%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO873^1 : 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 : n013.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 09:54:57 AM UTC 2026
% Result : Theorem 9.57s 2.74s
% Output : Refutation 9.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO873^1 : 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 : n013.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
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:49:23 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
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYO873^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : ProofGold problem Random2_127_neg_th0
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Urb20]
% 0.29/0.45 % Names : Random2_127_neg_th0.p [Urb20]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.89 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.85 v8.1.0, 0.73 v7.5.0
% 0.29/0.45 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.29/0.45 % Number of atoms : 496 ( 136 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 17 ( 4 avg)
% 0.29/0.45 % Number of connectives : 1194 ( 0 ~; 0 |; 0 &;1100 @)
% 0.29/0.45 % ( 0 <=>; 94 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 25 ( 2 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 559 ( 559 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.29/0.45 % Number of variables : 412 ( 275 ^; 96 !; 41 ?; 412 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : See https://proofgold.org
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(c_Eps_i_tp,type,
% 0.29/0.45 c_Eps_i: ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_False_tp,type,
% 0.29/0.45 c_False: $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_True_tp,type,
% 0.29/0.45 c_True: $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_not_tp,type,
% 0.29/0.45 c_not: $o > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_and_tp,type,
% 0.29/0.45 c_and: $o > $o > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_or_tp,type,
% 0.29/0.45 c_or: $o > $o > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_iff_tp,type,
% 0.29/0.45 c_iff: $o > $o > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_In_tp,type,
% 0.29/0.45 c_In: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_Subq_tp,type,
% 0.29/0.45 c_Subq: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_Empty_tp,type,
% 0.29/0.45 c_Empty: $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Union_tp,type,
% 0.29/0.45 c_Union: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Power_tp,type,
% 0.29/0.45 c_Power: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Repl_tp,type,
% 0.29/0.45 c_Repl: $i > ( $i > $i ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_TransSet_tp,type,
% 0.29/0.45 c_TransSet: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_atleast2_tp,type,
% 0.29/0.45 c_atleast2: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_atleast3_tp,type,
% 0.29/0.45 c_atleast3: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_atleast4_tp,type,
% 0.29/0.45 c_atleast4: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_atleast5_tp,type,
% 0.29/0.45 c_atleast5: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_atleast6_tp,type,
% 0.29/0.45 c_atleast6: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_exactly2_tp,type,
% 0.29/0.45 c_exactly2: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_exactly3_tp,type,
% 0.29/0.45 c_exactly3: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_exactly4_tp,type,
% 0.29/0.45 c_exactly4: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_exactly5_tp,type,
% 0.29/0.45 c_exactly5: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_exu_i_tp,type,
% 0.29/0.45 c_exu_i: ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_reflexive_i_tp,type,
% 0.29/0.45 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_irreflexive_i_tp,type,
% 0.29/0.45 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_symmetric_i_tp,type,
% 0.29/0.45 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_antisymmetric_i_tp,type,
% 0.29/0.45 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_transitive_i_tp,type,
% 0.29/0.45 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_eqreln_i_tp,type,
% 0.29/0.45 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_per_i_tp,type,
% 0.29/0.45 c_per_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_linear_i_tp,type,
% 0.29/0.45 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_trichotomous_or_i_tp,type,
% 0.29/0.45 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_partialorder_i_tp,type,
% 0.29/0.45 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_totalorder_i_tp,type,
% 0.29/0.45 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_strictpartialorder_i_tp,type,
% 0.29/0.45 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_stricttotalorder_i_tp,type,
% 0.29/0.45 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_If_i_tp,type,
% 0.29/0.45 c_If_i: $o > $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_exactly1of2_tp,type,
% 0.29/0.45 c_exactly1of2: $o > $o > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_exactly1of3_tp,type,
% 0.29/0.45 c_exactly1of3: $o > $o > $o > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_nIn_tp,type,
% 0.29/0.45 c_nIn: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_nSubq_tp,type,
% 0.29/0.45 c_nSubq: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_UPair_tp,type,
% 0.29/0.45 c_UPair: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Sing_tp,type,
% 0.29/0.45 c_Sing: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_binunion_tp,type,
% 0.29/0.45 c_binunion: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_SetAdjoin_tp,type,
% 0.29/0.45 c_SetAdjoin: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_famunion_tp,type,
% 0.29/0.45 c_famunion: $i > ( $i > $i ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Sep_tp,type,
% 0.29/0.45 c_Sep: $i > ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_ReplSep_tp,type,
% 0.29/0.45 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_binintersect_tp,type,
% 0.29/0.45 c_binintersect: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_setminus_tp,type,
% 0.29/0.45 c_setminus: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_inj_tp,type,
% 0.29/0.45 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_bij_tp,type,
% 0.29/0.45 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_atleastp_tp,type,
% 0.29/0.45 c_atleastp: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_equip_tp,type,
% 0.29/0.45 c_equip: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_In_rec_poly_G_i_tp,type,
% 0.29/0.45 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_In_rec_poly_i_tp,type,
% 0.29/0.45 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_ordsucc_tp,type,
% 0.29/0.45 c_ordsucc: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_nat_p_tp,type,
% 0.29/0.45 c_nat_p: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_nat_primrec_tp,type,
% 0.29/0.45 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_add_nat_tp,type,
% 0.29/0.45 c_add_nat: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_mul_nat_tp,type,
% 0.29/0.45 c_mul_nat: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_ordinal_tp,type,
% 0.29/0.45 c_ordinal: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_V__tp,type,
% 0.29/0.45 c_V_: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Inj1_tp,type,
% 0.29/0.45 c_Inj1: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Inj0_tp,type,
% 0.29/0.45 c_Inj0: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Unj_tp,type,
% 0.29/0.45 c_Unj: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_combine_funcs_tp,type,
% 0.29/0.45 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_setsum_tp,type,
% 0.29/0.45 c_setsum: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_proj0_tp,type,
% 0.29/0.45 c_proj0: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_proj1_tp,type,
% 0.29/0.45 c_proj1: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_binrep_tp,type,
% 0.29/0.45 c_binrep: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_lam_tp,type,
% 0.29/0.45 c_lam: $i > ( $i > $i ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_setprod_tp,type,
% 0.29/0.45 c_setprod: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_ap_tp,type,
% 0.29/0.45 c_ap: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_setsum_p_tp,type,
% 0.29/0.45 c_setsum_p: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_tuple_p_tp,type,
% 0.29/0.45 c_tuple_p: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_Pi_tp,type,
% 0.29/0.45 c_Pi: $i > ( $i > $i ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_setexp_tp,type,
% 0.29/0.45 c_setexp: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_Sep2_tp,type,
% 0.29/0.45 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_set_of_pairs_tp,type,
% 0.29/0.45 c_set_of_pairs: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_lam2_tp,type,
% 0.29/0.45 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_PNoEq__tp,type,
% 0.29/0.45 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_PNoLt__tp,type,
% 0.29/0.45 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_PNoLt_tp,type,
% 0.29/0.45 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_PNoLe_tp,type,
% 0.29/0.45 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_PNo_downc_tp,type,
% 0.29/0.45 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_PNo_upc_tp,type,
% 0.29/0.45 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNoElts__tp,type,
% 0.29/0.45 c_SNoElts_: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNo__tp,type,
% 0.29/0.45 c_SNo_: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_PSNo_tp,type,
% 0.29/0.45 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNo_tp,type,
% 0.29/0.45 c_SNo: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNoLev_tp,type,
% 0.29/0.45 c_SNoLev: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNoEq__tp,type,
% 0.29/0.45 c_SNoEq_: $i > $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNoLt_tp,type,
% 0.29/0.45 c_SNoLt: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_SNoLe_tp,type,
% 0.29/0.45 c_SNoLe: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_binop_on_tp,type,
% 0.29/0.45 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_Loop_tp,type,
% 0.29/0.45 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_Loop_with_defs_tp,type,
% 0.29/0.45 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 ).
% 0.29/0.45
% 0.29/0.45 thf(c_Loop_with_defs_cex1_tp,type,
% 0.29/0.45 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 ).
% 0.29/0.45
% 0.29/0.45 thf(c_Loop_with_defs_cex2_tp,type,
% 0.29/0.45 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 ).
% 0.29/0.45
% 0.29/0.45 thf(c_combinator_tp,type,
% 0.29/0.45 c_combinator: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_combinator_equiv_tp,type,
% 0.29/0.45 c_combinator_equiv: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(c_equip_mod_tp,type,
% 0.29/0.45 c_equip_mod: $i > $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(ax1,axiom,
% 0.29/0.45 ! [X0: $i > $o,X1: $i] :
% 0.29/0.45 ( ( X0 @ X1 )
% 0.29/0.45 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax2,axiom,
% 0.29/0.45 ! [X0: $o] :
% 0.29/0.45 ( ( c_not @ ( c_not @ X0 ) )
% 0.29/0.45 => X0 ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax3,axiom,
% 0.29/0.45 ! [X0: $o,X1: $o] :
% 0.29/0.45 ( ( c_iff @ X0 @ X1 )
% 0.29/0.45 => ( X0 = X1 ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax4,axiom,
% 0.29/0.45 ! [X0: $i,X1: $i] :
% 0.29/0.45 ( ( c_Subq @ X0 @ X1 )
% 0.29/0.45 => ( ( c_Subq @ X1 @ X0 )
% 0.29/0.45 => ( X0 = X1 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax5,axiom,
% 0.29/0.45 ( c_not
% 0.29/0.45 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax6,axiom,
% 0.29/0.45 ! [X0: $i,X1: $i] :
% 0.29/0.45 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.29/0.45 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax7,axiom,
% 0.29/0.45 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax8,axiom,
% 0.29/0.45 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.29/0.45 ( c_iff
% 0.29/0.45 @ ( c_In @ X2
% 0.29/0.45 @ ( c_Repl @ X0
% 0.29/0.45 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.29/0.45 @ ? [X3: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X3 @ X0 )
% 0.29/0.45 @ ( X2
% 0.29/0.45 = ( X1 @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax9,axiom,
% 0.29/0.45 ! [X0: $i > $o] :
% 0.29/0.45 ( ! [X1: $i] :
% 0.29/0.45 ( ( X0 @ X1 )
% 0.29/0.45 => ! [X2: $i] :
% 0.29/0.45 ( ( c_In @ X2 @ X1 )
% 0.29/0.45 => ( X0 @ X2 ) ) )
% 0.29/0.45 => ( ( X0 @ c_Empty )
% 0.29/0.45 => ( ! [X1: $i] :
% 0.29/0.45 ( ( X0 @ X1 )
% 0.29/0.45 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.29/0.45 => ( ! [X1: $i] :
% 0.29/0.45 ( ( X0 @ X1 )
% 0.29/0.45 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.29/0.45 => ( ! [X1: $i] :
% 0.29/0.45 ( ( X0 @ X1 )
% 0.29/0.45 => ! [X2: $i > $i] :
% 0.29/0.45 ( ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X1 )
% 0.29/0.45 => ( X0 @ ( X2 @ X3 ) ) )
% 0.29/0.45 => ( X0
% 0.29/0.45 @ ( c_Repl @ X1
% 0.29/0.45 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.29/0.45 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax10,axiom,
% 0.29/0.45 ! [X0: $i > $o] :
% 0.29/0.45 ( ! [X1: $i] :
% 0.29/0.45 ( ! [X2: $i] :
% 0.29/0.45 ( ( c_In @ X2 @ X1 )
% 0.29/0.45 => ( X0 @ X2 ) )
% 0.29/0.45 => ( X0 @ X1 ) )
% 0.29/0.45 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax11,axiom,
% 0.29/0.45 ( c_False
% 0.29/0.45 = ( ! [X0: $o] : X0 ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax12,axiom,
% 0.29/0.45 ( c_True
% 0.29/0.45 = ( ! [X0: $o] :
% 0.29/0.45 ( X0
% 0.29/0.45 => X0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax13,axiom,
% 0.29/0.45 ( c_not
% 0.29/0.45 = ( ^ [X0: $o] :
% 0.29/0.45 ( X0
% 0.29/0.45 => c_False ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax14,axiom,
% 0.29/0.45 ( c_and
% 0.29/0.45 = ( ^ [X0: $o,X1: $o] :
% 0.29/0.45 ! [X2: $o] :
% 0.29/0.45 ( ( X0
% 0.29/0.45 => ( X1
% 0.29/0.45 => X2 ) )
% 0.29/0.45 => X2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax15,axiom,
% 0.29/0.45 ( c_or
% 0.29/0.45 = ( ^ [X0: $o,X1: $o] :
% 0.29/0.45 ! [X2: $o] :
% 0.29/0.45 ( ( X0
% 0.29/0.45 => X2 )
% 0.29/0.45 => ( ( X1
% 0.29/0.45 => X2 )
% 0.29/0.45 => X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax16,axiom,
% 0.29/0.45 ( c_iff
% 0.29/0.45 = ( ^ [X0: $o,X1: $o] :
% 0.29/0.45 ( c_and
% 0.29/0.45 @ ( X0
% 0.29/0.45 => X1 )
% 0.29/0.45 @ ( X1
% 0.29/0.45 => X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax17,axiom,
% 0.29/0.45 ( c_Subq
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ! [X2: $i] :
% 0.29/0.45 ( ( c_In @ X2 @ X0 )
% 0.29/0.45 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax18,axiom,
% 0.29/0.45 ( c_TransSet
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ! [X1: $i] :
% 0.29/0.45 ( ( c_In @ X1 @ X0 )
% 0.29/0.45 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax19,axiom,
% 0.29/0.45 ( c_atleast2
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax20,axiom,
% 0.29/0.45 ( c_atleast3
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax21,axiom,
% 0.29/0.45 ( c_atleast4
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax22,axiom,
% 0.29/0.45 ( c_atleast5
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax23,axiom,
% 0.29/0.45 ( c_atleast6
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax24,axiom,
% 0.29/0.45 ( c_exactly2
% 0.29/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax25,axiom,
% 0.29/0.45 ( c_exactly3
% 0.29/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax26,axiom,
% 0.29/0.45 ( c_exactly4
% 0.29/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax27,axiom,
% 0.29/0.45 ( c_exactly5
% 0.29/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax28,axiom,
% 0.29/0.45 ( c_exu_i
% 0.29/0.45 = ( ^ [X0: $i > $o] :
% 0.29/0.45 ( c_and
% 0.29/0.45 @ ? [X1: $i] : ( X0 @ X1 )
% 0.29/0.45 @ ! [X1: $i,X2: $i] :
% 0.29/0.45 ( ( X0 @ X1 )
% 0.29/0.45 => ( ( X0 @ X2 )
% 0.29/0.45 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax29,axiom,
% 0.29/0.45 ( c_reflexive_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax30,axiom,
% 0.29/0.45 ( c_irreflexive_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax31,axiom,
% 0.29/0.45 ( c_symmetric_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i,X2: $i] :
% 0.29/0.45 ( ( X0 @ X1 @ X2 )
% 0.29/0.45 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax32,axiom,
% 0.29/0.45 ( c_antisymmetric_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i,X2: $i] :
% 0.29/0.45 ( ( X0 @ X1 @ X2 )
% 0.29/0.45 => ( ( X0 @ X2 @ X1 )
% 0.29/0.45 => ( X1 = X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax33,axiom,
% 0.29/0.45 ( c_transitive_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i,X2: $i,X3: $i] :
% 0.29/0.45 ( ( X0 @ X1 @ X2 )
% 0.29/0.45 => ( ( X0 @ X2 @ X3 )
% 0.29/0.45 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax34,axiom,
% 0.29/0.45 ( c_eqreln_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax35,axiom,
% 0.29/0.45 ( c_per_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax36,axiom,
% 0.29/0.45 ( c_linear_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax37,axiom,
% 0.29/0.45 ( c_trichotomous_or_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.29/0.45 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax38,axiom,
% 0.29/0.45 ( c_partialorder_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax39,axiom,
% 0.29/0.45 ( c_totalorder_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax40,axiom,
% 0.29/0.45 ( c_strictpartialorder_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax41,axiom,
% 0.29/0.45 ( c_stricttotalorder_i
% 0.29/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax42,axiom,
% 0.29/0.45 ( c_If_i
% 0.29/0.45 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.29/0.45 ( c_Eps_i
% 0.29/0.45 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax43,axiom,
% 0.29/0.45 ( c_exactly1of2
% 0.29/0.45 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax44,axiom,
% 0.29/0.45 ( c_exactly1of3
% 0.29/0.45 = ( ^ [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 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax45,axiom,
% 0.29/0.45 ( c_nIn
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax46,axiom,
% 0.29/0.45 ( c_nSubq
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax47,axiom,
% 0.29/0.45 ( c_UPair
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.29/0.45 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax48,axiom,
% 0.29/0.45 ( c_Sing
% 0.29/0.45 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax49,axiom,
% 0.29/0.45 ( c_binunion
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax50,axiom,
% 0.29/0.45 ( c_SetAdjoin
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax51,axiom,
% 0.29/0.45 ( c_famunion
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i] :
% 0.29/0.45 ( c_Union
% 0.29/0.45 @ ( c_Repl @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax52,axiom,
% 0.29/0.45 ( c_Sep
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $o] :
% 0.29/0.45 ( c_If_i
% 0.29/0.45 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.29/0.45 @ ( c_Repl @ X0
% 0.29/0.45 @ ^ [X2: $i] :
% 0.29/0.45 ( ^ [X3: $i] :
% 0.29/0.45 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.29/0.45 @ ( c_Eps_i
% 0.29/0.45 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.29/0.45 @ X2 ) )
% 0.29/0.45 @ c_Empty ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax53,axiom,
% 0.29/0.45 ( c_ReplSep
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.29/0.45 ( c_Repl
% 0.29/0.45 @ ( c_Sep @ X0
% 0.29/0.45 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.29/0.45 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax54,axiom,
% 0.29/0.45 ( c_binintersect
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_Sep @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax55,axiom,
% 0.29/0.45 ( c_setminus
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_Sep @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax56,axiom,
% 0.29/0.45 ( c_inj
% 0.29/0.45 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.29/0.45 ( c_and
% 0.29/0.45 @ ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X0 )
% 0.29/0.45 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.29/0.45 @ ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X0 )
% 0.29/0.45 => ! [X4: $i] :
% 0.29/0.45 ( ( c_In @ X4 @ X0 )
% 0.29/0.45 => ( ( ( X2 @ X3 )
% 0.29/0.45 = ( X2 @ X4 ) )
% 0.29/0.45 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax57,axiom,
% 0.29/0.45 ( c_bij
% 0.29/0.45 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.29/0.45 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.29/0.45 @ ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X1 )
% 0.29/0.45 => ? [X4: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X4 @ X0 )
% 0.29/0.45 @ ( ( X2 @ X4 )
% 0.29/0.45 = X3 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax58,axiom,
% 0.29/0.45 ( c_atleastp
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax59,axiom,
% 0.29/0.45 ( c_equip
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax60,axiom,
% 0.29/0.45 ( c_In_rec_poly_G_i
% 0.29/0.45 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.29/0.45 ! [X3: $i > $i > $o] :
% 0.29/0.45 ( ! [X4: $i,X5: $i > $i] :
% 0.29/0.45 ( ! [X6: $i] :
% 0.29/0.45 ( ( c_In @ X6 @ X4 )
% 0.29/0.45 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.29/0.45 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.29/0.45 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax61,axiom,
% 0.29/0.45 ( c_In_rec_poly_i
% 0.29/0.45 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.29/0.45 ( c_Eps_i
% 0.29/0.45 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax62,axiom,
% 0.29/0.45 ( c_ordsucc
