78 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f216])).
% 9.46/2.78 thf(f216,plain,(
% 9.46/2.78 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f47])).
% 9.46/2.78 thf(f47,axiom,(
% 9.46/2.78 ((^[X0 : $i, X1 : $i] : (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : (c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))) = c_UPair)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax47)).
% 9.46/2.78 thf(f321,plain,(
% 9.46/2.78 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f144])).
% 9.46/2.78 thf(f144,plain,(
% 9.46/2.78 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f48])).
% 9.46/2.78 thf(f48,axiom,(
% 9.46/2.78 ((^[X0 : $i] : (c_UPair @ X0 @ X0)) = c_Sing)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax48)).
% 9.46/2.78 thf(f423,plain,(
% 9.46/2.78 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => (!! @ $o @ (^[Y10 : $o]: (Y10))))) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y0 @ Y1))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f347,f421])).
% 9.46/2.78 thf(f347,plain,(
% 9.46/2.78 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f282])).
% 9.46/2.78 thf(f282,plain,(
% 9.46/2.78 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f49])).
% 9.46/2.78 thf(f49,axiom,(
% 9.46/2.78 (c_binunion = (^[X0 : $i, X1 : $i] : (c_Union @ (c_UPair @ X0 @ X1))))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax49)).
% 9.46/2.78 thf(f324,plain,(
% 9.46/2.78 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f256])).
% 9.46/2.78 thf(f256,plain,(
% 9.46/2.78 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f61])).
% 9.46/2.78 thf(f61,axiom,(
% 9.46/2.78 (c_In_rec_poly_i = (^[X0 : $i > ($i > $i) > $i, X1 : $i] : (c_Eps_i @ (^[X2 : $i] : (c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax61)).
% 9.46/2.78 thf(f358,plain,(
% 9.46/2.78 (c_Inj1 = (c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f217])).
% 9.46/2.78 thf(f217,plain,(
% 9.46/2.78 (c_Inj1 = (c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f69])).
% 9.46/2.78 thf(f69,axiom,(
% 9.46/2.78 ((c_In_rec_poly_i @ (^[X0 : $i, X1 : $i > $i] : (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : (X1 @ X2)))))) = c_Inj1)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax69)).
% 9.46/2.78 thf(f437,plain,(
% 9.46/2.78 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => (!! @ $o @ (^[Y12 : $o]: (Y12))))) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (c_In_rec_poly_G_i @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => (!! @ $o @ (^[Y17 : $o]: (Y17))))) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4)))) @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_In_rec_poly_G_i @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => (!! @ $o @ (^[Y14 : $o]: (Y14))))) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y2))))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f366,f423,f434,f433])).
% 9.46/2.78 thf(f434,plain,(
% 9.46/2.78 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > ($i > $i) > $i]: ((^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (c_In_rec_poly_G_i @ Y2 @ Y3 @ Y4)))))) @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => (!! @ $o @ (^[Y14 : $o]: (Y14))))) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => (!! @ $o @ (^[Y13 : $o]: (Y13))))) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y4 @ Y4)) @ c_Empty) @ (c_Repl @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1)))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f328,f433])).
% 9.46/2.78 thf(f328,plain,(
% 9.46/2.78 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f253])).
% 9.46/2.78 thf(f253,plain,(
% 9.46/2.78 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f70])).
% 9.46/2.78 thf(f70,axiom,(
% 9.46/2.78 ((^[X0 : $i] : (c_Repl @ X0 @ (^[X1 : $i] : (c_Inj1 @ X1)))) = c_Inj0)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax70)).
% 9.46/2.78 thf(f366,plain,(
% 9.46/2.78 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f285])).
% 9.46/2.78 thf(f285,plain,(
% 9.46/2.78 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f284])).
% 9.46/2.78 thf(f284,plain,(
% 9.46/2.78 (c_setsum = (^[X0 : $i, X1 : $i] : (c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : (c_Inj0 @ X2))) @ (c_Repl @ X1 @ (^[X3 : $i] : (c_Inj1 @ X3))))))),
% 9.46/2.78 inference(rectify,[status(thm)],[f73])).