% 0.29/0.45 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax63,axiom,
% 0.29/0.45 ( c_nat_p
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ! [X1: $i > $o] :
% 0.29/0.45 ( ( X1 @ c_Empty )
% 0.29/0.45 => ( ! [X2: $i] :
% 0.29/0.45 ( ( X1 @ X2 )
% 0.29/0.45 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.29/0.45 => ( X1 @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax64,axiom,
% 0.29/0.45 ( c_nat_primrec
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.29/0.45 ( c_In_rec_poly_i
% 0.29/0.45 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax65,axiom,
% 0.29/0.45 ( c_add_nat
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_nat_primrec @ X0
% 0.29/0.45 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.29/0.45 @ X1 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax66,axiom,
% 0.29/0.45 ( c_mul_nat
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_nat_primrec @ c_Empty
% 0.29/0.45 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.29/0.45 @ X1 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax67,axiom,
% 0.29/0.45 ( c_ordinal
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( c_and @ ( c_TransSet @ X0 )
% 0.29/0.45 @ ! [X1: $i] :
% 0.29/0.45 ( ( c_In @ X1 @ X0 )
% 0.29/0.45 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax68,axiom,
% 0.29/0.45 ( c_V_
% 0.29/0.45 = ( c_In_rec_poly_i
% 0.29/0.45 @ ^ [X0: $i,X1: $i > $i] :
% 0.29/0.45 ( c_famunion @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax69,axiom,
% 0.29/0.45 ( c_Inj1
% 0.29/0.45 = ( c_In_rec_poly_i
% 0.29/0.45 @ ^ [X0: $i,X1: $i > $i] :
% 0.29/0.45 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.29/0.45 @ ( c_Repl @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax70,axiom,
% 0.29/0.45 ( c_Inj0
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( c_Repl @ X0
% 0.29/0.45 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax71,axiom,
% 0.29/0.45 ( c_Unj
% 0.29/0.45 = ( c_In_rec_poly_i
% 0.29/0.45 @ ^ [X0: $i,X1: $i > $i] :
% 0.29/0.45 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.29/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax72,axiom,
% 0.29/0.45 ( c_combine_funcs
% 0.29/0.45 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.29/0.45 ( c_If_i
% 0.29/0.45 @ ( X4
% 0.29/0.45 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.29/0.45 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.29/0.45 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax73,axiom,
% 0.29/0.45 ( c_setsum
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_binunion
% 0.29/0.45 @ ( c_Repl @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.29/0.45 @ ( c_Repl @ X1
% 0.29/0.45 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax74,axiom,
% 0.29/0.45 ( c_proj0
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( c_ReplSep @ X0
% 0.29/0.45 @ ^ [X1: $i] :
% 0.29/0.45 ? [X2: $i] :
% 0.29/0.45 ( ( c_Inj0 @ X2 )
% 0.29/0.45 = X1 )
% 0.29/0.45 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax75,axiom,
% 0.29/0.45 ( c_proj1
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( c_ReplSep @ X0
% 0.29/0.45 @ ^ [X1: $i] :
% 0.29/0.45 ? [X2: $i] :
% 0.29/0.45 ( ( c_Inj1 @ X2 )
% 0.29/0.45 = X1 )
% 0.29/0.45 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax76,axiom,
% 0.29/0.45 ( c_binrep
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax77,axiom,
% 0.29/0.45 ( c_lam
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i] :
% 0.29/0.45 ( c_famunion @ X0
% 0.29/0.45 @ ^ [X2: $i] :
% 0.29/0.45 ( c_Repl @ ( X1 @ X2 )
% 0.29/0.45 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax78,axiom,
% 0.29/0.45 ( c_setprod
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_lam @ X0
% 0.29/0.45 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax79,axiom,
% 0.29/0.45 ( c_ap
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_ReplSep @ X0
% 0.29/0.45 @ ^ [X2: $i] :
% 0.29/0.45 ? [X3: $i] :
% 0.29/0.45 ( X2
% 0.29/0.45 = ( c_setsum @ X1 @ X3 ) )
% 0.29/0.45 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax80,axiom,
% 0.29/0.45 ( c_setsum_p
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.45 = X0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax81,axiom,
% 0.29/0.45 ( c_tuple_p
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ! [X2: $i] :
% 0.29/0.45 ( ( c_In @ X2 @ X1 )
% 0.29/0.45 => ? [X3: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X3 @ X0 )
% 0.29/0.45 @ ? [X4: $i] :
% 0.29/0.45 ( X2
% 0.29/0.45 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax82,axiom,
% 0.29/0.45 ( c_Pi
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i] :
% 0.29/0.45 ( c_Sep
% 0.29/0.45 @ ( c_Power
% 0.29/0.45 @ ( c_lam @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.29/0.45 @ ^ [X2: $i] :
% 0.29/0.45 ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X0 )
% 0.29/0.45 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax83,axiom,
% 0.29/0.45 ( c_setexp
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_Pi @ X1
% 0.29/0.45 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax84,axiom,
% 0.29/0.45 ( c_Sep2
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.29/0.45 ( c_Sep
% 0.29/0.45 @ ( c_lam @ X0
% 0.29/0.45 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.29/0.45 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax85,axiom,
% 0.29/0.45 ( c_set_of_pairs
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ! [X1: $i] :
% 0.29/0.45 ( ( c_In @ X1 @ X0 )
% 0.29/0.45 => ? [X2: $i,X3: $i] :
% 0.29/0.45 ( X1
% 0.29/0.45 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.29/0.45 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax86,axiom,
% 0.29/0.45 ( c_lam2
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.29/0.45 ( c_lam @ X0
% 0.29/0.45 @ ^ [X3: $i] :
% 0.29/0.45 ( c_lam @ ( X1 @ X3 )
% 0.29/0.45 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax87,axiom,
% 0.29/0.45 ( c_PNoEq_
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.29/0.45 ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X0 )
% 0.29/0.45 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax88,axiom,
% 0.29/0.45 ( c_PNoLt_
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.29/0.45 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax89,axiom,
% 0.29/0.45 ( c_PNoLt
% 0.29/0.45 = ( ^ [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 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax90,axiom,
% 0.29/0.45 ( c_PNoLe
% 0.29/0.45 = ( ^ [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 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax91,axiom,
% 0.29/0.45 ( c_PNo_downc
% 0.29/0.45 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.29/0.45 ? [X3: $i] :
% 0.29/0.45 ( c_and @ ( c_ordinal @ X3 )
% 0.29/0.45 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax92,axiom,
% 0.29/0.45 ( c_PNo_upc
% 0.29/0.45 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.29/0.45 ? [X3: $i] :
% 0.29/0.45 ( c_and @ ( c_ordinal @ X3 )
% 0.29/0.45 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax93,axiom,
% 0.29/0.45 ( c_SNoElts_
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( c_binunion @ X0
% 0.29/0.45 @ ( c_Repl @ X0
% 0.29/0.45 @ ^ [X1: $i] :
% 0.29/0.45 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.45 @ X1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax94,axiom,
% 0.29/0.45 ( c_SNo_
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.29/0.45 @ ! [X2: $i] :
% 0.29/0.45 ( ( c_In @ X2 @ X0 )
% 0.29/0.45 => ( c_exactly1of2
% 0.29/0.45 @ ( c_In
% 0.29/0.45 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.45 @ X2 )
% 0.29/0.45 @ X1 )
% 0.29/0.45 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax95,axiom,
% 0.29/0.45 ( c_PSNo
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $o] :
% 0.29/0.45 ( c_binunion
% 0.29/0.45 @ ( c_Sep @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.29/0.45 @ ( c_ReplSep @ X0
% 0.29/0.45 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.29/0.45 @ ^ [X2: $i] :
% 0.29/0.45 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.29/0.45 @ X2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax96,axiom,
% 0.29/0.45 ( c_SNo
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax97,axiom,
% 0.29/0.45 ( c_SNoLev
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ( c_Eps_i
% 0.29/0.45 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax98,axiom,
% 0.29/0.45 ( c_SNoEq_
% 0.29/0.45 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.29/0.45 ( c_PNoEq_ @ X0
% 0.29/0.45 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.29/0.45 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax99,axiom,
% 0.29/0.45 ( c_SNoLt
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.29/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.29/0.45 @ ( c_SNoLev @ X1 )
% 0.29/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax100,axiom,
% 0.29/0.45 ( c_SNoLe
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.29/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.29/0.45 @ ( c_SNoLev @ X1 )
% 0.29/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax101,axiom,
% 0.29/0.45 ( c_binop_on
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.29/0.45 ! [X2: $i] :
% 0.29/0.45 ( ( c_In @ X2 @ X0 )
% 0.29/0.45 => ! [X3: $i] :
% 0.29/0.45 ( ( c_In @ X3 @ X0 )
% 0.29/0.45 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax102,axiom,
% 0.29/0.45 ( c_Loop
% 0.29/0.45 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.29/0.45 ( c_and
% 0.29/0.45 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.29/0.45 @ ! [X5: $i] :
% 0.29/0.45 ( ( c_In @ X5 @ X0 )
% 0.29/0.45 => ( c_and
% 0.29/0.45 @ ( ( X1 @ X4 @ X5 )
% 0.29/0.45 = X5 )
% 0.29/0.45 @ ( ( X1 @ X5 @ X4 )
% 0.29/0.45 = X5 ) ) ) )
% 0.29/0.45 @ ! [X5: $i] :
% 0.29/0.45 ( ( c_In @ X5 @ X0 )
% 0.29/0.45 => ! [X6: $i] :
% 0.29/0.45 ( ( c_In @ X6 @ X0 )
% 0.29/0.45 => ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.29/0.45 = X6 )
% 0.29/0.45 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.29/0.45 = X6 ) )
% 0.29/0.45 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.29/0.45 = X5 ) )
% 0.29/0.45 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.29/0.45 = X5 ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax103,axiom,
% 0.29/0.45 ( c_Loop_with_defs
% 0.29/0.45 = ( ^ [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] :
% 0.29/0.45 ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.29/0.45 @ ! [X14: $i] :
% 0.29/0.45 ( ( c_In @ X14 @ X0 )
% 0.29/0.45 => ! [X15: $i] :
% 0.29/0.45 ( ( c_In @ X15 @ X0 )
% 0.29/0.45 => ( ( X5 @ X14 @ X15 )
% 0.29/0.45 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.29/0.45 @ ! [X14: $i] :
% 0.29/0.45 ( ( c_In @ X14 @ X0 )
% 0.29/0.45 => ! [X15: $i] :
% 0.29/0.45 ( ( c_In @ X15 @ X0 )
% 0.29/0.45 => ! [X16: $i] :
% 0.29/0.45 ( ( c_In @ X16 @ X0 )
% 0.29/0.45 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.29/0.45 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.29/0.45 @ ! [X14: $i] :
% 0.29/0.45 ( ( c_In @ X14 @ X0 )
% 0.29/0.45 => ! [X15: $i] :
% 0.29/0.45 ( ( c_In @ X15 @ X0 )
% 0.29/0.45 => ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( c_and
% 0.29/0.45 @ ( ( X7 @ X14 @ X15 )
% 0.29/0.45 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.29/0.45 @ ( ( X10 @ X14 @ X15 )
% 0.29/0.45 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.29/0.45 @ ( ( X11 @ X14 @ X15 )
% 0.29/0.45 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.29/0.45 @ ( ( X12 @ X14 @ X15 )
% 0.29/0.45 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.29/0.45 @ ( ( X13 @ X14 @ X15 )
% 0.29/0.45 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.29/0.45 @ ! [X14: $i] :
% 0.29/0.45 ( ( c_In @ X14 @ X0 )
% 0.29/0.45 => ! [X15: $i] :
% 0.29/0.45 ( ( c_In @ X15 @ X0 )
% 0.29/0.45 => ! [X16: $i] :
% 0.29/0.45 ( ( c_In @ X16 @ X0 )
% 0.29/0.45 => ( c_and
% 0.29/0.45 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.29/0.45 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.29/0.45 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.29/0.45 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax104,axiom,
% 0.29/0.45 ( c_Loop_with_defs_cex1
% 0.29/0.45 = ( ^ [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] :
% 0.29/0.45 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.29/0.45 @ ? [X14: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X14 @ X0 )
% 0.29/0.45 @ ? [X15: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X15 @ X0 )
% 0.29/0.45 @ ? [X16: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X16 @ X0 )
% 0.29/0.45 @ ? [X17: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X17 @ X0 )
% 0.29/0.45 @ ( c_not
% 0.29/0.45 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.29/0.45 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax105,axiom,
% 0.29/0.45 ( c_Loop_with_defs_cex2
% 0.29/0.45 = ( ^ [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] :
% 0.29/0.45 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.29/0.45 @ ? [X14: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X14 @ X0 )
% 0.29/0.45 @ ? [X15: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X15 @ X0 )
% 0.29/0.45 @ ? [X16: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X16 @ X0 )
% 0.29/0.45 @ ? [X17: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X17 @ X0 )
% 0.29/0.45 @ ? [X18: $i] :
% 0.29/0.45 ( c_and @ ( c_In @ X18 @ X0 )
% 0.29/0.45 @ ( c_not
% 0.29/0.45 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.29/0.45 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax106,axiom,
% 0.29/0.45 ( c_combinator
% 0.29/0.45 = ( ^ [X0: $i] :
% 0.29/0.45 ! [X1: $i > $o] :
% 0.29/0.45 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.29/0.45 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.29/0.45 => ( ! [X2: $i,X3: $i] :
% 0.29/0.45 ( ( X1 @ X2 )
% 0.29/0.45 => ( ( X1 @ X3 )
% 0.29/0.45 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.29/0.45 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax107,axiom,
% 0.29/0.45 ( c_combinator_equiv
% 0.29/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.29/0.45 ! [X2: $i > $i > $o] :
% 0.29/0.45 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.29/0.45 ( ( c_per_i @ X2 )
% 0.29/0.45 => ( ! [X6: $i] :
% 0.29/0.45 ( ( c_combinator @ X6 )
% 0.29/0.45 => ( X2 @ X6 @ X6 ) )
% 0.29/0.45 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.29/0.45 ( ( c_combinator @ X6 )
% 0.29/0.45 => ( ( c_combinator @ X7 )
% 0.29/0.45 => ( ( c_combinator @ X8 )
% 0.29/0.45 => ( ( c_combinator @ X9 )
% 0.29/0.45 => ( ( X2 @ X6 @ X8 )
% 0.29/0.45 => ( ( X2 @ X7 @ X9 )
% 0.29/0.45 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.29/0.45 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.29/0.45 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.29/0.45 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.29/0.45 @ ( c_Inj0 @ c_Empty )
% 0.29/0.45 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.29/0.45 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(ax108,axiom,
% 0.29/0.45 ( c_equip_mod
% 0.29/0.45 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.29/0.45 ? [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 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(conj,conjecture,
% 0.29/0.45 ( c_not
% 0.29/0.45 @ ! [X0: $i > $o,X1: $i > $i] :
% 0.29/0.45 ( c_and
% 0.29/0.45 @ ( ( ( X0 @ ( X1 @ ( c_binintersect @ ( X1 @ ( c_Power @ c_Empty ) ) @ ( X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
% 0.29/0.45 => ( ( c_TransSet @ ( X1 @ c_Empty ) )
% 0.29/0.46 => ! [X2: $i] :
% 0.29/0.46 ( ( c_In @ X2 @ c_Empty )
% 0.29/0.46 => ? [X3: $i] : ( c_and @ ( c_Subq @ X3 @ X2 ) @ ( c_exactly2 @ ( c_ordsucc @ ( X1 @ X3 ) ) ) ) ) ) )
% 0.29/0.46 => ? [X2: $i] :
% 0.29/0.46 ( c_and
% 0.29/0.46 @ ? [X3: $i] :
% 0.29/0.46 ( c_and @ ( c_Subq @ X3 @ X2 )
% 0.29/0.46 @ ( ( X2
% 0.29/0.46 = ( X1 @ X2 ) )
% 0.29/0.46 => ? [X4: $i] : ( c_and @ ( c_Subq @ X4 @ X2 ) @ ( c_not @ ( X0 @ ( c_setprod @ X3 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) ) ) ) ) )
% 0.29/0.46 @ ( c_not @ ( c_SNo @ X2 ) ) ) )
% 0.29/0.46 @ ( c_not @ ( X0 @ ( X1 @ ( X1 @ ( X1 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.99/1.39 ---- Embedded in THF ---
% 1.99/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.99/1.39 %%% Generated on Tue Feb 24 14:49:24 EST 2026
% 1.99/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.99/1.39 %%% Logic specification used:
% 1.99/1.39 %%% thf(spec, logic, $$dhol).
% 1.99/1.39
% 1.99/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2DTF2340.p
% 1.99/1.39 thf(c_Eps_i_tp, type, c_Eps_i: (($i > $o) > $i)).
% 1.99/1.39 thf(c_False_tp, type, c_False: $o).
% 1.99/1.39 thf(c_True_tp, type, c_True: $o).
% 1.99/1.39 thf(c_not_tp, type, c_not: ($o > $o)).
% 1.99/1.39 thf(c_and_tp, type, c_and: ($o > ($o > $o))).
% 1.99/1.39 thf(c_or_tp, type, c_or: ($o > ($o > $o))).
% 1.99/1.39 thf(c_iff_tp, type, c_iff: ($o > ($o > $o))).
% 1.99/1.39 thf(c_In_tp, type, c_In: ($i > ($i > $o))).
% 1.99/1.39 thf(c_Subq_tp, type, c_Subq: ($i > ($i > $o))).
% 1.99/1.39 thf(c_Empty_tp, type, c_Empty: $i).
% 1.99/1.39 thf(c_Union_tp, type, c_Union: ($i > $i)).
% 1.99/1.39 thf(c_Power_tp, type, c_Power: ($i > $i)).
% 1.99/1.39 thf(c_Repl_tp, type, c_Repl: ($i > (($i > $i) > $i))).
% 1.99/1.39 thf(c_TransSet_tp, type, c_TransSet: ($i > $o)).
% 1.99/1.39 thf(c_atleast2_tp, type, c_atleast2: ($i > $o)).
% 1.99/1.39 thf(c_atleast3_tp, type, c_atleast3: ($i > $o)).
% 1.99/1.39 thf(c_atleast4_tp, type, c_atleast4: ($i > $o)).
% 1.99/1.39 thf(c_atleast5_tp, type, c_atleast5: ($i > $o)).
% 1.99/1.39 thf(c_atleast6_tp, type, c_atleast6: ($i > $o)).
% 1.99/1.39 thf(c_exactly2_tp, type, c_exactly2: ($i > $o)).
% 1.99/1.39 thf(c_exactly3_tp, type, c_exactly3: ($i > $o)).
% 1.99/1.39 thf(c_exactly4_tp, type, c_exactly4: ($i > $o)).
% 1.99/1.39 thf(c_exactly5_tp, type, c_exactly5: ($i > $o)).
% 1.99/1.39 thf(c_exu_i_tp, type, c_exu_i: (($i > $o) > $o)).
% 1.99/1.39 thf(c_reflexive_i_tp, type, c_reflexive_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_irreflexive_i_tp, type, c_irreflexive_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_symmetric_i_tp, type, c_symmetric_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_antisymmetric_i_tp, type, c_antisymmetric_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_transitive_i_tp, type, c_transitive_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_eqreln_i_tp, type, c_eqreln_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_per_i_tp, type, c_per_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_linear_i_tp, type, c_linear_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_trichotomous_or_i_tp, type, c_trichotomous_or_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_partialorder_i_tp, type, c_partialorder_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_totalorder_i_tp, type, c_totalorder_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_strictpartialorder_i_tp, type, c_strictpartialorder_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_stricttotalorder_i_tp, type, c_stricttotalorder_i: (($i > ($i > $o)) > $o)).
% 1.99/1.39 thf(c_If_i_tp, type, c_If_i: ($o > ($i > ($i > $i)))).
% 1.99/1.39 thf(c_exactly1of2_tp, type, c_exactly1of2: ($o > ($o > $o))).
% 1.99/1.39 thf(c_exactly1of3_tp, type, c_exactly1of3: ($o > ($o > ($o > $o)))).
% 1.99/1.39 thf(c_nIn_tp, type, c_nIn: ($i > ($i > $o))).
% 1.99/1.39 thf(c_nSubq_tp, type, c_nSubq: ($i > ($i > $o))).
% 1.99/1.39 thf(c_UPair_tp, type, c_UPair: ($i > ($i > $i))).
% 1.99/1.39 thf(c_Sing_tp, type, c_Sing: ($i > $i)).
% 1.99/1.39 thf(c_binunion_tp, type, c_binunion: ($i > ($i > $i))).
% 1.99/1.39 thf(c_SetAdjoin_tp, type, c_SetAdjoin: ($i > ($i > $i))).
% 1.99/1.39 thf(c_famunion_tp, type, c_famunion: ($i > (($i > $i) > $i))).
% 1.99/1.39 thf(c_Sep_tp, type, c_Sep: ($i > (($i > $o) > $i))).
% 1.99/1.39 thf(c_ReplSep_tp, type, c_ReplSep: ($i > (($i > $o) > (($i > $i) > $i)))).
% 1.99/1.39 thf(c_binintersect_tp, type, c_binintersect: ($i > ($i > $i))).
% 1.99/1.39 thf(c_setminus_tp, type, c_setminus: ($i > ($i > $i))).
% 1.99/1.39 thf(c_inj_tp, type, c_inj: ($i > ($i > (($i > $i) > $o)))).
% 1.99/1.39 thf(c_bij_tp, type, c_bij: ($i > ($i > (($i > $i) > $o)))).
% 1.99/1.39 thf(c_atleastp_tp, type, c_atleastp: ($i > ($i > $o))).
% 1.99/1.39 thf(c_equip_tp, type, c_equip: ($i > ($i > $o))).
% 1.99/1.39 thf(c_In_rec_poly_G_i_tp, type, c_In_rec_poly_G_i: (($i > (($i > $i) > $i)) > ($i > ($i > $o)))).
% 1.99/1.39 thf(c_In_rec_poly_i_tp, type, c_In_rec_poly_i: (($i > (($i > $i) > $i)) > ($i > $i))).
% 1.99/1.39 thf(c_ordsucc_tp, type, c_ordsucc: ($i > $i)).
% 1.99/1.39 thf(c_nat_p_tp, type, c_nat_p: ($i > $o)).
% 1.99/1.39 thf(c_nat_primrec_tp, type, c_nat_primrec: ($i > (($i > ($i > $i)) > ($i > $i)))).
% 1.99/1.39 thf(c_add_nat_tp, type, c_add_nat: ($i > ($i > $i))).
% 1.99/1.39 thf(c_mul_nat_tp, type, c_mul_nat: ($i > ($i > $i))).
% 1.99/1.39 thf(c_ordinal_tp, type, c_ordinal: ($i > $o)).
% 1.99/1.39 thf(c_V__tp, type, c_V_: ($i > $i)).
% 1.99/1.39 thf(c_Inj1_tp, type, c_Inj1: ($i > $i)).
% 1.99/1.39 thf(c_Inj0_tp, type, c_Inj0: ($i > $i)).
% 1.99/1.39 thf(c_Unj_tp, type, c_Unj: ($i > $i)).
% 1.99/1.39 thf(c_combine_funcs_tp, type, c_combine_funcs: ($i > ($i > (($i > $i) > (($i > $i) > ($i > $i)))))).
% 1.99/1.39 thf(c_setsum_tp, type, c_setsum: ($i > ($i > $i))).
% 1.99/1.39 thf(c_proj0_tp, type, c_proj0: ($i > $i)).
% 1.99/1.39 thf(c_proj1_tp, type, c_proj1: ($i > $i)).
% 1.99/1.39 thf(c_binrep_tp, type, c_binrep: ($i > ($i > $i))).
% 1.99/1.39 thf(c_lam_tp, type, c_lam: ($i > (($i > $i) > $i))).
% 1.99/1.39 thf(c_setprod_tp, type, c_setprod: ($i > ($i > $i))).
% 1.99/1.39 thf(c_ap_tp, type, c_ap: ($i > ($i > $i))).
% 1.99/1.39 thf(c_setsum_p_tp, type, c_setsum_p: ($i > $o)).
% 1.99/1.39 thf(c_tuple_p_tp, type, c_tuple_p: ($i > ($i > $o))).
% 1.99/1.39 thf(c_Pi_tp, type, c_Pi: ($i > (($i > $i) > $i))).
% 1.99/1.39 thf(c_setexp_tp, type, c_setexp: ($i > ($i > $i))).
% 1.99/1.39 thf(c_Sep2_tp, type, c_Sep2: ($i > (($i > $i) > (($i > ($i > $o)) > $i)))).