% 9.46/2.78 thf(f73,axiom,(
% 9.46/2.78 (c_setsum = (^[X0 : $i, X1 : $i] : (c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : (c_Inj0 @ X2))) @ (c_Repl @ X1 @ (^[X2 : $i] : (c_Inj1 @ X2))))))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax73)).
% 9.46/2.78 thf(f388,plain,(
% 9.46/2.78 ( ! [X4 : $i,X5 : $i > $i] : (((X5 @ X4) = (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) )),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f320])).
% 9.46/2.78 thf(f1149,plain,(
% 9.46/2.78 ( ! [X0 : $i > $i] : (((X0 @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ c_Empty @ Y4) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))) = Y5) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ c_Empty @ Y4) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => (((c_Repl @ Y2 @ Y3) = Y5) => Y7)) => Y7))) => Y6) => Y6)))))))))))) @ Y1))))) @ (^[Y0 : $i > $i > $i]: (sK11 @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i]: (c_Empty)))))) = (c_Union @ c_Empty))) )),
% 9.46/2.78 inference(forward_demodulation,[status(thm)],[f778,f661])).
% 9.46/2.78 thf(f661,plain,(
% 9.46/2.78 ( ! [X0 : $i] : (((sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y12 : $i]: ((^[Y13 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => (!! @ $o @ (^[Y22 : $o]: (Y22)))) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => (!! @ $o @ (^[Y18 : $o]: (Y18)))) => (((c_Repl @ Y12 @ Y13) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))))))) @ Y11)))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty)))))))) @ (^[Y0 : $i]: (X0)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) = X0)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f493,f384])).
% 9.46/2.78 thf(f778,plain,(
% 9.46/2.78 ( ! [X0 : $i > $i] : (((X0 @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ c_Empty @ Y4) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))) = Y5) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ c_Empty @ Y4) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => (((c_Repl @ Y2 @ Y3) = Y5) => Y7)) => Y7))) => Y6) => Y6)))))))))))) @ Y1))))) @ (^[Y0 : $i > $i > $i]: (sK11 @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i]: (c_Empty)))))) = (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK9 @ (^[Y3 : $i]: (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK12 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y12 : $i]: ((^[Y13 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: (!! @ $o @ (^[Y16 : $o]: (((!! @ $o @ (^[Y17 : $o]: (((c_In @ c_Empty @ Y14) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y18 : $i]: (c_Eps_i @ (^[Y19 : $i]: (!! @ $o @ (^[Y20 : $o]: (((!! @ $o @ (^[Y21 : $o]: (((c_In @ c_Empty @ Y18) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => (((!! @ $o @ (^[Y21 : $o]: ((((c_In @ c_Empty @ Y18) => (!! @ $o @ (^[Y22 : $o]: (Y22)))) => ((c_Empty = Y19) => Y21)) => Y21))) => Y20) => Y20)))))))) = Y15) => Y17)) => Y17))) => Y16) => (((!! @ $o @ (^[Y17 : $o]: ((((c_In @ c_Empty @ Y14) => (!! @ $o @ (^[Y18 : $o]: (Y18)))) => (((c_Repl @ Y12 @ Y13) = Y15) => Y17)) => Y17))) => Y16) => Y16)))))))))))) @ Y11)))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty)))))))) @ (^[Y0 : $i]: (c_Union @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f770,f493])).
% 9.46/2.78 thf(f770,plain,(
% 9.46/2.78 ( ! [X8 : $i > ($i > $i > $i) > $i,X6 : $i > $i,X7 : $i > $i] : (((c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y0 : $i]: (c_Eps_i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $o @ (^[Y3 : $o]: (((c_In @ c_Empty @ Y0) => (((c_Repl @ (X6 @ (X7 @ (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (sK10 @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Empty)))))) @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i > $i > $i]: (c_Empty)))) @ (^[Y4 : $i > $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y10 : $i]: ((^[Y11 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => (!! @ $o @ (^[Y20 : $o]: (Y20)))) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => (((c_Repl @ Y10 @ Y11) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))))))) @ Y9)))) = Y6) => Y8)) => Y8))) => Y7) => Y7))))))))))))) @ (^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))))) = Y1) => Y3)) => Y3))) => Y2) => (((!! @ $o @ (^[Y3 : $o]: ((((c_In @ c_Empty @ Y0) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => (((c_Repl @ (sK9 @ (^[Y4 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (sK9 @ (^[Y4 : $i]: (c_Empty)) @ c_Empty) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Empty))))))) @ (^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ Y4)))) = Y1) => Y3)) => Y3))) => Y2) => Y2))))))))) = (X6 @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (c_Repl @ c_Empty @ (^[Y1 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((c_In @ c_Empty @ Y4) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => ((c_Empty = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))) = Y5) => Y7)) => Y7))) => Y6) => (((!! @ $o @ (^[Y7 : $o]: ((((c_In @ c_Empty @ Y4) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => (((c_Repl @ Y2 @ Y3) = Y5) => Y7)) => Y7))) => Y6) => Y6)))))))))))) @ Y1))))) @ (^[Y0 : $i > $i > $i]: (sK11 @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i]: (c_Empty)))))))) )),
% 9.46/2.78 inference(forward_demodulation,[status(thm)],[f769,f665])).
% 9.46/2.78 thf(f769,plain,(
% 9.46/2.78 ( ! [X8 : $i > ($i > $i > $i) > $i,X6 : $i > $i,X7 : $i > $i] : (((c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y0 : $i]: (c_Eps_i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $o @ (^[Y3 : $o]: (((c_In @ c_Empty @ Y0) => (((c_Repl @ (X6 @ (X7 @ (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (sK10 @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Empty)))))) @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i > $i > $i]: (c_Empty)))) @ (^[Y4 : $i > $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y10 : $i]: ((^[Y11 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => (!! @ $o @ (^[Y20 : $o]: (Y20)))) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => (((c_Repl @ Y10 @ Y11) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))))))) @ Y9)))) = Y6) => Y8)) => Y8))) => Y7) => Y7))))))))))))) @ (^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))))) = Y1) => Y3)) => Y3))) => Y2) => (((!! @ $o @ (^[Y3 : $o]: ((((c_In @ c_Empty @ Y0) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => (((c_Repl @ (sK9 @ (^[Y4 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (sK9 @ (^[Y4 : $i]: (c_Empty)) @ c_Empty) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Empty))))))) @ (^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ Y4)))) = Y1) => Y3)) => Y3))) => Y2) => Y2))))))))) = (X6 @ (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ c_Empty))))))) @ (^[Y2 : $i]: (c_Repl @ c_Empty @ (^[Y3 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y4 : $i]: ((^[Y5 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ $o @ (^[Y12 : $o]: (((!! @ $o @ (^[Y13 : $o]: (((c_In @ c_Empty @ Y10) => ((c_Empty = Y11) => Y13)) => Y13))) => Y12) => (((!! @ $o @ (^[Y13 : $o]: ((((c_In @ c_Empty @ Y10) => (!! @ $o @ (^[Y14 : $o]: (Y14)))) => ((c_Empty = Y11) => Y13)) => Y13))) => Y12) => Y12)))))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => (((c_Repl @ Y4 @ Y5) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))))) @ (^[Y2 : $i > $i > $i]: (sK11 @ (^[Y3 : $i]: (c_Empty)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (c_Repl @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Empty)))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))) @ (^[Y0 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y1 : $i]: ((^[Y2 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((c_In @ c_Empty @ Y3) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => ((c_Empty = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => ((c_Empty = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))) = Y4) => Y6)) => Y6))) => Y5) => (((!! @ $o @ (^[Y6 : $o]: ((((c_In @ c_Empty @ Y3) => (!! @ $o @ (^[Y7 : $o]: (Y7)))) => (((c_Repl @ Y1 @ Y2) = Y4) => Y6)) => Y6))) => Y5) => Y5)))))))))))) @ Y0)))))))) )),
% 9.46/2.78 inference(forward_demodulation,[status(thm)],[f596,f665])).