% 1.99/1.39 thf(c_set_of_pairs_tp, type, c_set_of_pairs: ($i > $o)).
% 1.99/1.39 thf(c_lam2_tp, type, c_lam2: ($i > (($i > $i) > (($i > ($i > $i)) > $i)))).
% 1.99/1.39 thf(c_PNoEq__tp, type, c_PNoEq_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 1.99/1.39 thf(c_PNoLt__tp, type, c_PNoLt_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 1.99/1.39 thf(c_PNoLt_tp, type, c_PNoLt: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 1.99/1.39 thf(c_PNoLe_tp, type, c_PNoLe: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 1.99/1.39 thf(c_PNo_downc_tp, type, c_PNo_downc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 1.99/1.39 thf(c_PNo_upc_tp, type, c_PNo_upc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 1.99/1.39 thf(c_SNoElts__tp, type, c_SNoElts_: ($i > $i)).
% 1.99/1.39 thf(c_SNo__tp, type, c_SNo_: ($i > ($i > $o))).
% 1.99/1.39 thf(c_PSNo_tp, type, c_PSNo: ($i > (($i > $o) > $i))).
% 1.99/1.39 thf(c_SNo_tp, type, c_SNo: ($i > $o)).
% 1.99/1.39 thf(c_SNoLev_tp, type, c_SNoLev: ($i > $i)).
% 1.99/1.39 thf(c_SNoEq__tp, type, c_SNoEq_: ($i > ($i > ($i > $o)))).
% 1.99/1.39 thf(c_SNoLt_tp, type, c_SNoLt: ($i > ($i > $o))).
% 1.99/1.39 thf(c_SNoLe_tp, type, c_SNoLe: ($i > ($i > $o))).
% 1.99/1.39 thf(c_binop_on_tp, type, c_binop_on: ($i > (($i > ($i > $i)) > $o))).
% 1.99/1.39 thf(c_Loop_tp, type, c_Loop: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > $o)))))).
% 1.99/1.39 thf(c_Loop_with_defs_tp, type, c_Loop_with_defs: ($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)) > $o))))))))))))))).
% 1.99/1.39 thf(c_Loop_with_defs_cex1_tp, type, c_Loop_with_defs_cex1: ($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)) > $o))))))))))))))).
% 1.99/1.39 thf(c_Loop_with_defs_cex2_tp, type, c_Loop_with_defs_cex2: ($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)) > $o))))))))))))))).
% 1.99/1.39 thf(c_combinator_tp, type, c_combinator: ($i > $o)).
% 1.99/1.39 thf(c_combinator_equiv_tp, type, c_combinator_equiv: ($i > ($i > $o))).
% 1.99/1.39 thf(c_equip_mod_tp, type, c_equip_mod: ($i > ($i > ($i > $o)))).
% 1.99/1.39 thf(ax1, axiom, (! [X0:($i > $o),X1:$i]: (((X0 @ X1) => (X0 @ (c_Eps_i @ X0)))))).
% 1.99/1.39 thf(ax2, axiom, (! [X0:$o]: (((c_not @ (c_not @ X0)) => X0)))).
% 1.99/1.39 thf(ax3, axiom, (! [X0:$o,X1:$o]: ((((c_iff @ X0) @ X1) => (X0 = X1))))).
% 1.99/1.39 thf(ax4, axiom, (! [X0:$i,X1:$i]: ((((c_Subq @ X0) @ X1) => (((c_Subq @ X1) @ X0) => (X0 = X1)))))).
% 1.99/1.39 thf(ax5, axiom, (c_not @ (? [X0:$i]: (((c_In @ X0) @ c_Empty))))).
% 1.99/1.39 thf(ax6, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ (? [X2:$i]: (((c_and @ ((c_In @ X1) @ X2)) @ ((c_In @ X2) @ X0)))))))).
% 1.99/1.39 thf(ax7, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))))).
% 1.99/1.39 thf(ax8, axiom, (! [X0:$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))))))))).
% 1.99/1.39 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))))))))))).
% 1.99/1.39 thf(ax10, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2)))) => (X0 @ X1)))) => (! [X1:$i]: ((X0 @ X1))))))).
% 1.99/1.39 thf(ax11, axiom, (c_False = (! [X0:$o]: (X0)))).
% 1.99/1.39 thf(ax12, axiom, (c_True = (! [X0:$o]: ((X0 => X0))))).
% 1.99/1.39 thf(ax13, axiom, (c_not = (^ [X0:$o]: ((X0 => c_False))))).
% 1.99/1.39 thf(ax14, axiom, (c_and = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => (X1 => X2)) => X2))))))).
% 1.99/1.39 thf(ax15, axiom, (c_or = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => X2) => ((X1 => X2) => X2)))))))).
% 1.99/1.39 thf(ax16, axiom, (c_iff = (^ [X0:$o,X1:$o]: (((c_and @ (X0 => X1)) @ (X1 => X0)))))).
% 1.99/1.39 thf(ax17, axiom, (c_Subq = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))))).
% 1.99/1.39 thf(ax18, axiom, (c_TransSet = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => ((c_Subq @ X1) @ X0)))))))).
% 1.99/1.39 thf(ax19, axiom, (c_atleast2 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_In @ X1) @ X0)) @ (c_not @ ((c_Subq @ X0) @ (c_Power @ X1)))))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 thf(ax24, axiom, (c_exactly2 = (^ [X0:$i]: (((c_and @ (c_atleast2 @ X0)) @ (c_not @ (c_atleast3 @ X0))))))).
% 1.99/1.39 thf(ax25, axiom, (c_exactly3 = (^ [X0:$i]: (((c_and @ (c_atleast3 @ X0)) @ (c_not @ (c_atleast4 @ X0))))))).
% 1.99/1.39 thf(ax26, axiom, (c_exactly4 = (^ [X0:$i]: (((c_and @ (c_atleast4 @ X0)) @ (c_not @ (c_atleast5 @ X0))))))).
% 1.99/1.39 thf(ax27, axiom, (c_exactly5 = (^ [X0:$i]: (((c_and @ (c_atleast5 @ X0)) @ (c_not @ (c_atleast6 @ X0))))))).
% 1.99/1.39 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)))))))))).
% 1.99/1.39 thf(ax29, axiom, (c_reflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: (((X0 @ X1) @ X1))))))).
% 1.99/1.39 thf(ax30, axiom, (c_irreflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: ((c_not @ ((X0 @ X1) @ X1)))))))).
% 1.99/1.39 thf(ax31, axiom, (c_symmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => ((X0 @ X2) @ X1)))))))).
% 1.99/1.39 thf(ax32, axiom, (c_antisymmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X1) => (X1 = X2))))))))).
% 1.99/1.39 thf(ax33, axiom, (c_transitive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i,X3:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X3) => ((X0 @ X1) @ X3))))))))).
% 1.99/1.39 thf(ax34, axiom, (c_eqreln_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_symmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 1.99/1.39 thf(ax35, axiom, (c_per_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_symmetric_i @ X0)) @ (c_transitive_i @ X0)))))).
% 1.99/1.39 thf(ax36, axiom, (c_linear_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((X0 @ X1) @ X2)) @ ((X0 @ X2) @ X1)))))))).
% 1.99/1.39 thf(ax37, axiom, (c_trichotomous_or_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((c_or @ ((X0 @ X1) @ X2)) @ (X1 = X2))) @ ((X0 @ X2) @ X1)))))))).
% 1.99/1.39 thf(ax38, axiom, (c_partialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_antisymmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 1.99/1.39 thf(ax39, axiom, (c_totalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_partialorder_i @ X0)) @ (c_linear_i @ X0)))))).
% 1.99/1.39 thf(ax40, axiom, (c_strictpartialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_irreflexive_i @ X0)) @ (c_transitive_i @ X0)))))).
% 1.99/1.39 thf(ax41, axiom, (c_stricttotalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_strictpartialorder_i @ X0)) @ (c_trichotomous_or_i @ X0)))))).
% 1.99/1.39 thf(ax42, axiom, (c_If_i = (^ [X0:$o,X1:$i,X2:$i]: ((c_Eps_i @ (^ [X3:$i]: (((c_or @ ((c_and @ X0) @ (X3 = X1))) @ ((c_and @ (c_not @ X0)) @ (X3 = X2)))))))))).
% 1.99/1.39 thf(ax43, axiom, (c_exactly1of2 = (^ [X0:$o,X1:$o]: (((c_or @ ((c_and @ X0) @ (c_not @ X1))) @ ((c_and @ (c_not @ X0)) @ X1)))))).
% 1.99/1.39 thf(ax44, axiom, (c_exactly1of3 = (^ [X0:$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)))))).
% 1.99/1.39 thf(ax45, axiom, (c_nIn = (^ [X0:$i,X1:$i]: ((c_not @ ((c_In @ X0) @ X1)))))).
% 1.99/1.39 thf(ax46, axiom, (c_nSubq = (^ [X0:$i,X1:$i]: ((c_not @ ((c_Subq @ X0) @ X1)))))).
% 1.99/1.39 thf(ax47, axiom, (c_UPair = (^ [X0:$i,X1:$i]: (((c_Repl @ (c_Power @ (c_Power @ c_Empty))) @ (^ [X2:$i]: ((((c_If_i @ ((c_In @ c_Empty) @ X2)) @ X0) @ X1)))))))).
% 1.99/1.39 thf(ax48, axiom, (c_Sing = (^ [X0:$i]: (((c_UPair @ X0) @ X0))))).
% 1.99/1.39 thf(ax49, axiom, (c_binunion = (^ [X0:$i,X1:$i]: ((c_Union @ ((c_UPair @ X0) @ X1)))))).
% 1.99/1.39 thf(ax50, axiom, (c_SetAdjoin = (^ [X0:$i,X1:$i]: (((c_binunion @ X0) @ (c_Sing @ X1)))))).
% 1.99/1.39 thf(ax51, axiom, (c_famunion = (^ [X0:$i,X1:($i > $i)]: ((c_Union @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 1.99/1.39 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:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ (X1 @ X4)))))))) @ X2))))) @ c_Empty))))).
% 1.99/1.39 thf(ax53, axiom, (c_ReplSep = (^ [X0:$i,X1:($i > $o),X2:($i > $i)]: (((c_Repl @ ((c_Sep @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: ((X2 @ X3)))))))).
% 1.99/1.39 thf(ax54, axiom, (c_binintersect = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 1.99/1.39 thf(ax55, axiom, (c_setminus = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_nIn @ X2) @ X1)))))))).
% 1.99/1.39 thf(ax56, axiom, (c_inj = (^ [X0:$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))))))))))))).
% 1.99/1.39 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:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ ((X2 @ X4) = X3)))))))))))).
% 1.99/1.39 thf(ax58, axiom, (c_atleastp = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_inj @ X0) @ X1) @ X2))))))).
% 1.99/1.39 thf(ax59, axiom, (c_equip = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_bij @ X0) @ X1) @ X2))))))).
% 1.99/1.39 thf(ax60, axiom, (c_In_rec_poly_G_i = (^ [X0:($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)))))))).
% 1.99/1.39 thf(ax61, axiom, (c_In_rec_poly_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i]: ((c_Eps_i @ (^ [X2:$i]: ((((c_In_rec_poly_G_i @ X0) @ X1) @ X2)))))))).
% 1.99/1.39 thf(ax62, axiom, (c_ordsucc = (^ [X0:$i]: (((c_binunion @ X0) @ (c_Sing @ X0)))))).
% 1.99/1.39 thf(ax63, axiom, (c_nat_p = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ c_Empty) => ((! [X2:$i]: (((X1 @ X2) => (X1 @ (c_ordsucc @ X2))))) => (X1 @ X0))))))))).
% 1.99/1.39 thf(ax64, axiom, (c_nat_primrec = (^ [X0:$i,X1:($i > ($i > $i))]: ((c_In_rec_poly_i @ (^ [X2:$i,X3:($i > $i)]: ((((c_If_i @ ((c_In @ (c_Union @ X2)) @ X2)) @ ((X1 @ (c_Union @ X2)) @ (X3 @ (c_Union @ X2)))) @ X0)))))))).
% 1.99/1.39 thf(ax65, axiom, (c_add_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ X0) @ (^ [X2:$i,X3:$i]: ((c_ordsucc @ X3)))) @ X1))))).
% 1.99/1.39 thf(ax66, axiom, (c_mul_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ c_Empty) @ (^ [X2:$i,X3:$i]: (((c_add_nat @ X0) @ X3)))) @ X1))))).
% 1.99/1.39 thf(ax67, axiom, (c_ordinal = (^ [X0:$i]: (((c_and @ (c_TransSet @ X0)) @ (! [X1:$i]: ((((c_In @ X1) @ X0) => (c_TransSet @ X1))))))))).
% 1.99/1.39 thf(ax68, axiom, (c_V_ = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: ((c_Power @ (X1 @ X2)))))))))).
% 1.99/1.39 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)))))))))).
% 1.99/1.39 thf(ax70, axiom, (c_Inj0 = (^ [X0:$i]: (((c_Repl @ X0) @ (^ [X1:$i]: ((c_Inj1 @ X1)))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 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))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 thf(ax74, axiom, (c_proj0 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj0 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 1.99/1.39 thf(ax75, axiom, (c_proj1 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj1 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 1.99/1.39 thf(ax76, axiom, (c_binrep = (^ [X0:$i,X1:$i]: (((c_setsum @ X0) @ (c_Power @ X1)))))).
% 1.99/1.39 thf(ax77, axiom, (c_lam = (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: (((c_Repl @ (X1 @ X2)) @ (^ [X3:$i]: (((c_setsum @ X2) @ X3))))))))))).
% 1.99/1.39 thf(ax78, axiom, (c_setprod = (^ [X0:$i,X1:$i]: (((c_lam @ X0) @ (^ [X2:$i]: (X1))))))).
% 1.99/1.39 thf(ax79, axiom, (c_ap = (^ [X0:$i,X1:$i]: ((((c_ReplSep @ X0) @ (^ [X2:$i]: ((? [X3:$i]: ((X2 = ((c_setsum @ X1) @ X3))))))) @ (^ [X2:$i]: ((c_proj1 @ X2)))))))).
% 1.99/1.39 thf(ax80, axiom, (c_setsum_p = (^ [X0:$i]: ((((c_setsum @ ((c_ap @ X0) @ c_Empty)) @ ((c_ap @ X0) @ (c_ordsucc @ c_Empty))) = X0))))).
% 1.99/1.39 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:$i]: ((X2 = ((c_setsum @ X3) @ X4)))))))))))))).
% 1.99/1.39 thf(ax82, axiom, (c_Pi = (^ [X0:$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)))))))))))).
% 1.99/1.39 thf(ax83, axiom, (c_setexp = (^ [X0:$i,X1:$i]: (((c_Pi @ X1) @ (^ [X2:$i]: (X0))))))).
% 1.99/1.39 thf(ax84, axiom, (c_Sep2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $o))]: (((c_Sep @ ((c_lam @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: (((X2 @ ((c_ap @ X3) @ c_Empty)) @ ((c_ap @ X3) @ (c_ordsucc @ c_Empty)))))))))).
% 1.99/1.39 thf(ax85, axiom, (c_set_of_pairs = (^ [X0:$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)))))))))))))).
% 1.99/1.39 thf(ax86, axiom, (c_lam2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $i))]: (((c_lam @ X0) @ (^ [X3:$i]: (((c_lam @ (X1 @ X3)) @ (^ [X4:$i]: (((X2 @ X3) @ X4))))))))))).
% 1.99/1.39 thf(ax87, axiom, (c_PNoEq_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_iff @ (X1 @ X3)) @ (X2 @ X3))))))))).
% 1.99/1.39 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))))))))).
% 1.99/1.39 thf(ax89, axiom, (c_PNoLt = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((c_or @ (((c_PNoLt_ @ ((c_binintersect @ X0) @ X2)) @ X1) @ X3)) @ ((c_and @ ((c_and @ ((c_In @ X0) @ X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))) @ (X3 @ X0)))) @ ((c_and @ ((c_and @ ((c_In @ X2) @ X0)) @ (((c_PNoEq_ @ X2) @ X1) @ X3))) @ (c_not @ (X1 @ X2)))))))).
% 1.99/1.39 thf(ax90, axiom, (c_PNoLe = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((((c_PNoLt @ X0) @ X1) @ X2) @ X3)) @ ((c_and @ (X0 = X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))))))).
% 1.99/1.39 thf(ax91, axiom, (c_PNo_downc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X1) @ X2) @ X3) @ X4))))))))))).
% 1.99/1.39 thf(ax92, axiom, (c_PNo_upc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X3) @ X4) @ X1) @ X2))))))))))).
% 1.99/1.39 thf(ax93, axiom, (c_SNoElts_ = (^ [X0:$i]: (((c_binunion @ X0) @ ((c_Repl @ X0) @ (^ [X1:$i]: (((^ [X2:$i]: (((c_SetAdjoin @ X2) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))).
% 1.99/1.39 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)))))))))).
% 1.99/1.39 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:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2))))))))).
% 1.99/1.39 thf(ax96, axiom, (c_SNo = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0)))))))).
% 1.99/1.39 thf(ax97, axiom, (c_SNoLev = (^ [X0:$i]: ((c_Eps_i @ (^ [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0))))))))).
% 1.99/1.39 thf(ax98, axiom, (c_SNoEq_ = (^ [X0:$i,X1:$i,X2:$i]: ((((c_PNoEq_ @ X0) @ (^ [X3:$i]: (((c_In @ X3) @ X1)))) @ (^ [X3:$i]: (((c_In @ X3) @ X2)))))))).
% 1.99/1.39 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)))))))).
% 1.99/1.39 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)))))))).
% 1.99/1.39 thf(ax101, axiom, (c_binop_on = (^ [X0:$i,X1:($i > ($i > $i))]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((X1 @ X2) @ X3)) @ X0))))))))))).
% 1.99/1.39 thf(ax102, axiom, (c_Loop = (^ [X0:$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:$i]: ((((c_In @ X6) @ X0) => ((c_and @ ((c_and @ ((c_and @ (((X2 @ X5) @ ((X1 @ X5) @ X6)) = X6)) @ (((X1 @ X5) @ ((X2 @ X5) @ X6)) = X6))) @ (((X3 @ ((X1 @ X5) @ X6)) @ X6) = X5))) @ (((X1 @ ((X3 @ X5) @ X6)) @ X6) = X5))))))))))))).
% 1.99/1.39 thf(ax103, axiom, (c_Loop_with_defs = (^ [X0:$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:$i]: ((((c_In @ X16) @ X0) => ((c_and @ ((((X8 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X15) @ ((X1 @ X14) @ X16))))) @ ((((X9 @ X14) @ X15) @ X16) = ((X3 @ ((X1 @ ((X1 @ X16) @ X14)) @ X15)) @ ((X1 @ X14) @ X15)))))))))))))))))).
% 1.99/1.39 thf(ax104, axiom, (c_Loop_with_defs_cex1 = (^ [X0:$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:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (c_not @ (((X5 @ ((X1 @ ((X2 @ (((X8 @ X15) @ X16) @ X14)) @ X4)) @ X14)) @ X17) = X4))))))))))))))))))).
% 1.99/1.39 thf(ax105, axiom, (c_Loop_with_defs_cex2 = (^ [X0:$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)))))))))))))))))))))).
% 1.99/1.39 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:$i]: (((X1 @ X2) => ((X1 @ X3) => (X1 @ (c_Inj1 @ ((c_setsum @ X2) @ X3))))))) => (X1 @ X0)))))))))).
% 1.99/1.39 thf(ax107, axiom, (c_combinator_equiv = (^ [X0:$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:$i]: ((c_Inj1 @ ((c_setsum @ X3) @ X4))))))))))).
% 1.99/1.39 thf(ax108, axiom, (c_equip_mod = (^ [X0:$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))))))))).
% 1.99/1.39 thf(conj, conjecture, (c_not @ (! [X0:($i > $o),X1:($i > $i)]: (((c_and @ (((X0 @ (X1 @ ((c_binintersect @ (X1 @ (c_Power @ c_Empty))) @ (X1 @ ((c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty)))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => (! [X2:$i]: ((((c_In @ X2) @ c_Empty) => (? [X3:$i]: (((c_and @ ((c_Subq @ X3) @ X2)) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))))))) => (? [X2:$i]: (((c_and @ (? [X3:$i]: (((c_and @ ((c_Subq @ X3) @ X2)) @ ((X2 = (X1 @ X2)) => (? [X4:$i]: (((c_and @ ((c_Subq @ X4) @ X2)) @ (c_not @ (X0 @ ((c_setprod @ X3) @ ((c_binrep @ (c_Power @ ((c_binrep @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty)))))))))))))) @ (c_not @ (c_SNo @ X2))))))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ ((c_binrep @ ((c_binrep @ (c_Power @ ((c_binrep @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))) @ (c_Power @ c_Empty))) @ c_Empty))))))))))).