% 9.46/2.78 thf(f596,plain,(
% 9.46/2.78 ( ! [X8 : $i > ($i > $i > $i) > $i,X6 : $i > $i,X7 : $i > $i] : (((c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y0 : $i]: (c_Eps_i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $o @ (^[Y3 : $o]: (((c_In @ c_Empty @ Y0) => (((c_Repl @ (X6 @ (X7 @ (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (sK10 @ (^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Empty)))))) @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i > $i > $i]: (c_Empty)))) @ (^[Y4 : $i > $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y11 : $i]: ((^[Y12 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: (!! @ $o @ (^[Y19 : $o]: (((!! @ $o @ (^[Y20 : $o]: (((c_In @ c_Empty @ Y17) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => (((!! @ $o @ (^[Y20 : $o]: ((((c_In @ c_Empty @ Y17) => (!! @ $o @ (^[Y21 : $o]: (Y21)))) => ((c_Empty = Y18) => Y20)) => Y20))) => Y19) => Y19)))))))) = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => (((c_Repl @ Y11 @ Y12) = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))))))) @ Y10)))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ c_Empty @ (^[Y9 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y10 : $i]: ((^[Y11 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => (!! @ $o @ (^[Y20 : $o]: (Y20)))) => ((c_Empty = Y17) => Y19)) => Y19))) => Y18) => Y18)))))))) = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => (((c_Repl @ Y10 @ Y11) = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))))))) @ Y9)))) = Y6) => Y8)) => Y8))) => Y7) => Y7))))))))))))) @ (^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))))) = Y1) => Y3)) => Y3))) => Y2) => (((!! @ $o @ (^[Y3 : $o]: ((((c_In @ c_Empty @ Y0) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => (((c_Repl @ (sK9 @ (^[Y4 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (sK9 @ (^[Y4 : $i]: (c_Empty)) @ c_Empty) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Empty))))))) @ (^[Y4 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => (!! @ $o @ (^[Y15 : $o]: (Y15)))) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => (!! @ $o @ (^[Y11 : $o]: (Y11)))) => (((c_Repl @ Y5 @ Y6) = Y8) => Y10)) => Y10))) => Y9) => Y9)))))))))))) @ Y4)))) = Y1) => Y3)) => Y3))) => Y2) => Y2))))))))) = (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6 @ (sK12 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ c_Empty))))))) @ (^[Y4 : $i]: (c_Repl @ c_Empty @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5))))) @ (^[Y4 : $i > $i > $i]: (sK11 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Repl @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))) @ (^[Y2 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $o @ (^[Y8 : $o]: (((c_In @ c_Empty @ Y5) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => ((c_Empty = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))) = Y6) => Y8)) => Y8))) => Y7) => (((!! @ $o @ (^[Y8 : $o]: ((((c_In @ c_Empty @ Y5) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => (((c_Repl @ Y3 @ Y4) = Y6) => Y8)) => Y8))) => Y7) => Y7)))))))))))) @ Y2))))))))) @ (sK11 @ (^[Y0 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((c_In @ c_Empty @ Y1) => (((c_Repl @ Y0 @ (^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((!! @ $o @ (^[Y12 : $o]: (((c_In @ c_Empty @ Y9) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: (!! @ $o @ (^[Y15 : $o]: (((!! @ $o @ (^[Y16 : $o]: (((c_In @ c_Empty @ Y13) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => (((!! @ $o @ (^[Y16 : $o]: ((((c_In @ c_Empty @ Y13) => (!! @ $o @ (^[Y17 : $o]: (Y17)))) => ((c_Empty = Y14) => Y16)) => Y16))) => Y15) => Y15)))))))) = Y10) => Y12)) => Y12))) => Y11) => (((!! @ $o @ (^[Y12 : $o]: ((((c_In @ c_Empty @ Y9) => (!! @ $o @ (^[Y13 : $o]: (Y13)))) => (((c_Repl @ Y7 @ Y8) = Y10) => Y12)) => Y12))) => Y11) => Y11)))))))))))) @ Y6)))))) = Y2) => Y4)) => Y4))) => Y3) => (((!! @ $o @ (^[Y4 : $o]: ((((c_In @ c_Empty @ Y1) => (!! @ $o @ (^[Y5 : $o]: (Y5)))) => (((c_Repl @ c_Empty @ (^[Y5 : $i]: (c_Eps_i @ (c_In_rec_poly_G_i @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((!! @ $o @ (^[Y11 : $o]: (((c_In @ c_Empty @ Y8) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: (!! @ $o @ (^[Y14 : $o]: (((!! @ $o @ (^[Y15 : $o]: (((c_In @ c_Empty @ Y12) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => (((!! @ $o @ (^[Y15 : $o]: ((((c_In @ c_Empty @ Y12) => (!! @ $o @ (^[Y16 : $o]: (Y16)))) => ((c_Empty = Y13) => Y15)) => Y15))) => Y14) => Y14)))))))) = Y9) => Y11)) => Y11))) => Y10) => (((!! @ $o @ (^[Y11 : $o]: ((((c_In @ c_Empty @ Y8) => (!! @ $o @ (^[Y12 : $o]: (Y12)))) => (((c_Repl @ Y6 @ Y7) = Y9) => Y11)) => Y11))) => Y10) => Y10)))))))))))) @ Y5)))) = Y2) => Y4)) => Y4))) => Y3) => Y3)))))))))) @ (^[Y0 : $i]: (c_Empty)))))) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f463])).
% 9.46/2.78 thf(f463,plain,(
% 9.46/2.78 ( ! 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@ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ c_Empty)))))) @ (^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ Y5 @ (^[Y6 : $i]: ((^[Y7 : $i > ($i > $i) > $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (c_In_rec_poly_G_i @ Y7 @ Y8 @ Y9)))))) @ (^[Y7 : $i]: ((^[Y8 : $i > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Union @ ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $i]: ((^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => Y20) => ((Y19 => Y20) => Y20))))))) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ Y14 @ (Y15 = Y17)) @ ((^[Y18 : $o]: ((^[Y19 : $o]: (!! @ $o @ (^[Y20 : $o]: ((Y18 => (Y19 => Y20)) => Y20)))))) @ ((^[Y18 : $o]: (Y18 => (!! @ $o @ (^[Y19 : $o]: (Y19))))) @ Y14) @ (Y16 = Y17)))))))))) @ (c_In @ c_Empty @ Y13) @ Y11 @ Y12)))))) @ Y9 @ Y10))))) @ ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y9 @ Y9)) @ c_Empty) @ (c_Repl @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y6)))) @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK11 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ ((^[Y2 : $i]: (c_Repl @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i > ($i > $i) > $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_In_rec_poly_G_i @ Y4 @ Y5 @ Y6)))))) @ (^[Y4 : $i]: ((^[Y5 : $i > $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Union @ ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y6 @ Y7))))) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y6 @ Y6)) @ c_Empty) @ (c_Repl @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y3)))) @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK11 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Union @ ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => (!! @ $o @ (^[Y13 : $o]: (Y13))))) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y3 @ Y4))))) @ (c_Repl @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ Y4 @ (^[Y5 : $i]: ((^[Y6 : $i > ($i > $i) > $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (c_In_rec_poly_G_i @ Y6 @ Y7 @ Y8)))))) @ (^[Y6 : $i]: ((^[Y7 : $i > $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => (!! @ $o @ (^[Y17 : $o]: (Y17))))) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y8 @ Y8)) @ c_Empty) @ (c_Repl @ Y6 @ (^[Y8 : $i]: (Y7 @ Y8))))))) @ Y5)))) @ Y3))) @ (c_Repl @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i > ($i > $i) > $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_In_rec_poly_G_i @ Y4 @ Y5 @ Y6)))))) @ (^[Y4 : $i]: ((^[Y5 : $i > $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Union @ ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y6 @ Y7))))) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => (!! @ $o @ (^[Y15 : $o]: (Y15))))) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y6 @ Y6)) @ c_Empty) @ (c_Repl @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y3))))))) @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))) = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! 