% 1.99/1.39 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2DTF2340.p
% 1.99/1.39 ------------------------
% 2.28/1.41 ---- Cleaned THF ---
% 2.28/1.41 thf(c_Eps_i_tp,type,
% 2.28/1.41 c_Eps_i: ( $i > $o ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_False_tp,type,
% 2.28/1.41 c_False: $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_True_tp,type,
% 2.28/1.41 c_True: $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_not_tp,type,
% 2.28/1.41 c_not: $o > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_and_tp,type,
% 2.28/1.41 c_and: $o > $o > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_or_tp,type,
% 2.28/1.41 c_or: $o > $o > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_iff_tp,type,
% 2.28/1.41 c_iff: $o > $o > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_In_tp,type,
% 2.28/1.41 c_In: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_Subq_tp,type,
% 2.28/1.41 c_Subq: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_Empty_tp,type,
% 2.28/1.41 c_Empty: $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Union_tp,type,
% 2.28/1.41 c_Union: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Power_tp,type,
% 2.28/1.41 c_Power: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Repl_tp,type,
% 2.28/1.41 c_Repl: $i > ( $i > $i ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_TransSet_tp,type,
% 2.28/1.41 c_TransSet: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_atleast2_tp,type,
% 2.28/1.41 c_atleast2: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_atleast3_tp,type,
% 2.28/1.41 c_atleast3: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_atleast4_tp,type,
% 2.28/1.41 c_atleast4: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_atleast5_tp,type,
% 2.28/1.41 c_atleast5: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_atleast6_tp,type,
% 2.28/1.41 c_atleast6: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_exactly2_tp,type,
% 2.28/1.41 c_exactly2: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_exactly3_tp,type,
% 2.28/1.41 c_exactly3: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_exactly4_tp,type,
% 2.28/1.41 c_exactly4: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_exactly5_tp,type,
% 2.28/1.41 c_exactly5: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_exu_i_tp,type,
% 2.28/1.41 c_exu_i: ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_reflexive_i_tp,type,
% 2.28/1.41 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_irreflexive_i_tp,type,
% 2.28/1.41 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_symmetric_i_tp,type,
% 2.28/1.41 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_antisymmetric_i_tp,type,
% 2.28/1.41 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_transitive_i_tp,type,
% 2.28/1.41 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_eqreln_i_tp,type,
% 2.28/1.41 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_per_i_tp,type,
% 2.28/1.41 c_per_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_linear_i_tp,type,
% 2.28/1.41 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_trichotomous_or_i_tp,type,
% 2.28/1.41 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_partialorder_i_tp,type,
% 2.28/1.41 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_totalorder_i_tp,type,
% 2.28/1.41 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_strictpartialorder_i_tp,type,
% 2.28/1.41 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_stricttotalorder_i_tp,type,
% 2.28/1.41 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_If_i_tp,type,
% 2.28/1.41 c_If_i: $o > $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_exactly1of2_tp,type,
% 2.28/1.41 c_exactly1of2: $o > $o > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_exactly1of3_tp,type,
% 2.28/1.41 c_exactly1of3: $o > $o > $o > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_nIn_tp,type,
% 2.28/1.41 c_nIn: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_nSubq_tp,type,
% 2.28/1.41 c_nSubq: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_UPair_tp,type,
% 2.28/1.41 c_UPair: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Sing_tp,type,
% 2.28/1.41 c_Sing: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_binunion_tp,type,
% 2.28/1.41 c_binunion: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_SetAdjoin_tp,type,
% 2.28/1.41 c_SetAdjoin: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_famunion_tp,type,
% 2.28/1.41 c_famunion: $i > ( $i > $i ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Sep_tp,type,
% 2.28/1.41 c_Sep: $i > ( $i > $o ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_ReplSep_tp,type,
% 2.28/1.41 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_binintersect_tp,type,
% 2.28/1.41 c_binintersect: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_setminus_tp,type,
% 2.28/1.41 c_setminus: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_inj_tp,type,
% 2.28/1.41 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_bij_tp,type,
% 2.28/1.41 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_atleastp_tp,type,
% 2.28/1.41 c_atleastp: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_equip_tp,type,
% 2.28/1.41 c_equip: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_In_rec_poly_G_i_tp,type,
% 2.28/1.41 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_In_rec_poly_i_tp,type,
% 2.28/1.41 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_ordsucc_tp,type,
% 2.28/1.41 c_ordsucc: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_nat_p_tp,type,
% 2.28/1.41 c_nat_p: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_nat_primrec_tp,type,
% 2.28/1.41 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_add_nat_tp,type,
% 2.28/1.41 c_add_nat: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_mul_nat_tp,type,
% 2.28/1.41 c_mul_nat: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_ordinal_tp,type,
% 2.28/1.41 c_ordinal: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_V__tp,type,
% 2.28/1.41 c_V_: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Inj1_tp,type,
% 2.28/1.41 c_Inj1: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Inj0_tp,type,
% 2.28/1.41 c_Inj0: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Unj_tp,type,
% 2.28/1.41 c_Unj: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_combine_funcs_tp,type,
% 2.28/1.41 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_setsum_tp,type,
% 2.28/1.41 c_setsum: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_proj0_tp,type,
% 2.28/1.41 c_proj0: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_proj1_tp,type,
% 2.28/1.41 c_proj1: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_binrep_tp,type,
% 2.28/1.41 c_binrep: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_lam_tp,type,
% 2.28/1.41 c_lam: $i > ( $i > $i ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_setprod_tp,type,
% 2.28/1.41 c_setprod: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_ap_tp,type,
% 2.28/1.41 c_ap: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_setsum_p_tp,type,
% 2.28/1.41 c_setsum_p: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_tuple_p_tp,type,
% 2.28/1.41 c_tuple_p: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_Pi_tp,type,
% 2.28/1.41 c_Pi: $i > ( $i > $i ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_setexp_tp,type,
% 2.28/1.41 c_setexp: $i > $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_Sep2_tp,type,
% 2.28/1.41 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_set_of_pairs_tp,type,
% 2.28/1.41 c_set_of_pairs: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_lam2_tp,type,
% 2.28/1.41 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_PNoEq__tp,type,
% 2.28/1.41 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_PNoLt__tp,type,
% 2.28/1.41 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_PNoLt_tp,type,
% 2.28/1.41 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_PNoLe_tp,type,
% 2.28/1.41 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_PNo_downc_tp,type,
% 2.28/1.41 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_PNo_upc_tp,type,
% 2.28/1.41 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNoElts__tp,type,
% 2.28/1.41 c_SNoElts_: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNo__tp,type,
% 2.28/1.41 c_SNo_: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_PSNo_tp,type,
% 2.28/1.41 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNo_tp,type,
% 2.28/1.41 c_SNo: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNoLev_tp,type,
% 2.28/1.41 c_SNoLev: $i > $i ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNoEq__tp,type,
% 2.28/1.41 c_SNoEq_: $i > $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNoLt_tp,type,
% 2.28/1.41 c_SNoLt: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_SNoLe_tp,type,
% 2.28/1.41 c_SNoLe: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_binop_on_tp,type,
% 2.28/1.41 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_Loop_tp,type,
% 2.28/1.41 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_Loop_with_defs_tp,type,
% 2.28/1.41 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 ).
% 2.28/1.41
% 2.28/1.41 thf(c_Loop_with_defs_cex1_tp,type,
% 2.28/1.41 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 ).
% 2.28/1.41
% 2.28/1.41 thf(c_Loop_with_defs_cex2_tp,type,
% 2.28/1.41 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 ).
% 2.28/1.41
% 2.28/1.41 thf(c_combinator_tp,type,
% 2.28/1.41 c_combinator: $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_combinator_equiv_tp,type,
% 2.28/1.41 c_combinator_equiv: $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(c_equip_mod_tp,type,
% 2.28/1.41 c_equip_mod: $i > $i > $i > $o ).
% 2.28/1.41
% 2.28/1.41 thf(ax1,axiom,
% 2.28/1.41 ! [X0: $i > $o,X1: $i] :
% 2.28/1.41 ( ( X0 @ X1 )
% 2.28/1.41 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax2,axiom,
% 2.28/1.41 ! [X0: $o] :
% 2.28/1.41 ( ( c_not @ ( c_not @ X0 ) )
% 2.28/1.41 => X0 ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax3,axiom,
% 2.28/1.41 ! [X0: $o,X1: $o] :
% 2.28/1.41 ( ( c_iff @ X0 @ X1 )
% 2.28/1.41 => ( X0 = X1 ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax4,axiom,
% 2.28/1.41 ! [X0: $i,X1: $i] :
% 2.28/1.41 ( ( c_Subq @ X0 @ X1 )
% 2.28/1.41 => ( ( c_Subq @ X1 @ X0 )
% 2.28/1.41 => ( X0 = X1 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax5,axiom,
% 2.28/1.41 ( c_not
% 2.28/1.41 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax6,axiom,
% 2.28/1.41 ! [X0: $i,X1: $i] :
% 2.28/1.41 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.28/1.41 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax7,axiom,
% 2.28/1.41 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax8,axiom,
% 2.28/1.41 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.28/1.41 ( c_iff
% 2.28/1.41 @ ( c_In @ X2
% 2.28/1.41 @ ( c_Repl @ X0
% 2.28/1.41 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.28/1.41 @ ? [X3: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X3 @ X0 )
% 2.28/1.41 @ ( X2
% 2.28/1.41 = ( X1 @ X3 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax9,axiom,
% 2.28/1.41 ! [X0: $i > $o] :
% 2.28/1.41 ( ! [X1: $i] :
% 2.28/1.41 ( ( X0 @ X1 )
% 2.28/1.41 => ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ X1 )
% 2.28/1.41 => ( X0 @ X2 ) ) )
% 2.28/1.41 => ( ( X0 @ c_Empty )
% 2.28/1.41 => ( ! [X1: $i] :
% 2.28/1.41 ( ( X0 @ X1 )
% 2.28/1.41 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.28/1.41 => ( ! [X1: $i] :
% 2.28/1.41 ( ( X0 @ X1 )
% 2.28/1.41 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.28/1.41 => ( ! [X1: $i] :
% 2.28/1.41 ( ( X0 @ X1 )
% 2.28/1.41 => ! [X2: $i > $i] :
% 2.28/1.41 ( ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X1 )
% 2.28/1.41 => ( X0 @ ( X2 @ X3 ) ) )
% 2.28/1.41 => ( X0
% 2.28/1.41 @ ( c_Repl @ X1
% 2.28/1.41 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.28/1.41 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax10,axiom,
% 2.28/1.41 ! [X0: $i > $o] :
% 2.28/1.41 ( ! [X1: $i] :
% 2.28/1.41 ( ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ X1 )
% 2.28/1.41 => ( X0 @ X2 ) )
% 2.28/1.41 => ( X0 @ X1 ) )
% 2.28/1.41 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax11,axiom,
% 2.28/1.41 ( c_False
% 2.28/1.41 = ( ! [X0: $o] : X0 ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax12,axiom,
% 2.28/1.41 ( c_True
% 2.28/1.41 = ( ! [X0: $o] :
% 2.28/1.41 ( X0
% 2.28/1.41 => X0 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax13,axiom,
% 2.28/1.41 ( c_not
% 2.28/1.41 = ( ^ [X0: $o] :
% 2.28/1.41 ( X0
% 2.28/1.41 => c_False ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax14,axiom,
% 2.28/1.41 ( c_and
% 2.28/1.41 = ( ^ [X0: $o,X1: $o] :
% 2.28/1.41 ! [X2: $o] :
% 2.28/1.41 ( ( X0
% 2.28/1.41 => ( X1
% 2.28/1.41 => X2 ) )
% 2.28/1.41 => X2 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax15,axiom,
% 2.28/1.41 ( c_or
% 2.28/1.41 = ( ^ [X0: $o,X1: $o] :
% 2.28/1.41 ! [X2: $o] :
% 2.28/1.41 ( ( X0
% 2.28/1.41 => X2 )
% 2.28/1.41 => ( ( X1
% 2.28/1.41 => X2 )
% 2.28/1.41 => X2 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax16,axiom,
% 2.28/1.41 ( c_iff
% 2.28/1.41 = ( ^ [X0: $o,X1: $o] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ( X0
% 2.28/1.41 => X1 )
% 2.28/1.41 @ ( X1
% 2.28/1.41 => X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax17,axiom,
% 2.28/1.41 ( c_Subq
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ X0 )
% 2.28/1.41 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax18,axiom,
% 2.28/1.41 ( c_TransSet
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ! [X1: $i] :
% 2.28/1.41 ( ( c_In @ X1 @ X0 )
% 2.28/1.41 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax19,axiom,
% 2.28/1.41 ( c_atleast2
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax20,axiom,
% 2.28/1.41 ( c_atleast3
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax21,axiom,
% 2.28/1.41 ( c_atleast4
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax22,axiom,
% 2.28/1.41 ( c_atleast5
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax23,axiom,
% 2.28/1.41 ( c_atleast6
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax24,axiom,
% 2.28/1.41 ( c_exactly2
% 2.28/1.41 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax25,axiom,
% 2.28/1.41 ( c_exactly3
% 2.28/1.41 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax26,axiom,
% 2.28/1.41 ( c_exactly4
% 2.28/1.41 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax27,axiom,
% 2.28/1.41 ( c_exactly5
% 2.28/1.41 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax28,axiom,
% 2.28/1.41 ( c_exu_i
% 2.28/1.41 = ( ^ [X0: $i > $o] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ? [X1: $i] : ( X0 @ X1 )
% 2.28/1.41 @ ! [X1: $i,X2: $i] :
% 2.28/1.41 ( ( X0 @ X1 )
% 2.28/1.41 => ( ( X0 @ X2 )
% 2.28/1.41 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax29,axiom,
% 2.28/1.41 ( c_reflexive_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax30,axiom,
% 2.28/1.41 ( c_irreflexive_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax31,axiom,
% 2.28/1.41 ( c_symmetric_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i,X2: $i] :
% 2.28/1.41 ( ( X0 @ X1 @ X2 )
% 2.28/1.41 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax32,axiom,
% 2.28/1.41 ( c_antisymmetric_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i,X2: $i] :
% 2.28/1.41 ( ( X0 @ X1 @ X2 )
% 2.28/1.41 => ( ( X0 @ X2 @ X1 )
% 2.28/1.41 => ( X1 = X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax33,axiom,
% 2.28/1.41 ( c_transitive_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i,X2: $i,X3: $i] :
% 2.28/1.41 ( ( X0 @ X1 @ X2 )
% 2.28/1.41 => ( ( X0 @ X2 @ X3 )
% 2.28/1.41 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax34,axiom,
% 2.28/1.41 ( c_eqreln_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax35,axiom,
% 2.28/1.41 ( c_per_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax36,axiom,
% 2.28/1.41 ( c_linear_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax37,axiom,
% 2.28/1.41 ( c_trichotomous_or_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] :
% 2.28/1.41 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax38,axiom,
% 2.28/1.41 ( c_partialorder_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax39,axiom,
% 2.28/1.41 ( c_totalorder_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax40,axiom,
% 2.28/1.41 ( c_strictpartialorder_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax41,axiom,
% 2.28/1.41 ( c_stricttotalorder_i
% 2.28/1.41 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax42,axiom,
% 2.28/1.41 ( c_If_i
% 2.28/1.41 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.28/1.41 ( c_Eps_i
% 2.28/1.41 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax43,axiom,
% 2.28/1.41 ( c_exactly1of2
% 2.28/1.41 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax44,axiom,
% 2.28/1.41 ( c_exactly1of3
% 2.28/1.41 = ( ^ [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 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax45,axiom,
% 2.28/1.41 ( c_nIn
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax46,axiom,
% 2.28/1.41 ( c_nSubq
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax47,axiom,
% 2.28/1.41 ( c_UPair
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.28/1.41 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax48,axiom,
% 2.28/1.41 ( c_Sing
% 2.28/1.41 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax49,axiom,
% 2.28/1.41 ( c_binunion
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax50,axiom,
% 2.28/1.41 ( c_SetAdjoin
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax51,axiom,
% 2.28/1.41 ( c_famunion
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i] :
% 2.28/1.41 ( c_Union
% 2.28/1.41 @ ( c_Repl @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax52,axiom,
% 2.28/1.41 ( c_Sep
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $o] :
% 2.28/1.41 ( c_If_i
% 2.28/1.41 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.28/1.41 @ ( c_Repl @ X0
% 2.28/1.41 @ ^ [X2: $i] :
% 2.28/1.41 ( ^ [X3: $i] :
% 2.28/1.41 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.28/1.41 @ ( c_Eps_i
% 2.28/1.41 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.28/1.41 @ X2 ) )
% 2.28/1.41 @ c_Empty ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax53,axiom,
% 2.28/1.41 ( c_ReplSep
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.28/1.41 ( c_Repl
% 2.28/1.41 @ ( c_Sep @ X0
% 2.28/1.41 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.28/1.41 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax54,axiom,
% 2.28/1.41 ( c_binintersect
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_Sep @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax55,axiom,
% 2.28/1.41 ( c_setminus
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_Sep @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax56,axiom,
% 2.28/1.41 ( c_inj
% 2.28/1.41 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X0 )
% 2.28/1.41 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.28/1.41 @ ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X0 )
% 2.28/1.41 => ! [X4: $i] :
% 2.28/1.41 ( ( c_In @ X4 @ X0 )
% 2.28/1.41 => ( ( ( X2 @ X3 )
% 2.28/1.41 = ( X2 @ X4 ) )
% 2.28/1.41 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax57,axiom,
% 2.28/1.41 ( c_bij
% 2.28/1.41 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.28/1.41 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.28/1.41 @ ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X1 )
% 2.28/1.41 => ? [X4: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X4 @ X0 )
% 2.28/1.41 @ ( ( X2 @ X4 )
% 2.28/1.41 = X3 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax58,axiom,
% 2.28/1.41 ( c_atleastp
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax59,axiom,
% 2.28/1.41 ( c_equip
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax60,axiom,
% 2.28/1.41 ( c_In_rec_poly_G_i
% 2.28/1.41 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.28/1.41 ! [X3: $i > $i > $o] :
% 2.28/1.41 ( ! [X4: $i,X5: $i > $i] :
% 2.28/1.41 ( ! [X6: $i] :
% 2.28/1.41 ( ( c_In @ X6 @ X4 )
% 2.28/1.41 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.28/1.41 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.28/1.41 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax61,axiom,
% 2.28/1.41 ( c_In_rec_poly_i
% 2.28/1.41 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.28/1.41 ( c_Eps_i
% 2.28/1.41 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax62,axiom,
% 2.28/1.41 ( c_ordsucc
% 2.28/1.41 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax63,axiom,
% 2.28/1.41 ( c_nat_p
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ! [X1: $i > $o] :
% 2.28/1.41 ( ( X1 @ c_Empty )
% 2.28/1.41 => ( ! [X2: $i] :
% 2.28/1.41 ( ( X1 @ X2 )
% 2.28/1.41 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.28/1.41 => ( X1 @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax64,axiom,
% 2.28/1.41 ( c_nat_primrec
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.28/1.41 ( c_In_rec_poly_i
% 2.28/1.41 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax65,axiom,
% 2.28/1.41 ( c_add_nat
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_nat_primrec @ X0
% 2.28/1.41 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.28/1.41 @ X1 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax66,axiom,
% 2.28/1.41 ( c_mul_nat
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_nat_primrec @ c_Empty
% 2.28/1.41 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.28/1.41 @ X1 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax67,axiom,
% 2.28/1.41 ( c_ordinal
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( c_and @ ( c_TransSet @ X0 )
% 2.28/1.41 @ ! [X1: $i] :
% 2.28/1.41 ( ( c_In @ X1 @ X0 )
% 2.28/1.41 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax68,axiom,
% 2.28/1.41 ( c_V_
% 2.28/1.41 = ( c_In_rec_poly_i
% 2.28/1.41 @ ^ [X0: $i,X1: $i > $i] :
% 2.28/1.41 ( c_famunion @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax69,axiom,
% 2.28/1.41 ( c_Inj1
% 2.28/1.41 = ( c_In_rec_poly_i
% 2.28/1.41 @ ^ [X0: $i,X1: $i > $i] :
% 2.28/1.41 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.28/1.41 @ ( c_Repl @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax70,axiom,
% 2.28/1.41 ( c_Inj0
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( c_Repl @ X0
% 2.28/1.41 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax71,axiom,
% 2.28/1.41 ( c_Unj
% 2.28/1.41 = ( c_In_rec_poly_i
% 2.28/1.41 @ ^ [X0: $i,X1: $i > $i] :
% 2.28/1.41 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.28/1.41 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax72,axiom,
% 2.28/1.41 ( c_combine_funcs
% 2.28/1.41 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.28/1.41 ( c_If_i
% 2.28/1.41 @ ( X4
% 2.28/1.41 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.28/1.41 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.28/1.41 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax73,axiom,
% 2.28/1.41 ( c_setsum
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_binunion