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@ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => (!! @ $o @ (^[Y17 : $o]: (Y17))))) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => (!! @ $o @ (^[Y16 : $o]: (Y16))))) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4)))) @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_In_rec_poly_G_i @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! 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@ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => (!! @ $o @ (^[Y18 : $o]: (Y18))))) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => (!! @ $o @ (^[Y17 : $o]: (Y17))))) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y8 @ Y8)) @ c_Empty) @ (c_Repl @ Y6 @ (^[Y8 : $i]: (Y7 @ Y8))))))) @ Y5)))) @ Y3))) @ (c_Repl @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i > ($i > $i) > $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_In_rec_poly_G_i @ Y4 @ Y5 @ Y6)))))) @ (^[Y4 : $i]: ((^[Y5 : $i > $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Union @ ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! 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% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f387,f437,f433,f437,f433,f434,f434,f437])).
% 9.46/2.78 thf(f387,plain,(
% 9.46/2.78 ( ! [X8 : $i > ($i > $i > $i) > $i,X6 : $i > $i,X7 : $i > $i] : (((c_setsum @ (X6 @ (X7 @ (sK10 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK10 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK9 @ (^[Y0 : $i]: (X6 @ c_Empty)) @ (X7 @ (X8 @ (sK9 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))) = (sK12 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6 @ (sK12 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK10 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK11 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK10 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK11 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty)))))) )),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f320])).
% 9.46/2.78 thf(f1547,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ (sK14 @ X1 @ X0) @ X0) = $true) | ($true = X2)) )),
% 9.46/2.78 inference(subsumption_resolution,[status(thm)],[f491,f1420])).
% 9.46/2.78 thf(f1420,plain,(
% 9.46/2.78 ( ! [X2 : $i > $o,X3 : $i,X0 : $i,X1 : $i] : (((c_In @ X1 @ X0) != $true) | ((X2 @ X3) = $true)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f1390,f1220])).
% 9.46/2.78 thf(f1390,plain,(
% 9.46/2.78 ( ! [X2 : $i,X3 : $i,X0 : $i > $o] : (($true != (c_In @ X2 @ (c_Union @ c_Empty))) | ((X0 @ X3) = $true)) )),
% 9.46/2.78 inference(subsumption_resolution,[status(thm)],[f1277,f1373])).
% 9.46/2.78 thf(f1373,plain,(
% 9.46/2.78 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (((X1 @ X0) != $true) | ((X1 @ X2) = $true)) )),
% 9.46/2.78 inference(superposition,[status(thm)],[f1280,f1220])).
% 9.46/2.78 thf(f1280,plain,(
% 9.46/2.78 ( ! [X3 : $i,X0 : $i > $o] : (($true != (X0 @ (c_Union @ c_Empty))) | ((X0 @ X3) = $true)) )),
% 9.46/2.78 inference(backward_demodulation,[status(thm)],[f360,f1220])).
% 9.46/2.78 thf(f360,plain,(
% 9.46/2.78 ( ! [X3 : $i,X0 : $i > $o] : (($true != (X0 @ (sK2 @ X0))) | ((X0 @ X3) = $true)) )),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f304])).
% 9.46/2.78 thf(f304,plain,(
% 9.46/2.78 ! [X0 : $i > $o] : ((($true != (X0 @ (sK2 @ X0))) & ! [X2 : $i] : (($true != (c_In @ X2 @ (sK2 @ X0))) | ((X0 @ X2) = $true))) | ! [X3 : $i] : ((X0 @ X3) = $true))),
% 9.46/2.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f297,f303])).
% 9.46/2.78 thf(f303,plain,(
% 9.46/2.78 ! [X0 : $i > $o] : (? [X1 : $i] : (((X0 @ X1) != $true) & ! [X2 : $i] : (((c_In @ X2 @ X1) != $true) | ((X0 @ X2) = $true))) => (($true != (X0 @ (sK2 @ X0))) & ! [X2 : $i] : (($true != (c_In @ X2 @ (sK2 @ X0))) | ((X0 @ X2) = $true))))),
% 9.46/2.78 introduced(definition,[],[choice_axiom])).
% 9.46/2.78 thf(f297,plain,(
% 9.46/2.78 ! [X0 : $i > $o] : (? [X1 : $i] : (((X0 @ X1) != $true) & ! [X2 : $i] : (((c_In @ X2 @ X1) != $true) | ((X0 @ X2) = $true))) | ! [X3 : $i] : ((X0 @ X3) = $true))),
% 9.46/2.78 inference(ennf_transformation,[status(thm)],[f169])).
% 9.46/2.78 thf(f169,plain,(
% 9.46/2.78 ! [X0 : $i > $o] : (! [X1 : $i] : (! [X2 : $i] : (((c_In @ X2 @ X1) = $true) => ((X0 @ X2) = $true)) => ((X0 @ X1) = $true)) => ! [X3 : $i] : ((X0 @ X3) = $true))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f168])).
% 9.46/2.78 thf(f168,plain,(
% 9.46/2.78 ! [X0 : $i > $o] : (! [X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X3 : $i] : (X0 @ X3))),
% 9.46/2.78 inference(rectify,[status(thm)],[f10])).
% 9.46/2.78 thf(f10,axiom,(
% 9.46/2.78 ! [X0 : $i > $o] : (! [X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X1 : $i] : (X0 @ X1))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax10)).
% 9.46/2.78 thf(f1277,plain,(
% 9.46/2.78 ( ! [X2 : $i,X3 : $i,X0 : $i > $o] : (((X0 @ X2) = $true) | ($true != (c_In @ X2 @ (c_Union @ c_Empty))) | ((X0 @ X3) = $true)) )),
% 9.46/2.78 inference(backward_demodulation,[status(thm)],[f359,f1220])).
% 9.46/2.78 thf(f359,plain,(
% 9.46/2.78 ( ! [X2 : $i,X3 : $i,X0 : $i > $o] : (($true != (c_In @ X2 @ (sK2 @ X0))) | ((X0 @ X2) = $true) | ((X0 @ X3) = $true)) )),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f304])).
% 9.46/2.78 thf(f491,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((c_In @ X0 @ (c_Power @ X1)) = $true) | ((c_In @ (sK14 @ X1 @ X0) @ X0) = $true)) )),
% 9.46/2.78 inference(binary_proxy_clausification,[status(thm)],[f489])).
% 9.46/2.78 thf(f489,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((c_In @ (sK14 @ X1 @ X0) @ X0) => (c_In @ (sK14 @ X1 @ X0) @ X1)) = $false) | ($true = X2) | ((c_In @ X0 @ (c_Power @ X1)) = $true)) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f488])).
% 9.46/2.78 thf(f488,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X0 @ (c_Power @ X1)) = $true) | ($true = X2) | ($false = ((^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))) @ (sK14 @ X1 @ X0)))) )),
% 9.46/2.78 inference(sigma_clausification,[status(thm)],[f487])).
% 9.46/2.78 thf(f487,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X0 @ (c_Power @ X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) = $false) | ($true = X2)) )),
% 9.46/2.78 inference(binary_proxy_clausification,[status(thm)],[f486])).
% 9.46/2.78 thf(f486,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))))) )),
% 9.46/2.78 inference(binary_proxy_clausification,[status(thm)],[f479])).
% 9.46/2.78 thf(f479,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2))) )),
% 9.46/2.78 inference(binary_proxy_clausification,[status(thm)],[f478])).
% 9.46/2.78 thf(f478,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) = $false)) )),
% 9.46/2.78 inference(binary_proxy_clausification,[status(thm)],[f477])).