% 2.28/1.41 @ ( c_Repl @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.28/1.41 @ ( c_Repl @ X1
% 2.28/1.41 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax74,axiom,
% 2.28/1.41 ( c_proj0
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( c_ReplSep @ X0
% 2.28/1.41 @ ^ [X1: $i] :
% 2.28/1.41 ? [X2: $i] :
% 2.28/1.41 ( ( c_Inj0 @ X2 )
% 2.28/1.41 = X1 )
% 2.28/1.41 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax75,axiom,
% 2.28/1.41 ( c_proj1
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( c_ReplSep @ X0
% 2.28/1.41 @ ^ [X1: $i] :
% 2.28/1.41 ? [X2: $i] :
% 2.28/1.41 ( ( c_Inj1 @ X2 )
% 2.28/1.41 = X1 )
% 2.28/1.41 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax76,axiom,
% 2.28/1.41 ( c_binrep
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax77,axiom,
% 2.28/1.41 ( c_lam
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i] :
% 2.28/1.41 ( c_famunion @ X0
% 2.28/1.41 @ ^ [X2: $i] :
% 2.28/1.41 ( c_Repl @ ( X1 @ X2 )
% 2.28/1.41 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax78,axiom,
% 2.28/1.41 ( c_setprod
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_lam @ X0
% 2.28/1.41 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax79,axiom,
% 2.28/1.41 ( c_ap
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_ReplSep @ X0
% 2.28/1.41 @ ^ [X2: $i] :
% 2.28/1.41 ? [X3: $i] :
% 2.28/1.41 ( X2
% 2.28/1.41 = ( c_setsum @ X1 @ X3 ) )
% 2.28/1.41 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax80,axiom,
% 2.28/1.41 ( c_setsum_p
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.28/1.41 = X0 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax81,axiom,
% 2.28/1.41 ( c_tuple_p
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ X1 )
% 2.28/1.41 => ? [X3: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X3 @ X0 )
% 2.28/1.41 @ ? [X4: $i] :
% 2.28/1.41 ( X2
% 2.28/1.41 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax82,axiom,
% 2.28/1.41 ( c_Pi
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i] :
% 2.28/1.41 ( c_Sep
% 2.28/1.41 @ ( c_Power
% 2.28/1.41 @ ( c_lam @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.28/1.41 @ ^ [X2: $i] :
% 2.28/1.41 ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X0 )
% 2.28/1.41 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax83,axiom,
% 2.28/1.41 ( c_setexp
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_Pi @ X1
% 2.28/1.41 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax84,axiom,
% 2.28/1.41 ( c_Sep2
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.28/1.41 ( c_Sep
% 2.28/1.41 @ ( c_lam @ X0
% 2.28/1.41 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.28/1.41 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax85,axiom,
% 2.28/1.41 ( c_set_of_pairs
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ! [X1: $i] :
% 2.28/1.41 ( ( c_In @ X1 @ X0 )
% 2.28/1.41 => ? [X2: $i,X3: $i] :
% 2.28/1.41 ( X1
% 2.28/1.41 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.28/1.41 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax86,axiom,
% 2.28/1.41 ( c_lam2
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.28/1.41 ( c_lam @ X0
% 2.28/1.41 @ ^ [X3: $i] :
% 2.28/1.41 ( c_lam @ ( X1 @ X3 )
% 2.28/1.41 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax87,axiom,
% 2.28/1.41 ( c_PNoEq_
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.28/1.41 ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X0 )
% 2.28/1.41 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax88,axiom,
% 2.28/1.41 ( c_PNoLt_
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.28/1.41 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax89,axiom,
% 2.28/1.41 ( c_PNoLt
% 2.28/1.41 = ( ^ [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 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax90,axiom,
% 2.28/1.41 ( c_PNoLe
% 2.28/1.41 = ( ^ [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 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax91,axiom,
% 2.28/1.41 ( c_PNo_downc
% 2.28/1.41 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.28/1.41 ? [X3: $i] :
% 2.28/1.41 ( c_and @ ( c_ordinal @ X3 )
% 2.28/1.41 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax92,axiom,
% 2.28/1.41 ( c_PNo_upc
% 2.28/1.41 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.28/1.41 ? [X3: $i] :
% 2.28/1.41 ( c_and @ ( c_ordinal @ X3 )
% 2.28/1.41 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax93,axiom,
% 2.28/1.41 ( c_SNoElts_
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( c_binunion @ X0
% 2.28/1.41 @ ( c_Repl @ X0
% 2.28/1.41 @ ^ [X1: $i] :
% 2.28/1.41 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.28/1.41 @ X1 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax94,axiom,
% 2.28/1.41 ( c_SNo_
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.28/1.41 @ ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ X0 )
% 2.28/1.41 => ( c_exactly1of2
% 2.28/1.41 @ ( c_In
% 2.28/1.41 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.28/1.41 @ X2 )
% 2.28/1.41 @ X1 )
% 2.28/1.41 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax95,axiom,
% 2.28/1.41 ( c_PSNo
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $o] :
% 2.28/1.41 ( c_binunion
% 2.28/1.41 @ ( c_Sep @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.28/1.41 @ ( c_ReplSep @ X0
% 2.28/1.41 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.28/1.41 @ ^ [X2: $i] :
% 2.28/1.41 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.28/1.41 @ X2 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax96,axiom,
% 2.28/1.41 ( c_SNo
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax97,axiom,
% 2.28/1.41 ( c_SNoLev
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ( c_Eps_i
% 2.28/1.41 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax98,axiom,
% 2.28/1.41 ( c_SNoEq_
% 2.28/1.41 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.28/1.41 ( c_PNoEq_ @ X0
% 2.28/1.41 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.28/1.41 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax99,axiom,
% 2.28/1.41 ( c_SNoLt
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.28/1.41 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.28/1.41 @ ( c_SNoLev @ X1 )
% 2.28/1.41 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax100,axiom,
% 2.28/1.41 ( c_SNoLe
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.28/1.41 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.28/1.41 @ ( c_SNoLev @ X1 )
% 2.28/1.41 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax101,axiom,
% 2.28/1.41 ( c_binop_on
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.28/1.41 ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ X0 )
% 2.28/1.41 => ! [X3: $i] :
% 2.28/1.41 ( ( c_In @ X3 @ X0 )
% 2.28/1.41 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax102,axiom,
% 2.28/1.41 ( c_Loop
% 2.28/1.41 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.28/1.41 @ ! [X5: $i] :
% 2.28/1.41 ( ( c_In @ X5 @ X0 )
% 2.28/1.41 => ( c_and
% 2.28/1.41 @ ( ( X1 @ X4 @ X5 )
% 2.28/1.41 = X5 )
% 2.28/1.41 @ ( ( X1 @ X5 @ X4 )
% 2.28/1.41 = X5 ) ) ) )
% 2.28/1.41 @ ! [X5: $i] :
% 2.28/1.41 ( ( c_In @ X5 @ X0 )
% 2.28/1.41 => ! [X6: $i] :
% 2.28/1.41 ( ( c_In @ X6 @ X0 )
% 2.28/1.41 => ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.28/1.41 = X6 )
% 2.28/1.41 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.28/1.41 = X6 ) )
% 2.28/1.41 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.28/1.41 = X5 ) )
% 2.28/1.41 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.28/1.41 = X5 ) ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax103,axiom,
% 2.28/1.41 ( c_Loop_with_defs
% 2.28/1.41 = ( ^ [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] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.28/1.41 @ ! [X14: $i] :
% 2.28/1.41 ( ( c_In @ X14 @ X0 )
% 2.28/1.41 => ! [X15: $i] :
% 2.28/1.41 ( ( c_In @ X15 @ X0 )
% 2.28/1.41 => ( ( X5 @ X14 @ X15 )
% 2.28/1.41 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.28/1.41 @ ! [X14: $i] :
% 2.28/1.41 ( ( c_In @ X14 @ X0 )
% 2.28/1.41 => ! [X15: $i] :
% 2.28/1.41 ( ( c_In @ X15 @ X0 )
% 2.28/1.41 => ! [X16: $i] :
% 2.28/1.41 ( ( c_In @ X16 @ X0 )
% 2.28/1.41 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.28/1.41 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.28/1.41 @ ! [X14: $i] :
% 2.28/1.41 ( ( c_In @ X14 @ X0 )
% 2.28/1.41 => ! [X15: $i] :
% 2.28/1.41 ( ( c_In @ X15 @ X0 )
% 2.28/1.41 => ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( c_and
% 2.28/1.41 @ ( ( X7 @ X14 @ X15 )
% 2.28/1.41 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.28/1.41 @ ( ( X10 @ X14 @ X15 )
% 2.28/1.41 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.28/1.41 @ ( ( X11 @ X14 @ X15 )
% 2.28/1.41 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.28/1.41 @ ( ( X12 @ X14 @ X15 )
% 2.28/1.41 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.28/1.41 @ ( ( X13 @ X14 @ X15 )
% 2.28/1.41 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.28/1.41 @ ! [X14: $i] :
% 2.28/1.41 ( ( c_In @ X14 @ X0 )
% 2.28/1.41 => ! [X15: $i] :
% 2.28/1.41 ( ( c_In @ X15 @ X0 )
% 2.28/1.41 => ! [X16: $i] :
% 2.28/1.41 ( ( c_In @ X16 @ X0 )
% 2.28/1.41 => ( c_and
% 2.28/1.41 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.28/1.41 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.28/1.41 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.28/1.41 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax104,axiom,
% 2.28/1.41 ( c_Loop_with_defs_cex1
% 2.28/1.41 = ( ^ [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] :
% 2.28/1.41 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.28/1.41 @ ? [X14: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X14 @ X0 )
% 2.28/1.41 @ ? [X15: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X15 @ X0 )
% 2.28/1.41 @ ? [X16: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X16 @ X0 )
% 2.28/1.41 @ ? [X17: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X17 @ X0 )
% 2.28/1.41 @ ( c_not
% 2.28/1.41 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.28/1.41 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax105,axiom,
% 2.28/1.41 ( c_Loop_with_defs_cex2
% 2.28/1.41 = ( ^ [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] :
% 2.28/1.41 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.28/1.41 @ ? [X14: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X14 @ X0 )
% 2.28/1.41 @ ? [X15: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X15 @ X0 )
% 2.28/1.41 @ ? [X16: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X16 @ X0 )
% 2.28/1.41 @ ? [X17: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X17 @ X0 )
% 2.28/1.41 @ ? [X18: $i] :
% 2.28/1.41 ( c_and @ ( c_In @ X18 @ X0 )
% 2.28/1.41 @ ( c_not
% 2.28/1.41 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.28/1.41 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax106,axiom,
% 2.28/1.41 ( c_combinator
% 2.28/1.41 = ( ^ [X0: $i] :
% 2.28/1.41 ! [X1: $i > $o] :
% 2.28/1.41 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.28/1.41 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.28/1.41 => ( ! [X2: $i,X3: $i] :
% 2.28/1.41 ( ( X1 @ X2 )
% 2.28/1.41 => ( ( X1 @ X3 )
% 2.28/1.41 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.28/1.41 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax107,axiom,
% 2.28/1.41 ( c_combinator_equiv
% 2.28/1.41 = ( ^ [X0: $i,X1: $i] :
% 2.28/1.41 ! [X2: $i > $i > $o] :
% 2.28/1.41 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.28/1.41 ( ( c_per_i @ X2 )
% 2.28/1.41 => ( ! [X6: $i] :
% 2.28/1.41 ( ( c_combinator @ X6 )
% 2.28/1.41 => ( X2 @ X6 @ X6 ) )
% 2.28/1.41 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.28/1.41 ( ( c_combinator @ X6 )
% 2.28/1.41 => ( ( c_combinator @ X7 )
% 2.28/1.41 => ( ( c_combinator @ X8 )
% 2.28/1.41 => ( ( c_combinator @ X9 )
% 2.28/1.41 => ( ( X2 @ X6 @ X8 )
% 2.28/1.41 => ( ( X2 @ X7 @ X9 )
% 2.28/1.41 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.28/1.41 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.28/1.41 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.28/1.41 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.28/1.41 @ ( c_Inj0 @ c_Empty )
% 2.28/1.41 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.28/1.41 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(ax108,axiom,
% 2.28/1.41 ( c_equip_mod
% 2.28/1.41 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.28/1.41 ? [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 ) ) ) ) ) ).
% 2.28/1.41
% 2.28/1.41 thf(conj,conjecture,
% 2.28/1.41 ( c_not
% 2.28/1.41 @ ! [X0: $i > $o,X1: $i > $i] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ( ( ( X0 @ ( X1 @ ( c_binintersect @ ( X1 @ ( c_Power @ c_Empty ) ) @ ( X1 @ ( c_binrep @ ( c_Power @ ( c_Power @ ( c_Power @ c_Empty ) ) ) @ c_Empty ) ) ) ) )
% 2.28/1.41 => ( ( c_TransSet @ ( X1 @ c_Empty ) )
% 2.28/1.41 => ! [X2: $i] :
% 2.28/1.41 ( ( c_In @ X2 @ c_Empty )
% 2.28/1.41 => ? [X3: $i] : ( c_and @ ( c_Subq @ X3 @ X2 ) @ ( c_exactly2 @ ( c_ordsucc @ ( X1 @ X3 ) ) ) ) ) ) )
% 2.28/1.41 => ? [X2: $i] :
% 2.28/1.41 ( c_and
% 2.28/1.41 @ ? [X3: $i] :
% 2.28/1.41 ( c_and @ ( c_Subq @ X3 @ X2 )
% 2.28/1.41 @ ( ( X2
% 2.28/1.41 = ( X1 @ X2 ) )
% 2.28/1.41 => ? [X4: $i] : ( c_and @ ( c_Subq @ X4 @ X2 ) @ ( c_not @ ( X0 @ ( c_setprod @ X3 @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ ( c_Power @ c_Empty ) ) ) ) ) ) ) ) )
% 2.28/1.41 @ ( c_not @ ( c_SNo @ X2 ) ) ) )
% 2.28/1.41 @ ( c_not @ ( X0 @ ( X1 @ ( X1 @ ( X1 @ ( c_binrep @ ( c_binrep @ ( c_Power @ ( c_binrep @ ( c_Power @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) @ ( c_Power @ c_Empty ) ) @ c_Empty ) ) ) ) ) ) ) ) ).
% 2.28/1.41 ------------------------
% 2.28/1.43 % (2618)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/183Mi)
% 2.28/1.43 % (2619)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_2340 for (2999ds/4Mi)
% 2.28/1.43 % (2621)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/2Mi)
% 2.28/1.43 % (2621)Instruction limit reached!
% 2.28/1.43 % (2621)------------------------------
% 2.28/1.43 % (2621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.43 % (2621)Termination reason: Unknown
% 2.28/1.43 % (2621)Termination phase: shuffling
% 2.28/1.43
% 2.28/1.43 % (2621)Memory used [KB]: 1279
% 2.28/1.43 % (2621)Time elapsed: 0.002 s
% 2.28/1.43 % (2621)Instructions burned: 3 (million)
% 2.28/1.43 % (2621)------------------------------
% 2.28/1.43 % (2621)------------------------------
% 2.28/1.43 % (2619)Instruction limit reached!
% 2.28/1.43 % (2619)------------------------------
% 2.28/1.43 % (2619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.43 % (2619)Termination reason: Unknown
% 2.28/1.43 % (2619)Termination phase: shuffling
% 2.28/1.43
% 2.28/1.43 % (2619)Memory used [KB]: 1279
% 2.28/1.43 % (2619)Time elapsed: 0.003 s
% 2.28/1.43 % (2619)Instructions burned: 6 (million)
% 2.28/1.43 % (2619)------------------------------
% 2.28/1.43 % (2619)------------------------------
% 2.28/1.43 % (2620)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_2340 for (2999ds/27Mi)
% 2.28/1.43 % (2622)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_2340 for (2999ds/2Mi)
% 2.28/1.43 % (2624)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/18Mi)
% 2.28/1.43 % (2623)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_2340 for (2999ds/275Mi)
% 2.28/1.44 % (2622)Instruction limit reached!
% 2.28/1.44 % (2622)------------------------------
% 2.28/1.44 % (2622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.44 % (2622)Termination reason: Unknown
% 2.28/1.44 % (2622)Termination phase: shuffling
% 2.28/1.44
% 2.28/1.44 % (2622)Memory used [KB]: 1151
% 2.28/1.44 % (2622)Time elapsed: 0.004 s
% 2.28/1.44 % (2622)Instructions burned: 3 (million)
% 2.28/1.44 % (2622)------------------------------
% 2.28/1.44 % (2622)------------------------------
% 2.28/1.44 % (2625)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/3Mi)
% 2.28/1.44 % (2626)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_2340 for (2999ds/37Mi)
% 2.28/1.44 % (2625)Instruction limit reached!
% 2.28/1.44 % (2625)------------------------------
% 2.28/1.44 % (2625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.44 % (2625)Termination reason: Unknown
% 2.28/1.44 % (2625)Termination phase: shuffling
% 2.28/1.44
% 2.28/1.44 % (2625)Memory used [KB]: 1279
% 2.28/1.44 % (2625)Time elapsed: 0.003 s
% 2.28/1.44 % (2625)Instructions burned: 4 (million)
% 2.28/1.44 % (2625)------------------------------
% 2.28/1.44 % (2625)------------------------------
% 2.28/1.44 % (2624)Instruction limit reached!
% 2.28/1.44 % (2624)------------------------------
% 2.28/1.44 % (2624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.44 % (2624)Termination reason: Unknown
% 2.28/1.44 % (2624)Termination phase: Property scanning
% 2.28/1.44
% 2.28/1.44 % (2624)Memory used [KB]: 1535
% 2.28/1.44 % (2624)Time elapsed: 0.012 s
% 2.28/1.44 % (2624)Instructions burned: 19 (million)
% 2.28/1.44 % (2624)------------------------------
% 2.28/1.44 % (2624)------------------------------
% 2.28/1.45 % (2620)Instruction limit reached!
% 2.28/1.45 % (2620)------------------------------
% 2.28/1.45 % (2620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.45 % (2620)Termination reason: Unknown
% 2.28/1.45 % (2620)Termination phase: Preprocessing 1
% 2.28/1.45
% 2.28/1.45 % (2620)Memory used [KB]: 1535
% 2.28/1.45 % (2620)Time elapsed: 0.016 s
% 2.28/1.45 % (2620)Instructions burned: 28 (million)
% 2.28/1.45 % (2620)------------------------------
% 2.28/1.45 % (2620)------------------------------
% 2.28/1.45 % (2626)Instruction limit reached!
% 2.28/1.45 % (2626)------------------------------
% 2.28/1.45 % (2626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.45 % (2626)Termination reason: Unknown
% 2.28/1.45 % (2626)Termination phase: Property scanning
% 2.28/1.45
% 2.28/1.45 % (2626)Memory used [KB]: 1535
% 2.28/1.45 % (2626)Time elapsed: 0.012 s
% 2.28/1.45 % (2626)Instructions burned: 37 (million)
% 2.28/1.45 % (2626)------------------------------
% 2.28/1.45 % (2626)------------------------------
% 2.28/1.45 % (2628)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_2340 for (2999ds/3Mi)
% 2.28/1.45 % (2628)Instruction limit reached!
% 2.28/1.45 % (2628)------------------------------
% 2.28/1.45 % (2628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.45 % (2628)Termination reason: Unknown
% 2.28/1.45 % (2628)Termination phase: shuffling
% 2.28/1.45
% 2.28/1.45 % (2628)Memory used [KB]: 1279
% 2.28/1.45 % (2628)Time elapsed: 0.003 s
% 2.28/1.45 % (2628)Instructions burned: 4 (million)
% 2.28/1.45 % (2628)------------------------------
% 2.28/1.45 % (2628)------------------------------
% 2.28/1.45 % (2627)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_2340 for (2999ds/15Mi)
% 2.28/1.46 % (2623)Refutation not found, incomplete strategy
% 2.28/1.46 % (2623)------------------------------
% 2.28/1.46 % (2623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.46 % (2623)Termination reason: Refutation not found, incomplete strategy
% 2.28/1.46
% 2.28/1.46
% 2.28/1.46 % (2623)Memory used [KB]: 6140
% 2.28/1.46 % (2623)Time elapsed: 0.024 s
% 2.28/1.46 % (2623)Instructions burned: 43 (million)
% 2.28/1.46 % (2623)------------------------------
% 2.28/1.46 % (2623)------------------------------
% 2.28/1.46 % (2631)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/16Mi)
% 2.28/1.46 % (2632)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_2340 for (2999ds/3Mi)
% 2.28/1.46 % (2627)Instruction limit reached!
% 2.28/1.46 % (2627)------------------------------
% 2.28/1.46 % (2627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.46 % (2627)Termination reason: Unknown
% 2.28/1.46 % (2627)Termination phase: shuffling
% 2.28/1.46
% 2.28/1.46 % (2627)Memory used [KB]: 1535
% 2.28/1.46 % (2627)Time elapsed: 0.010 s
% 2.28/1.46 % (2627)Instructions burned: 16 (million)
% 2.28/1.46 % (2627)------------------------------
% 2.28/1.46 % (2627)------------------------------
% 2.28/1.46 % (2629)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_2340 for (2999ds/1041Mi)
% 2.28/1.46 % (2632)Instruction limit reached!
% 2.28/1.46 % (2632)------------------------------
% 2.28/1.46 % (2632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.46 % (2632)Termination reason: Unknown
% 2.28/1.46 % (2632)Termination phase: shuffling
% 2.28/1.46
% 2.28/1.46 % (2632)Memory used [KB]: 1279
% 2.28/1.46 % (2632)Time elapsed: 0.003 s
% 2.28/1.46 % (2632)Instructions burned: 4 (million)
% 2.28/1.46 % (2632)------------------------------
% 2.28/1.46 % (2632)------------------------------
% 2.28/1.46 % (2631)Instruction limit reached!
% 2.28/1.46 % (2631)------------------------------
% 2.28/1.46 % (2631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.46 % (2631)Termination reason: Unknown
% 2.28/1.46 % (2631)Termination phase: shuffling
% 2.28/1.46
% 2.28/1.46 % (2631)Memory used [KB]: 1535
% 2.28/1.46 % (2631)Time elapsed: 0.007 s
% 2.28/1.46 % (2631)Instructions burned: 18 (million)
% 2.28/1.46 % (2631)------------------------------
% 2.28/1.46 % (2631)------------------------------
% 2.28/1.46 % (2630)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/7Mi)
% 2.28/1.47 % (2630)Instruction limit reached!
% 2.28/1.47 % (2630)------------------------------
% 2.28/1.47 % (2630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.47 % (2630)Termination reason: Unknown
% 2.28/1.47 % (2630)Termination phase: shuffling
% 2.28/1.47
% 2.28/1.47 % (2630)Memory used [KB]: 1279
% 2.28/1.47 % (2630)Time elapsed: 0.006 s
% 2.28/1.47 % (2630)Instructions burned: 8 (million)
% 2.28/1.47 % (2630)------------------------------
% 2.28/1.47 % (2630)------------------------------
% 2.28/1.47 % (2618)Instruction limit reached!
% 2.28/1.47 % (2618)------------------------------
% 2.28/1.47 % (2618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.47 % (2618)Termination reason: Unknown
% 2.28/1.47 % (2618)Termination phase: Saturation
% 2.28/1.47
% 2.28/1.47 % (2618)Memory used [KB]: 6780
% 2.28/1.47 % (2618)Time elapsed: 0.047 s
% 2.28/1.47 % (2618)Instructions burned: 186 (million)
% 2.28/1.47 % (2618)------------------------------
% 2.28/1.47 % (2618)------------------------------
% 2.28/1.47 % (2635)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/3Mi)
% 2.28/1.47 % (2635)Instruction limit reached!
% 2.28/1.47 % (2635)------------------------------
% 2.28/1.47 % (2635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.47 % (2635)Termination reason: Unknown
% 2.28/1.47 % (2635)Termination phase: shuffling
% 2.28/1.47
% 2.28/1.47 % (2635)Memory used [KB]: 1279
% 2.28/1.47 % (2635)Time elapsed: 0.003 s
% 2.28/1.47 % (2635)Instructions burned: 5 (million)
% 2.28/1.47 % (2635)------------------------------
% 2.28/1.47 % (2635)------------------------------
% 2.28/1.47 % (2636)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/4Mi)
% 2.28/1.47 % (2633)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_2340 for (2999ds/3Mi)
% 2.28/1.48 % (2636)Instruction limit reached!