% 9.46/2.78 thf(f477,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) => X2) = $true)) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f476])).
% 9.46/2.78 thf(f476,plain,(
% 9.46/2.78 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((^[Y0 : $o]: ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => Y0)) => Y0)) @ X2))) )),
% 9.46/2.78 inference(pi_clausification,[status(thm)],[f475])).
% 9.46/2.78 thf(f475,plain,(
% 9.46/2.78 ( ! [X0 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => Y0)) => Y0))))) )),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f461])).
% 9.46/2.78 thf(f461,plain,(
% 9.46/2.78 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))) @ (c_In @ X0 @ (c_Power @ X1)) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))) @ X0 @ X1)))) )),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f378,f408,f345])).
% 9.46/2.78 thf(f345,plain,(
% 9.46/2.78 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f152])).
% 9.46/2.78 thf(f152,plain,(
% 9.46/2.78 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f151])).
% 9.46/2.78 thf(f151,plain,(
% 9.46/2.78 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)),
% 9.46/2.78 inference(rectify,[status(thm)],[f17])).
% 9.46/2.78 thf(f17,axiom,(
% 9.46/2.78 ((^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))) = c_Subq)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax17)).
% 9.46/2.78 thf(f408,plain,(
% 9.46/2.78 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f400,f350])).
% 9.46/2.78 thf(f400,plain,(
% 9.46/2.78 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f235])).
% 9.46/2.78 thf(f235,plain,(
% 9.46/2.78 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f234])).
% 9.46/2.78 thf(f234,plain,(
% 9.46/2.78 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)),
% 9.46/2.78 inference(rectify,[status(thm)],[f16])).
% 9.46/2.78 thf(f16,axiom,(
% 9.46/2.78 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax16)).
% 9.46/2.78 thf(f378,plain,(
% 9.46/2.78 ( ! [X0 : $i,X1 : $i] : (((c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1)) = $true)) )),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f215])).
% 9.46/2.78 thf(f215,plain,(
% 9.46/2.78 ! [X0 : $i,X1 : $i] : ((c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1)) = $true)),
% 9.46/2.78 inference(fool_elimination,[status(thm)],[f214])).
% 9.46/2.78 thf(f214,plain,(
% 9.46/2.78 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1))),
% 9.46/2.78 inference(rectify,[status(thm)],[f7])).
% 9.46/2.78 thf(f7,axiom,(
% 9.46/2.78 ! [X1 : $i,X0 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 9.46/2.78 file('/export/starexec/sandbox/tmp/tmp.ykmh1kGb91/DTF2THF_351.p',ax7)).
% 9.46/2.78 thf(f472,plain,(
% 9.46/2.78 (sK13 = $false)),
% 9.46/2.78 inference(beta_eta_normalization,[status(thm)],[f471])).
% 9.46/2.78 thf(f471,plain,(
% 9.46/2.78 (((^[Y0 : $o]: (Y0)) @ sK13) = $false)),
% 9.46/2.78 inference(sigma_clausification,[status(thm)],[f466])).
% 9.46/2.78 thf(f466,plain,(
% 9.46/2.78 ($true != (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 9.46/2.78 inference(definition_unfolding,[status(thm)],[f383,f363])).
% 9.46/2.78 thf(f383,plain,(
% 9.46/2.78 (c_False != $true)),
% 9.46/2.78 inference(cnf_transformation,[status(thm)],[f320])).
% 9.46/2.78 % SZS output end Proof for DTF2THF_351
% 9.46/2.78 % (591)------------------------------
% 9.46/2.78 % (591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.46/2.78 % (591)Termination reason: Refutation
% 9.46/2.78
% 9.46/2.78 % (591)Memory used [KB]: 4477
% 9.46/2.78 % (591)Time elapsed: 0.445 s
% 9.46/2.78 % (591)Instructions burned: 1641 (million)
% 9.46/2.78 % (591)------------------------------
% 9.46/2.78 % (591)------------------------------
% 9.46/2.78 % (456)Success in time 1.347 s
%------------------------------------------------------------------------------