% 2.28/1.48 % (2636)------------------------------
% 2.28/1.48 % (2636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.48 % (2636)Termination reason: Unknown
% 2.28/1.48 % (2636)Termination phase: shuffling
% 2.28/1.48
% 2.28/1.48 % (2636)Memory used [KB]: 1279
% 2.28/1.48 % (2636)Time elapsed: 0.003 s
% 2.28/1.48 % (2636)Instructions burned: 4 (million)
% 2.28/1.48 % (2636)------------------------------
% 2.28/1.48 % (2636)------------------------------
% 2.28/1.48 % (2633)Instruction limit reached!
% 2.28/1.48 % (2633)------------------------------
% 2.28/1.48 % (2633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.48 % (2633)Termination reason: Unknown
% 2.28/1.48 % (2633)Termination phase: shuffling
% 2.28/1.48
% 2.28/1.48 % (2633)Memory used [KB]: 1279
% 2.28/1.48 % (2633)Time elapsed: 0.004 s
% 2.28/1.48 % (2633)Instructions burned: 4 (million)
% 2.28/1.48 % (2633)------------------------------
% 2.28/1.48 % (2633)------------------------------
% 2.28/1.48 % (2634)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/7Mi)
% 2.28/1.48 % (2638)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/710Mi)
% 2.28/1.48 % (2637)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/18Mi)
% 2.28/1.48 % (2634)Instruction limit reached!
% 2.28/1.48 % (2634)------------------------------
% 2.28/1.48 % (2634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.48 % (2634)Termination reason: Unknown
% 2.28/1.48 % (2634)Termination phase: shuffling
% 2.28/1.48
% 2.28/1.48 % (2634)Memory used [KB]: 1279
% 2.28/1.48 % (2634)Time elapsed: 0.006 s
% 2.28/1.48 % (2634)Instructions burned: 8 (million)
% 2.28/1.48 % (2634)------------------------------
% 2.28/1.48 % (2634)------------------------------
% 2.28/1.48 % (2639)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/6Mi)
% 2.28/1.48 % (2639)Instruction limit reached!
% 2.28/1.48 % (2639)------------------------------
% 2.28/1.48 % (2639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.48 % (2639)Termination reason: Unknown
% 2.28/1.48 % (2639)Termination phase: shuffling
% 2.28/1.48
% 2.28/1.48 % (2639)Memory used [KB]: 1279
% 2.28/1.48 % (2639)Time elapsed: 0.004 s
% 2.28/1.48 % (2639)Instructions burned: 8 (million)
% 2.28/1.48 % (2639)------------------------------
% 2.28/1.48 % (2639)------------------------------
% 2.28/1.49 % (2640)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_2340 for (2999ds/902Mi)
% 2.28/1.49 % (2637)Instruction limit reached!
% 2.28/1.49 % (2637)------------------------------
% 2.28/1.49 % (2637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.49 % (2637)Termination reason: Unknown
% 2.28/1.49 % (2637)Termination phase: shuffling
% 2.28/1.49
% 2.28/1.49 % (2637)Memory used [KB]: 1535
% 2.28/1.49 % (2637)Time elapsed: 0.006 s
% 2.28/1.49 % (2637)Instructions burned: 18 (million)
% 2.28/1.49 % (2637)------------------------------
% 2.28/1.49 % (2637)------------------------------
% 2.28/1.49 % (2641)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_2340 for (2999ds/21Mi)
% 2.28/1.49 % (2643)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_2340 for (2999ds/6Mi)
% 2.29/1.50 % (2644)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/377Mi)
% 2.29/1.50 % (2643)Instruction limit reached!
% 2.29/1.50 % (2643)------------------------------
% 2.29/1.50 % (2643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.50 % (2643)Termination reason: Unknown
% 2.29/1.50 % (2643)Termination phase: shuffling
% 2.29/1.50
% 2.29/1.50 % (2643)Memory used [KB]: 1279
% 2.29/1.50 % (2643)Time elapsed: 0.004 s
% 2.29/1.50 % (2643)Instructions burned: 8 (million)
% 2.29/1.50 % (2643)------------------------------
% 2.29/1.50 % (2643)------------------------------
% 2.29/1.50 % (2642)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/5Mi)
% 2.29/1.50 % (2642)Instruction limit reached!
% 2.29/1.50 % (2642)------------------------------
% 2.29/1.50 % (2642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.50 % (2642)Termination reason: Unknown
% 2.29/1.50 % (2642)Termination phase: shuffling
% 2.29/1.50
% 2.29/1.50 % (2642)Memory used [KB]: 1279
% 2.29/1.50 % (2642)Time elapsed: 0.005 s
% 2.29/1.50 % (2642)Instructions burned: 6 (million)
% 2.29/1.50 % (2642)------------------------------
% 2.29/1.50 % (2642)------------------------------
% 2.29/1.50 % (2640)Refutation not found, incomplete strategy
% 2.29/1.50 % (2640)------------------------------
% 2.29/1.50 % (2640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.50 % (2640)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.50
% 2.29/1.50
% 2.29/1.50 % (2640)Memory used [KB]: 6140
% 2.29/1.50 % (2640)Time elapsed: 0.019 s
% 2.29/1.50 % (2640)Instructions burned: 60 (million)
% 2.29/1.50 % (2640)------------------------------
% 2.29/1.50 % (2640)------------------------------
% 2.29/1.50 % (2641)Instruction limit reached!
% 2.29/1.50 % (2641)------------------------------
% 2.29/1.50 % (2641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.50 % (2641)Termination reason: Unknown
% 2.29/1.50 % (2641)Termination phase: Property scanning
% 2.29/1.50
% 2.29/1.50 % (2641)Memory used [KB]: 1535
% 2.29/1.50 % (2641)Time elapsed: 0.013 s
% 2.29/1.50 % (2641)Instructions burned: 22 (million)
% 2.29/1.50 % (2641)------------------------------
% 2.29/1.50 % (2641)------------------------------
% 2.29/1.51 % (2645)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_2340 for (2999ds/779Mi)
% 2.29/1.51 % (2647)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/879Mi)
% 2.29/1.52 % (2646)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_2340 for (2999ds/19Mi)
% 2.29/1.52 % (2648)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/17Mi)
% 2.29/1.52 % (2646)Instruction limit reached!
% 2.29/1.52 % (2646)------------------------------
% 2.29/1.52 % (2646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.52 % (2646)Termination reason: Unknown
% 2.29/1.52 % (2646)Termination phase: Property scanning
% 2.29/1.52
% 2.29/1.52 % (2646)Memory used [KB]: 1535
% 2.29/1.52 % (2646)Time elapsed: 0.008 s
% 2.29/1.52 % (2646)Instructions burned: 21 (million)
% 2.29/1.52 % (2646)------------------------------
% 2.29/1.52 % (2646)------------------------------
% 2.29/1.53 % (2648)Instruction limit reached!
% 2.29/1.53 % (2648)------------------------------
% 2.29/1.53 % (2648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.53 % (2648)Termination reason: Unknown
% 2.29/1.53 % (2648)Termination phase: Property scanning
% 2.29/1.53
% 2.29/1.53 % (2648)Memory used [KB]: 1535
% 2.29/1.53 % (2648)Time elapsed: 0.010 s
% 2.29/1.53 % (2648)Instructions burned: 20 (million)
% 2.29/1.53 % (2648)------------------------------
% 2.29/1.53 % (2648)------------------------------
% 2.29/1.53 % (2649)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2340 for (2999ds/3Mi)
% 2.29/1.53 % (2649)Instruction limit reached!
% 2.29/1.53 % (2649)------------------------------
% 2.29/1.53 % (2649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.53 % (2649)Termination reason: Unknown
% 2.29/1.53 % (2649)Termination phase: shuffling
% 2.29/1.53
% 2.29/1.53 % (2649)Memory used [KB]: 1279
% 2.29/1.53 % (2649)Time elapsed: 0.003 s
% 2.29/1.53 % (2649)Instructions burned: 5 (million)
% 2.29/1.53 % (2649)------------------------------
% 2.29/1.53 % (2649)------------------------------
% 2.29/1.54 % (2650)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2340 for (2998ds/30Mi)
% 2.29/1.54 % (2651)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2340 for (2998ds/127Mi)
% 2.29/1.55 % (2650)Instruction limit reached!
% 2.29/1.55 % (2650)------------------------------
% 2.29/1.55 % (2650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.55 % (2650)Termination reason: Unknown
% 2.29/1.55 % (2650)Termination phase: Property scanning
% 2.29/1.55
% 2.29/1.55 % (2650)Memory used [KB]: 1535
% 2.29/1.55 % (2650)Time elapsed: 0.011 s
% 2.29/1.55 % (2650)Instructions burned: 33 (million)
% 2.29/1.55 % (2650)------------------------------
% 2.29/1.55 % (2650)------------------------------
% 2.29/1.56 % (2652)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2340 for (2998ds/100Mi)
% 2.29/1.58 % (2651)Instruction limit reached!
% 2.29/1.58 % (2651)------------------------------
% 2.29/1.58 % (2651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.58 % (2651)Termination reason: Unknown
% 2.29/1.58 % (2651)Termination phase: Saturation
% 2.29/1.58
% 2.29/1.58 % (2651)Memory used [KB]: 6396
% 2.29/1.58 % (2651)Time elapsed: 0.035 s
% 2.29/1.58 % (2651)Instructions burned: 129 (million)
% 2.29/1.58 % (2651)------------------------------
% 2.29/1.58 % (2651)------------------------------
% 2.29/1.58 % (2652)Instruction limit reached!
% 2.29/1.58 % (2652)------------------------------
% 2.29/1.58 % (2652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.58 % (2652)Termination reason: Unknown
% 2.29/1.58 % (2652)Termination phase: Saturation
% 2.29/1.58
% 2.29/1.58 % (2652)Memory used [KB]: 6268
% 2.29/1.58 % (2652)Time elapsed: 0.027 s
% 2.29/1.58 % (2652)Instructions burned: 100 (million)
% 2.29/1.58 % (2652)------------------------------
% 2.29/1.58 % (2652)------------------------------
% 2.29/1.59 % (2653)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_2340 for (2998ds/3Mi)
% 2.29/1.59 % (2653)Instruction limit reached!
% 2.29/1.59 % (2653)------------------------------
% 2.29/1.59 % (2653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.59 % (2653)Termination reason: Unknown
% 2.29/1.59 % (2653)Termination phase: shuffling
% 2.29/1.59
% 2.29/1.59 % (2653)Memory used [KB]: 1279
% 2.29/1.59 % (2653)Time elapsed: 0.003 s
% 2.29/1.59 % (2653)Instructions burned: 5 (million)
% 2.29/1.59 % (2653)------------------------------
% 2.29/1.59 % (2653)------------------------------
% 2.29/1.59 % (2644)Instruction limit reached!
% 2.29/1.59 % (2644)------------------------------
% 2.29/1.59 % (2644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.59 % (2644)Termination reason: Unknown
% 2.29/1.59 % (2644)Termination phase: Saturation
% 2.29/1.59
% 2.29/1.59 % (2644)Memory used [KB]: 6780
% 2.29/1.59 % (2644)Time elapsed: 0.095 s
% 2.29/1.59 % (2644)Instructions burned: 377 (million)
% 2.29/1.59 % (2644)------------------------------
% 2.29/1.59 % (2644)------------------------------
% 2.29/1.60 % (2654)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_2340 for (2998ds/20Mi)
% 2.29/1.60 % (2655)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_2340 for (2998ds/86Mi)
% 2.29/1.60 % (2656)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_2340 for (2998ds/107Mi)
% 2.29/1.60 % (2654)Instruction limit reached!
% 2.29/1.60 % (2654)------------------------------
% 2.29/1.60 % (2654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.60 % (2654)Termination reason: Unknown
% 2.29/1.60 % (2654)Termination phase: Property scanning
% 2.29/1.60
% 2.29/1.60 % (2654)Memory used [KB]: 1535
% 2.29/1.60 % (2654)Time elapsed: 0.008 s
% 2.29/1.60 % (2654)Instructions burned: 22 (million)
% 2.29/1.60 % (2654)------------------------------
% 2.29/1.60 % (2654)------------------------------
% 2.29/1.61 % (2657)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_2340 for (2998ds/39Mi)
% 2.29/1.62 % (2655)Instruction limit reached!
% 2.29/1.62 % (2655)------------------------------
% 2.29/1.62 % (2655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.62 % (2655)Termination reason: Unknown
% 2.29/1.62 % (2655)Termination phase: Property scanning
% 2.29/1.62
% 2.29/1.62 % (2655)Memory used [KB]: 1791
% 2.29/1.62 % (2655)Time elapsed: 0.024 s
% 2.29/1.62 % (2655)Instructions burned: 87 (million)
% 2.29/1.62 % (2655)------------------------------
% 2.29/1.62 % (2655)------------------------------
% 2.29/1.62 % (2657)Instruction limit reached!
% 2.29/1.62 % (2657)------------------------------
% 2.29/1.62 % (2657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.62 % (2657)Termination reason: Unknown
% 2.29/1.62 % (2657)Termination phase: Function definition elimination
% 2.29/1.62
% 2.29/1.62 % (2657)Memory used [KB]: 1535
% 2.29/1.62 % (2657)Time elapsed: 0.013 s
% 2.29/1.62 % (2657)Instructions burned: 42 (million)
% 2.29/1.62 % (2657)------------------------------
% 2.29/1.62 % (2657)------------------------------
% 2.29/1.63 % (2656)Instruction limit reached!
% 2.29/1.63 % (2656)------------------------------
% 2.29/1.63 % (2656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.63 % (2656)Termination reason: Unknown
% 2.29/1.63 % (2656)Termination phase: Saturation
% 2.29/1.63
% 2.29/1.63 % (2656)Memory used [KB]: 6396
% 2.29/1.63 % (2656)Time elapsed: 0.030 s
% 2.29/1.63 % (2656)Instructions burned: 108 (million)
% 2.29/1.63 % (2656)------------------------------
% 2.29/1.63 % (2656)------------------------------
% 2.29/1.63 % (2658)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_2340 for (2998ds/448Mi)
% 2.29/1.63 % (2659)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_2340 for (2997ds/46Mi)
% 2.29/1.64 % (2660)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_2340 for (2997ds/98Mi)
% 2.29/1.65 % (2659)Instruction limit reached!
% 2.29/1.65 % (2659)------------------------------
% 2.29/1.65 % (2659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.65 % (2659)Termination reason: Unknown
% 2.29/1.65 % (2659)Termination phase: Property scanning
% 2.29/1.65
% 2.29/1.65 % (2659)Memory used [KB]: 1535
% 2.29/1.65 % (2659)Time elapsed: 0.015 s
% 2.29/1.65 % (2659)Instructions burned: 48 (million)
% 2.29/1.65 % (2659)------------------------------
% 2.29/1.65 % (2659)------------------------------
% 2.29/1.66 % (2661)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_2340 for (2997ds/507Mi)
% 2.29/1.66 % (2660)Instruction limit reached!
% 2.29/1.66 % (2660)------------------------------
% 2.29/1.66 % (2660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.66 % (2660)Termination reason: Unknown
% 2.29/1.66 % (2660)Termination phase: Saturation
% 2.29/1.66
% 2.29/1.66 % (2660)Memory used [KB]: 1791
% 2.29/1.66 % (2660)Time elapsed: 0.027 s
% 2.29/1.66 % (2660)Instructions burned: 100 (million)
% 2.29/1.66 % (2660)------------------------------
% 2.29/1.66 % (2660)------------------------------
% 2.29/1.67 % (2662)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_2340 for (2997ds/149Mi)
% 2.29/1.69 % (2638)Instruction limit reached!
% 2.29/1.69 % (2638)------------------------------
% 2.29/1.69 % (2638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.69 % (2638)Termination reason: Unknown
% 2.29/1.69 % (2638)Termination phase: Saturation
% 2.29/1.69
% 2.29/1.69 % (2638)Memory used [KB]: 7803
% 2.29/1.69 % (2638)Time elapsed: 0.212 s
% 2.29/1.69 % (2638)Instructions burned: 710 (million)
% 2.29/1.69 % (2638)------------------------------
% 2.29/1.69 % (2638)------------------------------
% 2.29/1.70 % (2663)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2340 for (2997ds/39Mi)
% 2.29/1.71 % (2645)Instruction limit reached!
% 2.29/1.71 % (2645)------------------------------
% 2.29/1.71 % (2645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.71 % (2645)Termination reason: Unknown
% 2.29/1.71 % (2645)Termination phase: Saturation
% 2.29/1.71
% 2.29/1.71 % (2645)Memory used [KB]: 6908
% 2.29/1.71 % (2645)Time elapsed: 0.205 s
% 2.29/1.71 % (2645)Instructions burned: 781 (million)
% 2.29/1.71 % (2645)------------------------------
% 2.29/1.71 % (2645)------------------------------
% 2.29/1.71 % (2663)Instruction limit reached!
% 2.29/1.71 % (2663)------------------------------
% 2.29/1.71 % (2663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.71 % (2663)Termination reason: Unknown
% 2.29/1.71 % (2663)Termination phase: Function definition elimination
% 2.29/1.71
% 2.29/1.71 % (2663)Memory used [KB]: 1535
% 2.29/1.71 % (2663)Time elapsed: 0.011 s
% 2.29/1.71 % (2663)Instructions burned: 39 (million)
% 2.29/1.71 % (2663)------------------------------
% 2.29/1.71 % (2663)------------------------------
% 2.29/1.72 % (2662)Instruction limit reached!
% 2.29/1.72 % (2662)------------------------------
% 2.29/1.72 % (2662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.72 % (2662)Termination reason: Unknown
% 2.29/1.72 % (2662)Termination phase: Saturation
% 2.29/1.72
% 2.29/1.72 % (2662)Memory used [KB]: 6652
% 2.29/1.72 % (2662)Time elapsed: 0.047 s
% 2.29/1.72 % (2662)Instructions burned: 149 (million)
% 2.29/1.72 % (2662)------------------------------
% 2.29/1.72 % (2662)------------------------------
% 2.29/1.72 % (2664)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_2340 for (2996ds/6Mi)
% 2.29/1.72 % (2665)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_2340 for (2996ds/1087Mi)
% 2.29/1.72 % (2664)Instruction limit reached!
% 2.29/1.72 % (2664)------------------------------
% 2.29/1.72 % (2664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.72 % (2664)Termination reason: Unknown
% 2.29/1.72 % (2664)Termination phase: shuffling
% 2.29/1.72
% 2.29/1.72 % (2664)Memory used [KB]: 1279
% 2.29/1.72 % (2664)Time elapsed: 0.003 s
% 2.29/1.72 % (2664)Instructions burned: 7 (million)
% 2.29/1.72 % (2664)------------------------------
% 2.29/1.72 % (2664)------------------------------
% 2.29/1.73 % (2666)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/47Mi)
% 2.29/1.73 % (2667)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_2340 for (2996ds/44Mi)
% 2.29/1.74 % (2647)Instruction limit reached!
% 2.29/1.74 % (2647)------------------------------
% 2.29/1.74 % (2647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.74 % (2647)Termination reason: Unknown
% 2.29/1.74 % (2647)Termination phase: Saturation
% 2.29/1.74
% 2.29/1.74 % (2647)Memory used [KB]: 7291
% 2.29/1.74 % (2647)Time elapsed: 0.226 s
% 2.29/1.74 % (2647)Instructions burned: 880 (million)
% 2.29/1.74 % (2647)------------------------------
% 2.29/1.74 % (2647)------------------------------
% 2.29/1.74 % (2666)Instruction limit reached!
% 2.29/1.74 % (2666)------------------------------
% 2.29/1.74 % (2666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.74 % (2666)Termination reason: Unknown
% 2.29/1.74 % (2666)Termination phase: Function definition elimination
% 2.29/1.74
% 2.29/1.74 % (2666)Memory used [KB]: 1663
% 2.29/1.74 % (2666)Time elapsed: 0.015 s
% 2.29/1.74 % (2666)Instructions burned: 49 (million)
% 2.29/1.74 % (2666)------------------------------
% 2.29/1.74 % (2666)------------------------------
% 2.29/1.74 % (2667)Instruction limit reached!
% 2.29/1.74 % (2667)------------------------------
% 2.29/1.74 % (2667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.74 % (2667)Termination reason: Unknown
% 2.29/1.74 % (2667)Termination phase: Property scanning
% 2.29/1.74
% 2.29/1.74 % (2667)Memory used [KB]: 1535
% 2.29/1.74 % (2667)Time elapsed: 0.012 s
% 2.29/1.74 % (2667)Instructions burned: 44 (million)
% 2.29/1.74 % (2667)------------------------------
% 2.29/1.74 % (2667)------------------------------
% 2.29/1.75 % (2668)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_2340 for (2996ds/432Mi)
% 2.29/1.75 % (2670)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_2340 for (2996ds/31Mi)
% 2.29/1.75 % (2669)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/62Mi)
% 2.29/1.76 % (2629)Instruction limit reached!
% 2.29/1.76 % (2629)------------------------------
% 2.29/1.76 % (2629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.76 % (2629)Termination reason: Unknown
% 2.29/1.76 % (2629)Termination phase: Saturation
% 2.29/1.76
% 2.29/1.76 % (2629)Memory used [KB]: 7803
% 2.29/1.76 % (2629)Time elapsed: 0.297 s
% 2.29/1.76 % (2629)Instructions burned: 1041 (million)
% 2.29/1.76 % (2629)------------------------------
% 2.29/1.76 % (2629)------------------------------
% 2.29/1.76 % (2670)Instruction limit reached!
% 2.29/1.76 % (2670)------------------------------
% 2.29/1.76 % (2670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.76 % (2670)Termination reason: Unknown
% 2.29/1.76 % (2670)Termination phase: Property scanning
% 2.29/1.76
% 2.29/1.76 % (2670)Memory used [KB]: 1535
% 2.29/1.76 % (2670)Time elapsed: 0.010 s
% 2.29/1.76 % (2670)Instructions burned: 34 (million)
% 2.29/1.76 % (2670)------------------------------
% 2.29/1.76 % (2670)------------------------------
% 2.29/1.76 % (2658)Instruction limit reached!
% 2.29/1.76 % (2658)------------------------------
% 2.29/1.76 % (2658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.76 % (2658)Termination reason: Unknown
% 2.29/1.76 % (2658)Termination phase: Saturation
% 2.29/1.76
% 2.29/1.76 % (2658)Memory used [KB]: 6908
% 2.29/1.76 % (2658)Time elapsed: 0.156 s
% 2.29/1.76 % (2658)Instructions burned: 449 (million)
% 2.29/1.76 % (2658)------------------------------
% 2.29/1.76 % (2658)------------------------------
% 2.29/1.77 % (2671)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/96Mi)
% 2.29/1.77 % (2669)Instruction limit reached!
% 2.29/1.77 % (2669)------------------------------
% 2.29/1.77 % (2669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.77 % (2669)Termination reason: Unknown
% 2.29/1.77 % (2669)Termination phase: Function definition elimination
% 2.29/1.77
% 2.29/1.77 % (2669)Memory used [KB]: 1791
% 2.29/1.77 % (2669)Time elapsed: 0.018 s
% 2.29/1.77 % (2669)Instructions burned: 64 (million)
% 2.29/1.77 % (2669)------------------------------
% 2.29/1.77 % (2669)------------------------------
% 2.29/1.77 % (2672)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_2340 for (2996ds/453Mi)
% 2.29/1.77 % (2673)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_2340 for (2996ds/71Mi)
% 2.29/1.78 % (2674)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/83Mi)
% 2.29/1.79 % (2673)Instruction limit reached!
% 2.29/1.79 % (2673)------------------------------
% 2.29/1.79 % (2673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.79 % (2673)Termination reason: Unknown
% 2.29/1.79 % (2673)Termination phase: Property scanning
% 2.29/1.79
% 2.29/1.79 % (2673)Memory used [KB]: 1791
% 2.29/1.79 % (2673)Time elapsed: 0.020 s
% 2.29/1.79 % (2673)Instructions burned: 71 (million)
% 2.29/1.79 % (2673)------------------------------
% 2.29/1.79 % (2673)------------------------------
% 2.29/1.79 % (2661)Instruction limit reached!
% 2.29/1.79 % (2661)------------------------------
% 2.29/1.79 % (2661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.79 % (2661)Termination reason: Unknown
% 2.29/1.79 % (2661)Termination phase: Saturation
% 2.29/1.79
% 2.29/1.79 % (2661)Memory used [KB]: 6780
% 2.29/1.79 % (2661)Time elapsed: 0.136 s
% 2.29/1.79 % (2661)Instructions burned: 509 (million)
% 2.29/1.79 % (2661)------------------------------
% 2.29/1.79 % (2661)------------------------------
% 2.29/1.79 % (2671)Instruction limit reached!
% 2.29/1.79 % (2671)------------------------------
% 2.29/1.79 % (2671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.79 % (2671)Termination reason: Unknown
% 2.29/1.79 % (2671)Termination phase: Saturation
% 2.29/1.79
% 2.29/1.79 % (2671)Memory used [KB]: 6268
% 2.29/1.79 % (2671)Time elapsed: 0.027 s
% 2.29/1.79 % (2671)Instructions burned: 97 (million)
% 2.29/1.79 % (2671)------------------------------
% 2.29/1.79 % (2671)------------------------------
% 2.29/1.80 % (2675)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/11Mi)
% 2.29/1.80 % (2676)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_2340 for (2996ds/41Mi)
% 2.29/1.80 % (2674)Instruction limit reached!
% 2.29/1.80 % (2674)------------------------------
% 2.29/1.80 % (2674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.80 % (2674)Termination reason: Unknown
% 2.29/1.80 % (2674)Termination phase: Saturation
% 2.29/1.80
% 2.29/1.80 % (2674)Memory used [KB]: 6268
% 2.29/1.80 % (2674)Time elapsed: 0.025 s
% 2.29/1.80 % (2674)Instructions burned: 84 (million)
% 2.29/1.80 % (2674)------------------------------
% 2.29/1.80 % (2674)------------------------------
% 2.29/1.80 % (2677)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/6Mi)
% 2.29/1.80 % (2675)Instruction limit reached!
% 2.29/1.80 % (2675)------------------------------
% 2.29/1.80 % (2675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.80 % (2675)Termination reason: Unknown
% 2.29/1.80 % (2675)Termination phase: shuffling
% 2.29/1.80
% 2.29/1.80 % (2675)Memory used [KB]: 1407
% 2.29/1.80 % (2675)Time elapsed: 0.005 s
% 2.29/1.80 % (2675)Instructions burned: 11 (million)
% 2.29/1.80 % (2675)------------------------------
% 2.29/1.80 % (2675)------------------------------
% 2.29/1.80 % (2677)Instruction limit reached!
% 2.29/1.80 % (2677)------------------------------
% 2.29/1.80 % (2677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.80 % (2677)Termination reason: Unknown
% 2.29/1.80 % (2677)Termination phase: shuffling
% 2.29/1.80
% 2.29/1.80 % (2677)Memory used [KB]: 1279
% 2.29/1.80 % (2677)Time elapsed: 0.003 s
% 2.29/1.80 % (2677)Instructions burned: 7 (million)
% 2.29/1.80 % (2677)------------------------------
% 2.29/1.80 % (2677)------------------------------
% 2.29/1.81 % (2676)Instruction limit reached!
% 2.29/1.81 % (2676)------------------------------
% 2.29/1.81 % (2676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.81 % (2676)Termination reason: Unknown
% 2.29/1.81 % (2676)Termination phase: Function definition elimination
% 2.29/1.81
% 2.29/1.81 % (2676)Memory used [KB]: 1535
% 2.29/1.81 % (2676)Time elapsed: 0.013 s
% 2.29/1.81 % (2676)Instructions burned: 41 (million)
% 2.29/1.81 % (2676)------------------------------
% 2.29/1.81 % (2676)------------------------------
% 2.29/1.81 % (2678)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/150Mi)
% 2.29/1.81 % (2680)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_2340 for (2996ds/109Mi)
% 2.29/1.82 % (2679)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2340 for (2996ds/343Mi)
% 2.29/1.82 % (2681)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_2340 for (2996ds/253Mi)
% 2.29/1.84 % (2680)Instruction limit reached!
% 2.29/1.84 % (2680)------------------------------
% 2.29/1.84 % (2680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.84 % (2680)Termination reason: Unknown
% 2.29/1.84 % (2680)Termination phase: Saturation
% 2.29/1.84
% 2.29/1.84 % (2680)Memory used [KB]: 6396
% 2.29/1.84 % (2680)Time elapsed: 0.031 s
% 2.29/1.84 % (2680)Instructions burned: 113 (million)
% 2.29/1.84 % (2680)------------------------------
% 2.29/1.84 % (2680)------------------------------
% 2.29/1.85 % (2678)Instruction limit reached!
% 2.29/1.85 % (2678)------------------------------
% 2.29/1.85 % (2678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.85 % (2678)Termination reason: Unknown
% 2.29/1.85 % (2678)Termination phase: Saturation
% 2.29/1.85
% 2.29/1.85 % (2678)Memory used [KB]: 6396
% 2.29/1.85 % (2678)Time elapsed: 0.039 s
% 2.29/1.85 % (2678)Instructions burned: 152 (million)
% 2.29/1.85 % (2678)------------------------------
% 2.29/1.85 % (2678)------------------------------
% 2.29/1.85 % (2668)Instruction limit reached!
% 2.29/1.85 % (2668)------------------------------
% 2.29/1.85 % (2668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.85 % (2668)Termination reason: Unknown
% 2.29/1.85 % (2668)Termination phase: Saturation
% 2.29/1.85
% 2.29/1.85 % (2668)Memory used [KB]: 3326
% 2.29/1.85 % (2668)Time elapsed: 0.107 s
% 2.29/1.85 % (2668)Instructions burned: 432 (million)
% 2.29/1.85 % (2668)------------------------------
% 2.29/1.85 % (2668)------------------------------
% 2.29/1.85 % (2682)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2340 for (2995ds/140Mi)
% 2.29/1.86 % (2683)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_2340 for (2995ds/614Mi)
% 2.29/1.86 % (2684)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_2340 for (2995ds/202Mi)
% 2.29/1.87 % (2684)Refutation not found, incomplete strategy
% 2.29/1.87 % (2684)------------------------------
% 2.29/1.87 % (2684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.87 % (2684)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.87
% 2.29/1.87
% 2.29/1.87 % (2684)Memory used [KB]: 6140
% 2.29/1.87 % (2684)Time elapsed: 0.013 s
% 2.29/1.87 % (2684)Instructions burned: 39 (million)
% 2.29/1.87 % (2684)------------------------------
% 2.29/1.87 % (2684)------------------------------
% 2.29/1.88 % (2672)Instruction limit reached!
% 2.29/1.88 % (2672)------------------------------
% 2.29/1.88 % (2672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.88 % (2672)Termination reason: Unknown
% 2.29/1.88 % (2672)Termination phase: Saturation
% 2.29/1.88
% 2.29/1.88 % (2672)Memory used [KB]: 6780
% 2.29/1.88 % (2672)Time elapsed: 0.108 s
% 2.29/1.88 % (2672)Instructions burned: 454 (million)
% 2.29/1.88 % (2672)------------------------------
% 2.29/1.88 % (2672)------------------------------
% 2.29/1.88 % (2682)Refutation not found, incomplete strategy
% 2.29/1.88 % (2682)------------------------------
% 2.29/1.88 % (2682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.88 % (2682)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.88
% 2.29/1.88
% 2.29/1.88 % (2682)Memory used [KB]: 6524
% 2.29/1.88 % (2682)Time elapsed: 0.031 s
% 2.29/1.88 % (2682)Instructions burned: 92 (million)
% 2.29/1.88 % (2682)------------------------------
% 2.29/1.88 % (2682)------------------------------
% 2.29/1.88 % (2685)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_2340 for (2995ds/339Mi)
% 2.29/1.89 % (2686)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_2340 for (2995ds/283Mi)
% 2.29/1.89 % (2681)Instruction limit reached!
% 2.29/1.89 % (2681)------------------------------
% 2.29/1.89 % (2681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.89 % (2681)Termination reason: Unknown
% 2.29/1.89 % (2681)Termination phase: Saturation
% 2.29/1.89
% 2.29/1.89 % (2681)Memory used [KB]: 6524
% 2.29/1.89 % (2681)Time elapsed: 0.071 s
% 2.29/1.89 % (2681)Instructions burned: 254 (million)
% 2.29/1.89 % (2681)------------------------------
% 2.29/1.89 % (2681)------------------------------
% 2.29/1.89 % (2687)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_2340 for (2995ds/134Mi)
% 2.29/1.90 % (2688)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_2340 for (2995ds/298Mi)
% 2.29/1.93 % (2687)Instruction limit reached!
% 2.29/1.93 % (2687)------------------------------
% 2.29/1.93 % (2687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.93 % (2687)Termination reason: Unknown
% 2.29/1.93 % (2687)Termination phase: Saturation
% 2.29/1.93
% 2.29/1.93 % (2687)Memory used [KB]: 6396
% 2.29/1.93 % (2687)Time elapsed: 0.036 s
% 2.29/1.93 % (2687)Instructions burned: 137 (million)
% 2.29/1.93 % (2687)------------------------------
% 2.29/1.93 % (2687)------------------------------
% 2.29/1.94 % (2689)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_2340 for (2994ds/192Mi)
% 2.29/1.95 % (2686)Instruction limit reached!
% 2.29/1.95 % (2686)------------------------------
% 2.29/1.95 % (2686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.95 % (2686)Termination reason: Unknown
% 2.29/1.95 % (2686)Termination phase: Saturation
% 2.29/1.95
% 2.29/1.95 % (2686)Memory used [KB]: 6780
% 2.29/1.95 % (2686)Time elapsed: 0.069 s
% 2.29/1.95 % (2686)Instructions burned: 284 (million)
% 2.29/1.95 % (2686)------------------------------
% 2.29/1.95 % (2686)------------------------------
% 2.29/1.96 % (2679)Instruction limit reached!
% 2.29/1.96 % (2679)------------------------------
% 2.29/1.96 % (2679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.96 % (2679)Termination reason: Unknown
% 2.29/1.96 % (2679)Termination phase: Saturation
% 2.29/1.96
% 2.29/1.96 % (2679)Memory used [KB]: 6652
% 2.29/1.96 % (2679)Time elapsed: 0.136 s
% 2.29/1.96 % (2679)Instructions burned: 345 (million)
% 2.29/1.96 % (2679)------------------------------
% 2.29/1.96 % (2679)------------------------------
% 2.29/1.96 % (2690)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_2340 for (2994ds/258Mi)
% 2.29/1.97 % (2691)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_2340 for (2994ds/90Mi)
% 2.29/1.97 % (2688)Instruction limit reached!
% 2.29/1.97 % (2688)------------------------------
% 2.29/1.97 % (2688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.97 % (2688)Termination reason: Unknown
% 2.29/1.97 % (2688)Termination phase: Saturation
% 2.29/1.97
% 2.29/1.97 % (2688)Memory used [KB]: 6780
% 2.29/1.97 % (2688)Time elapsed: 0.073 s
% 2.29/1.97 % (2688)Instructions burned: 302 (million)
% 2.29/1.97 % (2688)------------------------------
% 2.29/1.97 % (2688)------------------------------
% 2.29/1.98 % (2692)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_2340 for (2994ds/231Mi)
% 2.29/1.98 % (2685)Instruction limit reached!
% 2.29/1.98 % (2685)------------------------------
% 2.29/1.98 % (2685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.98 % (2685)Termination reason: Unknown
% 2.29/1.98 % (2685)Termination phase: Saturation
% 2.29/1.98
% 2.29/1.98 % (2685)Memory used [KB]: 7164
% 2.29/1.98 % (2685)Time elapsed: 0.101 s
% 2.29/1.98 % (2685)Instructions burned: 340 (million)
% 2.29/1.98 % (2685)------------------------------
% 2.29/1.98 % (2685)------------------------------
% 2.29/1.98 % (2689)Instruction limit reached!
% 2.29/1.98 % (2689)------------------------------
% 2.29/1.98 % (2689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.98 % (2689)Termination reason: Unknown
% 2.29/1.98 % (2689)Termination phase: Saturation
% 2.29/1.98
% 2.29/1.98 % (2689)Memory used [KB]: 6780
% 2.29/1.98 % (2689)Time elapsed: 0.048 s
% 2.29/1.98 % (2689)Instructions burned: 192 (million)
% 2.29/1.98 % (2689)------------------------------
% 2.29/1.98 % (2689)------------------------------
% 2.29/1.99 % (2691)Instruction limit reached!
% 2.29/1.99 % (2691)------------------------------
% 2.29/1.99 % (2691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.99 % (2691)Termination reason: Unknown
% 2.29/1.99 % (2691)Termination phase: Saturation
% 2.29/1.99
% 2.29/1.99 % (2691)Memory used [KB]: 6396
% 2.29/1.99 % (2691)Time elapsed: 0.026 s
% 2.29/1.99 % (2691)Instructions burned: 90 (million)
% 2.29/1.99 % (2691)------------------------------
% 2.29/1.99 % (2691)------------------------------
% 2.29/1.99 % (2693)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_2340 for (2994ds/458Mi)
% 2.29/1.99 % (2694)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_2340 for (2994ds/31Mi)
% 2.29/2.00 % (2695)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_2340 for (2994ds/297Mi)
% 2.29/2.00 % (2683)Instruction limit reached!
% 2.29/2.00 % (2683)------------------------------
% 2.29/2.00 % (2683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/2.00 % (2683)Termination reason: Unknown
% 2.29/2.00 % (2683)Termination phase: Saturation
% 2.29/2.00
% 2.29/2.00 % (2683)Memory used [KB]: 6780
% 2.29/2.00 % (2683)Time elapsed: 0.143 s
% 2.29/2.00 % (2683)Instructions burned: 616 (million)
% 2.29/2.00 % (2683)------------------------------
% 2.29/2.00 % (2683)------------------------------
% 2.29/2.00 % (2694)Instruction limit reached!
% 2.29/2.00 % (2694)------------------------------
% 2.29/2.00 % (2694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/2.00 % (2694)Termination reason: Unknown
% 2.29/2.00 % (2694)Termination phase: Property scanning
% 2.29/2.00
% 2.29/2.00 % (2694)Memory used [KB]: 1535
% 2.29/2.00 % (2694)Time elapsed: 0.010 s
% 2.29/2.00 % (2694)Instructions burned: 34 (million)
% 2.29/2.00 % (2694)------------------------------
% 2.29/2.00 % (2694)------------------------------
% 2.29/2.01 % (2696)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_2340 for (2994ds/987Mi)
% 6.38/2.01 % (2697)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_2340 for (2994ds/182Mi)
% 6.38/2.03 % (2690)Instruction limit reached!
% 6.38/2.03 % (2690)------------------------------
% 6.38/2.03 % (2690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.03 % (2690)Termination reason: Unknown
% 6.38/2.03 % (2690)Termination phase: Saturation
% 6.38/2.03
% 6.38/2.03 % (2690)Memory used [KB]: 6780
% 6.38/2.03 % (2690)Time elapsed: 0.063 s
% 6.38/2.03 % (2690)Instructions burned: 260 (million)
% 6.38/2.03 % (2690)------------------------------
% 6.38/2.03 % (2690)------------------------------
% 6.38/2.04 % (2698)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_2340 for (2993ds/182Mi)
% 6.38/2.05 % (2692)Instruction limit reached!
% 6.38/2.05 % (2692)------------------------------
% 6.38/2.05 % (2692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.05 % (2692)Termination reason: Unknown
% 6.38/2.05 % (2692)Termination phase: Saturation
% 6.38/2.05
% 6.38/2.05 % (2692)Memory used [KB]: 6908
% 6.38/2.05 % (2692)Time elapsed: 0.071 s
% 6.38/2.05 % (2692)Instructions burned: 232 (million)
% 6.38/2.05 % (2692)------------------------------
% 6.38/2.05 % (2692)------------------------------
% 6.38/2.05 % (2665)Instruction limit reached!
% 6.38/2.05 % (2665)------------------------------
% 6.38/2.05 % (2665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.05 % (2665)Termination reason: Unknown
% 6.38/2.05 % (2665)Termination phase: Saturation
% 6.38/2.05
% 6.38/2.05 % (2665)Memory used [KB]: 8443
% 6.38/2.05 % (2665)Time elapsed: 0.333 s
% 6.38/2.05 % (2665)Instructions burned: 1089 (million)
% 6.38/2.05 % (2665)------------------------------
% 6.38/2.05 % (2665)------------------------------
% 6.38/2.06 % (2697)Instruction limit reached!
% 6.38/2.06 % (2697)------------------------------
% 6.38/2.06 % (2697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.06 % (2697)Termination reason: Unknown
% 6.38/2.06 % (2697)Termination phase: Saturation
% 6.38/2.06
% 6.38/2.06 % (2697)Memory used [KB]: 6524
% 6.38/2.06 % (2697)Time elapsed: 0.045 s
% 6.38/2.06 % (2697)Instructions burned: 183 (million)
% 6.38/2.06 % (2697)------------------------------
% 6.38/2.06 % (2697)------------------------------
% 6.38/2.06 % (2699)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_2340 for (2993ds/154Mi)
% 6.38/2.06 % (2700)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_2340 for (2993ds/79Mi)
% 6.38/2.07 % (2701)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_2340 for (2993ds/216Mi)
% 6.38/2.08 % (2700)Instruction limit reached!
% 6.38/2.08 % (2700)------------------------------
% 6.38/2.08 % (2700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.08 % (2700)Termination reason: Unknown
% 6.38/2.08 % (2700)Termination phase: Property scanning
% 6.38/2.08
% 6.38/2.08 % (2700)Memory used [KB]: 1791
% 6.38/2.08 % (2700)Time elapsed: 0.020 s
% 6.38/2.08 % (2700)Instructions burned: 80 (million)
% 6.38/2.08 % (2700)------------------------------
% 6.38/2.08 % (2700)------------------------------
% 6.38/2.09 % (2695)Instruction limit reached!
% 6.38/2.09 % (2695)------------------------------
% 6.38/2.09 % (2695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.09 % (2695)Termination reason: Unknown
% 6.38/2.09 % (2695)Termination phase: Saturation
% 6.38/2.09
% 6.38/2.09 % (2695)Memory used [KB]: 6908
% 6.38/2.09 % (2695)Time elapsed: 0.111 s
% 6.38/2.09 % (2695)Instructions burned: 297 (million)
% 6.38/2.09 % (2695)------------------------------
% 6.38/2.09 % (2695)------------------------------
% 6.38/2.09 % (2702)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_2340 for (2993ds/114Mi)
% 6.38/2.09 % (2698)Instruction limit reached!
% 6.38/2.09 % (2698)------------------------------
% 6.38/2.09 % (2698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.09 % (2698)Termination reason: Unknown
% 6.38/2.09 % (2698)Termination phase: Saturation
% 6.38/2.09
% 6.38/2.09 % (2698)Memory used [KB]: 6652
% 6.38/2.09 % (2698)Time elapsed: 0.057 s
% 6.38/2.09 % (2698)Instructions burned: 184 (million)
% 6.38/2.09 % (2698)------------------------------
% 6.38/2.09 % (2698)------------------------------
% 6.38/2.10 % (2703)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_2340 for (2993ds/922Mi)
% 6.38/2.10 % (2699)Instruction limit reached!
% 6.38/2.10 % (2699)------------------------------
% 6.38/2.10 % (2699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.10 % (2699)Termination reason: Unknown
% 6.38/2.10 % (2699)Termination phase: Saturation
% 6.38/2.10
% 6.38/2.10 % (2699)Memory used [KB]: 6524
% 6.38/2.10 % (2699)Time elapsed: 0.038 s
% 6.38/2.10 % (2699)Instructions burned: 155 (million)
% 6.38/2.10 % (2699)------------------------------
% 6.38/2.10 % (2699)------------------------------
% 6.38/2.10 % (2693)Instruction limit reached!
% 6.38/2.10 % (2693)------------------------------
% 6.38/2.10 % (2693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.10 % (2693)Termination reason: Unknown
% 6.38/2.10 % (2693)Termination phase: Saturation
% 6.38/2.10
% 6.38/2.10 % (2693)Memory used [KB]: 6780
% 6.38/2.10 % (2693)Time elapsed: 0.106 s
% 6.38/2.10 % (2693)Instructions burned: 458 (million)
% 6.38/2.10 % (2693)------------------------------
% 6.38/2.10 % (2693)------------------------------
% 6.38/2.10 % (2704)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_2340 for (2993ds/182Mi)
% 6.38/2.11 % (2705)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_2340 for (2993ds/164Mi)
% 6.38/2.11 % (2706)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_2340 for (2993ds/50Mi)
% 6.88/2.12 % (2702)Instruction limit reached!
% 6.88/2.12 % (2702)------------------------------
% 6.88/2.12 % (2702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.12 % (2702)Termination reason: Unknown
% 6.88/2.12 % (2702)Termination phase: Saturation
% 6.88/2.12
% 6.88/2.12 % (2702)Memory used [KB]: 6396
% 6.88/2.12 % (2702)Time elapsed: 0.029 s
% 6.88/2.12 % (2702)Instructions burned: 117 (million)
% 6.88/2.12 % (2702)------------------------------
% 6.88/2.12 % (2702)------------------------------
% 6.88/2.12 % (2706)Instruction limit reached!
% 6.88/2.12 % (2706)------------------------------
% 6.88/2.12 % (2706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.12 % (2706)Termination reason: Unknown
% 6.88/2.12 % (2706)Termination phase: Function definition elimination
% 6.88/2.12
% 6.88/2.12 % (2706)Memory used [KB]: 1663
% 6.88/2.12 % (2706)Time elapsed: 0.014 s
% 6.88/2.12 % (2706)Instructions burned: 54 (million)
% 6.88/2.12 % (2706)------------------------------
% 6.88/2.12 % (2706)------------------------------
% 6.88/2.12 % (2701)Instruction limit reached!
% 6.88/2.12 % (2701)------------------------------
% 6.88/2.12 % (2701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.12 % (2701)Termination reason: Unknown
% 6.88/2.12 % (2701)Termination phase: Saturation
% 6.88/2.12
% 6.88/2.12 % (2701)Memory used [KB]: 6524
% 6.88/2.12 % (2701)Time elapsed: 0.057 s
% 6.88/2.12 % (2701)Instructions burned: 217 (million)
% 6.88/2.12 % (2701)------------------------------
% 6.88/2.12 % (2701)------------------------------
% 6.88/2.13 % (2707)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_2340 for (2992ds/368Mi)
% 6.88/2.13 % (2708)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_2340 for (2992ds/1021Mi)
% 6.88/2.13 % (2709)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_2340 for (2992ds/267Mi)
% 6.88/2.14 % (2704)Instruction limit reached!
% 6.88/2.14 % (2704)------------------------------
% 6.88/2.14 % (2704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.14 % (2704)Termination reason: Unknown
% 6.88/2.14 % (2704)Termination phase: Saturation
% 6.88/2.14
% 6.88/2.14 % (2704)Memory used [KB]: 6780
% 6.88/2.14 % (2704)Time elapsed: 0.044 s
% 6.88/2.14 % (2704)Instructions burned: 183 (million)
% 6.88/2.14 % (2704)------------------------------
% 6.88/2.14 % (2704)------------------------------
% 6.88/2.15 % (2705)Instruction limit reached!
% 6.88/2.15 % (2705)------------------------------
% 6.88/2.15 % (2705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.15 % (2705)Termination reason: Unknown
% 6.88/2.15 % (2705)Termination phase: Saturation
% 6.88/2.15
% 6.88/2.15 % (2705)Memory used [KB]: 1918
% 6.88/2.15 % (2705)Time elapsed: 0.044 s
% 6.88/2.15 % (2705)Instructions burned: 165 (million)
% 6.88/2.15 % (2705)------------------------------
% 6.88/2.15 % (2705)------------------------------
% 6.88/2.15 % (2710)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_2340 for (2992ds/204Mi)
% 6.88/2.16 % (2711)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_2340 for (2992ds/26Mi)
% 6.88/2.17 % (2711)Instruction limit reached!
% 6.88/2.17 % (2711)------------------------------
% 6.88/2.17 % (2711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.17 % (2711)Termination reason: Unknown
% 6.88/2.17 % (2711)Termination phase: Preprocessing 1
% 6.88/2.17
% 6.88/2.17 % (2711)Memory used [KB]: 1535
% 6.88/2.17 % (2711)Time elapsed: 0.008 s
% 6.88/2.17 % (2711)Instructions burned: 28 (million)
% 6.88/2.17 % (2711)------------------------------
% 6.88/2.17 % (2711)------------------------------
% 6.88/2.18 % (2712)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_2340 for (2992ds/53Mi)
% 6.88/2.19 % (2712)Instruction limit reached!
% 6.88/2.19 % (2712)------------------------------
% 6.88/2.19 % (2712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.19 % (2712)Termination reason: Unknown
% 6.88/2.19 % (2712)Termination phase: Function definition elimination
% 6.88/2.19
% 6.88/2.19 % (2712)Memory used [KB]: 1663
% 6.88/2.19 % (2712)Time elapsed: 0.015 s
% 6.88/2.19 % (2712)Instructions burned: 54 (million)
% 6.88/2.19 % (2712)------------------------------
% 6.88/2.19 % (2712)------------------------------
% 6.88/2.19 % (2709)Instruction limit reached!
% 6.88/2.19 % (2709)------------------------------
% 6.88/2.19 % (2709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.19 % (2709)Termination reason: Unknown
% 6.88/2.19 % (2709)Termination phase: Saturation
% 6.88/2.19
% 6.88/2.19 % (2709)Memory used [KB]: 6780
% 6.88/2.19 % (2709)Time elapsed: 0.064 s
% 6.88/2.19 % (2709)Instructions burned: 267 (million)
% 6.88/2.19 % (2709)------------------------------
% 6.88/2.19 % (2709)------------------------------
% 7.22/2.20 % (2713)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_2340 for (2992ds/4436Mi)
% 7.22/2.20 % (2710)Instruction limit reached!
% 7.22/2.20 % (2710)------------------------------
% 7.22/2.20 % (2710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.20 % (2710)Termination reason: Unknown
% 7.22/2.20 % (2710)Termination phase: Saturation
% 7.22/2.20
% 7.22/2.20 % (2710)Memory used [KB]: 6780
% 7.22/2.20 % (2710)Time elapsed: 0.051 s
% 7.22/2.20 % (2710)Instructions burned: 207 (million)
% 7.22/2.20 % (2710)------------------------------
% 7.22/2.20 % (2710)------------------------------
% 7.22/2.20 % (2714)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_2340 for (2992ds/1539Mi)
% 7.22/2.21 % (2715)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_2340 for (2992ds/408Mi)
% 7.22/2.21 % (2707)Instruction limit reached!
% 7.22/2.21 % (2707)------------------------------
% 7.22/2.21 % (2707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.21 % (2707)Termination reason: Unknown
% 7.22/2.21 % (2707)Termination phase: Saturation
% 7.22/2.21
% 7.22/2.21 % (2707)Memory used [KB]: 6780
% 7.22/2.21 % (2707)Time elapsed: 0.087 s
% 7.22/2.21 % (2707)Instructions burned: 368 (million)
% 7.22/2.21 % (2707)------------------------------
% 7.22/2.21 % (2707)------------------------------
% 7.22/2.22 % (2716)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_2340 for (2992ds/5205Mi)
% 7.22/2.24 % (2696)Instruction limit reached!
% 7.22/2.24 % (2696)------------------------------
% 7.22/2.24 % (2696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.24 % (2696)Termination reason: Unknown
% 7.22/2.24 % (2696)Termination phase: Saturation
% 7.22/2.24
% 7.22/2.24 % (2696)Memory used [KB]: 6908
% 7.22/2.24 % (2696)Time elapsed: 0.247 s
% 7.22/2.24 % (2696)Instructions burned: 988 (million)
% 7.22/2.24 % (2696)------------------------------
% 7.22/2.24 % (2696)------------------------------
% 7.22/2.24 % (2717)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_2340 for (2991ds/1913Mi)
% 7.62/2.32 % (2715)Instruction limit reached!
% 7.62/2.32 % (2715)------------------------------
% 7.62/2.32 % (2715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.32 % (2715)Termination reason: Unknown
% 7.62/2.32 % (2715)Termination phase: Saturation
% 7.62/2.32
% 7.62/2.32 % (2715)Memory used [KB]: 7164
% 7.62/2.32 % (2715)Time elapsed: 0.109 s
% 7.62/2.32 % (2715)Instructions burned: 410 (million)
% 7.62/2.32 % (2715)------------------------------
% 7.62/2.32 % (2715)------------------------------
% 7.62/2.32 % (2703)Instruction limit reached!
% 7.62/2.32 % (2703)------------------------------
% 7.62/2.32 % (2703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.32 % (2703)Termination reason: Unknown
% 7.62/2.32 % (2703)Termination phase: Saturation
% 7.62/2.32
% 7.62/2.32 % (2703)Memory used [KB]: 8059
% 7.62/2.32 % (2703)Time elapsed: 0.228 s
% 7.62/2.32 % (2703)Instructions burned: 922 (million)
% 7.62/2.32 % (2703)------------------------------
% 7.62/2.32 % (2703)------------------------------
% 7.62/2.33 % (2718)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_2340 for (2990ds/4350Mi)
% 7.62/2.33 % (2719)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_2340 for (2990ds/68Mi)
% 7.62/2.35 % (2719)Instruction limit reached!
% 7.62/2.35 % (2719)------------------------------
% 7.62/2.35 % (2719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.35 % (2719)Termination reason: Unknown
% 7.62/2.35 % (2719)Termination phase: Function definition elimination
% 7.62/2.35
% 7.62/2.35 % (2719)Memory used [KB]: 1791
% 7.62/2.35 % (2719)Time elapsed: 0.018 s
% 7.62/2.35 % (2719)Instructions burned: 71 (million)
% 7.62/2.35 % (2719)------------------------------
% 7.62/2.35 % (2719)------------------------------
% 7.62/2.36 % (2708)Instruction limit reached!
% 7.62/2.36 % (2708)------------------------------
% 7.62/2.36 % (2708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.36 % (2708)Termination reason: Unknown
% 7.62/2.36 % (2708)Termination phase: Saturation
% 7.62/2.36
% 7.62/2.36 % (2708)Memory used [KB]: 6780
% 7.62/2.36 % (2708)Time elapsed: 0.231 s
% 7.62/2.36 % (2708)Instructions burned: 1024 (million)
% 7.62/2.36 % (2708)------------------------------
% 7.62/2.36 % (2708)------------------------------
% 7.62/2.36 % (2720)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_2340 for (2990ds/358Mi)
% 7.62/2.37 % (2721)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_2340 for (2990ds/31Mi)
% 7.62/2.38 % (2721)Instruction limit reached!
% 7.62/2.38 % (2721)------------------------------
% 7.62/2.38 % (2721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.62/2.38 % (2721)Termination reason: Unknown
% 7.62/2.38 % (2721)Termination phase: Property scanning
% 7.62/2.38
% 7.62/2.38 % (2721)Memory used [KB]: 1535
% 7.62/2.38 % (2721)Time elapsed: 0.010 s
% 7.62/2.38 % (2721)Instructions burned: 35 (million)
% 7.62/2.38 % (2721)------------------------------
% 7.62/2.38 % (2721)------------------------------
% 7.62/2.39 % (2722)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_2340 for (2990ds/279Mi)
% 8.26/2.45 % (2720)Instruction limit reached!
% 8.26/2.45 % (2720)------------------------------
% 8.26/2.45 % (2720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.45 % (2720)Termination reason: Unknown
% 8.26/2.45 % (2720)Termination phase: Saturation
% 8.26/2.45
% 8.26/2.45 % (2720)Memory used [KB]: 6780
% 8.26/2.45 % (2720)Time elapsed: 0.088 s
% 8.26/2.45 % (2720)Instructions burned: 360 (million)
% 8.26/2.45 % (2720)------------------------------
% 8.26/2.45 % (2720)------------------------------
% 8.26/2.46 % (2723)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_2340 for (2989ds/258Mi)
% 8.26/2.46 % (2722)Instruction limit reached!
% 8.26/2.46 % (2722)------------------------------
% 8.26/2.46 % (2722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.46 % (2722)Termination reason: Unknown
% 8.26/2.46 % (2722)Termination phase: Saturation
% 8.26/2.46
% 8.26/2.46 % (2722)Memory used [KB]: 6396
% 8.26/2.46 % (2722)Time elapsed: 0.070 s
% 8.26/2.46 % (2722)Instructions burned: 282 (million)
% 8.26/2.46 % (2722)------------------------------
% 8.26/2.46 % (2722)------------------------------
% 8.26/2.47 % (2724)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_2340 for (2989ds/26Mi)
% 8.26/2.47 % (2724)Instruction limit reached!
% 8.26/2.47 % (2724)------------------------------
% 8.26/2.47 % (2724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.47 % (2724)Termination reason: Unknown
% 8.26/2.47 % (2724)Termination phase: Property scanning
% 8.26/2.47
% 8.26/2.47 % (2724)Memory used [KB]: 1535
% 8.26/2.47 % (2724)Time elapsed: 0.009 s
% 8.26/2.47 % (2724)Instructions burned: 29 (million)
% 8.26/2.47 % (2724)------------------------------
% 8.26/2.47 % (2724)------------------------------
% 8.26/2.48 % (2725)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_2340 for (2989ds/995Mi)
% 8.45/2.53 % (2723)Instruction limit reached!
% 8.45/2.53 % (2723)------------------------------
% 8.45/2.53 % (2723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.45/2.53 % (2723)Termination reason: Unknown
% 8.45/2.53 % (2723)Termination phase: Saturation
% 8.45/2.53
% 8.45/2.53 % (2723)Memory used [KB]: 7036
% 8.45/2.53 % (2723)Time elapsed: 0.078 s
% 8.45/2.53 % (2723)Instructions burned: 260 (million)
% 8.45/2.53 % (2723)------------------------------
% 8.45/2.53 % (2723)------------------------------
% 8.45/2.54 % (2726)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_2340 for (2988ds/373Mi)
% 8.45/2.55 % (2714)Instruction limit reached!
% 8.45/2.55 % (2714)------------------------------
% 8.45/2.55 % (2714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.45/2.55 % (2714)Termination reason: Unknown
% 8.45/2.55 % (2714)Termination phase: Saturation
% 8.45/2.55
% 8.45/2.55 % (2714)Memory used [KB]: 6780
% 8.45/2.55 % (2714)Time elapsed: 0.346 s
% 8.45/2.55 % (2714)Instructions burned: 1542 (million)
% 8.45/2.55 % (2714)------------------------------
% 8.45/2.55 % (2714)------------------------------
% 8.45/2.56 % (2727)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_2340 for (2988ds/253Mi)
% 8.89/2.62 % (2727)Instruction limit reached!
% 8.89/2.62 % (2727)------------------------------
% 8.89/2.62 % (2727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.62 % (2727)Termination reason: Unknown
% 8.89/2.62 % (2727)Termination phase: Saturation
% 8.89/2.62
% 8.89/2.62 % (2727)Memory used [KB]: 6780
% 8.89/2.62 % (2727)Time elapsed: 0.060 s
% 8.89/2.62 % (2727)Instructions burned: 255 (million)
% 8.89/2.62 % (2727)------------------------------
% 8.89/2.62 % (2727)------------------------------
% 8.89/2.63 % (2728)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_2340 for (2988ds/832Mi)
% 8.89/2.63 % (2726)Instruction limit reached!
% 8.89/2.63 % (2726)------------------------------
% 8.89/2.63 % (2726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.63 % (2726)Termination reason: Unknown
% 8.89/2.63 % (2726)Termination phase: Saturation
% 8.89/2.63
% 8.89/2.63 % (2726)Memory used [KB]: 6780
% 8.89/2.63 % (2726)Time elapsed: 0.087 s
% 8.89/2.63 % (2726)Instructions burned: 375 (million)
% 8.89/2.63 % (2726)------------------------------
% 8.89/2.63 % (2726)------------------------------
% 8.89/2.64 % (2729)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_2340 for (2987ds/668Mi)
% 8.89/2.64 % (2728)Refutation not found, incomplete strategy
% 8.89/2.64 % (2728)------------------------------
% 8.89/2.64 % (2728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.64 % (2728)Termination reason: Refutation not found, incomplete strategy
% 8.89/2.64
% 8.89/2.64
% 8.89/2.64 % (2728)Memory used [KB]: 6140
% 8.89/2.64 % (2728)Time elapsed: 0.014 s
% 8.89/2.64 % (2728)Instructions burned: 47 (million)
% 8.89/2.64 % (2728)------------------------------
% 8.89/2.64 % (2728)------------------------------
% 8.89/2.65 % (2730)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=40:si=on:rtra=on_0 on DTF2THF_2340 for (2987ds/40Mi)
% 8.89/2.66 % (2730)Instruction limit reached!
% 8.89/2.66 % (2730)------------------------------
% 8.89/2.66 % (2730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.66 % (2730)Termination reason: Unknown
% 8.89/2.66 % (2730)Termination phase: Function definition elimination
% 8.89/2.66
% 8.89/2.66 % (2730)Memory used [KB]: 1535
% 8.89/2.66 % (2730)Time elapsed: 0.012 s
% 8.89/2.66 % (2730)Instructions burned: 41 (million)
% 8.89/2.66 % (2730)------------------------------
% 8.89/2.66 % (2730)------------------------------
% 8.89/2.67 % (2731)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_2340 for (2987ds/294Mi)
% 8.89/2.68 % (2717)Instruction limit reached!
% 8.89/2.68 % (2717)------------------------------
% 8.89/2.68 % (2717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.68 % (2717)Termination reason: Unknown
% 8.89/2.68 % (2717)Termination phase: Saturation
% 8.89/2.68
% 8.89/2.68 % (2717)Memory used [KB]: 2302
% 8.89/2.68 % (2717)Time elapsed: 0.436 s
% 8.89/2.68 % (2717)Instructions burned: 1914 (million)
% 8.89/2.68 % (2717)------------------------------
% 8.89/2.68 % (2717)------------------------------
% 8.89/2.69 % (2732)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_2340 for (2987ds/187Mi)
% 9.57/2.72 % (2725)Instruction limit reached!
% 9.57/2.72 % (2725)------------------------------
% 9.57/2.72 % (2725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.72 % (2725)Termination reason: Unknown
% 9.57/2.72 % (2725)Termination phase: Saturation
% 9.57/2.72
% 9.57/2.72 % (2725)Memory used [KB]: 7036
% 9.57/2.72 % (2725)Time elapsed: 0.234 s
% 9.57/2.72 % (2725)Instructions burned: 996 (million)
% 9.57/2.72 % (2725)------------------------------
% 9.57/2.72 % (2725)------------------------------
% 9.57/2.73 % (2733)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_2340 for (2987ds/371Mi)
% 9.57/2.73 % (2732)Instruction limit reached!
% 9.57/2.73 % (2732)------------------------------
% 9.57/2.73 % (2732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.73 % (2732)Termination reason: Unknown
% 9.57/2.73 % (2732)Termination phase: Saturation
% 9.57/2.73
% 9.57/2.73 % (2732)Memory used [KB]: 6780
% 9.57/2.73 % (2732)Time elapsed: 0.046 s
% 9.57/2.73 % (2732)Instructions burned: 187 (million)
% 9.57/2.73 % (2732)------------------------------
% 9.57/2.73 % (2732)------------------------------
% 9.57/2.73 % (2731)First to succeed.
% 9.57/2.74 % (2734)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_2340 for (2986ds/1827Mi)
% 9.57/2.74 % (2731)Refutation found. Thanks to Tanya!
% 9.57/2.74 % SZS status Theorem for DTF2THF_2340
% 9.57/2.74 % SZS output start Proof for DTF2THF_2340
% 9.57/2.74 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 9.57/2.74 thf(func_def_3, type, c_not: $o > $o).
% 9.57/2.74 thf(func_def_4, type, c_and: $o > $o > $o).
% 9.57/2.74 thf(func_def_5, type, c_or: $o > $o > $o).
% 9.57/2.74 thf(func_def_6, type, c_iff: $o > $o > $o).
% 9.57/2.74 thf(func_def_7, type, c_In: $i > $i > $o).
% 9.57/2.74 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 9.57/2.74 thf(func_def_10, type, c_Union: $i > $i).
% 9.57/2.74 thf(func_def_11, type, c_Power: $i > $i).
% 9.57/2.74 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 9.57/2.74 thf(func_def_13, type, c_TransSet: $i > $o).
% 9.57/2.74 thf(func_def_14, type, c_atleast2: $i > $o).
% 9.57/2.74 thf(func_def_15, type, c_atleast3: $i > $o).
% 9.57/2.74 thf(func_def_16, type, c_atleast4: $i > $o).
% 9.57/2.74 thf(func_def_17, type, c_atleast5: $i > $o).
% 9.57/2.74 thf(func_def_18, type, c_atleast6: $i > $o).
% 9.57/2.74 thf(func_def_19, type, c_exactly2: $i > $o).
% 9.57/2.74 thf(func_def_20, type, c_exactly3: $i > $o).
% 9.57/2.74 thf(func_def_21, type, c_exactly4: $i > $o).
% 9.57/2.74 thf(func_def_22, type, c_exactly5: $i > $o).
% 9.57/2.74 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 9.57/2.74 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 9.57/2.74 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 9.57/2.74 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 9.57/2.74 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 9.57/2.74 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 9.57/2.74 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 9.57/2.74 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 9.57/2.74 thf(func_def_43, type, c_Sing: $i > $i).
% 9.57/2.74 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 9.57/2.74 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 9.57/2.74 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 9.57/2.74 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 9.57/2.74 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 9.57/2.74 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 9.57/2.74 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 9.57/2.74 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 9.57/2.74 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 9.57/2.74 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 9.57/2.74 thf(func_def_54, type, c_equip: $i > $i > $o).
% 9.57/2.74 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 9.57/2.74 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 9.57/2.74 thf(func_def_57, type, c_ordsucc: $i > $i).
% 9.57/2.74 thf(func_def_58, type, c_nat_p: $i > $o).
% 9.57/2.74 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 9.57/2.74 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 9.57/2.74 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 9.57/2.74 thf(func_def_62, type, c_ordinal: $i > $o).
% 9.57/2.74 thf(func_def_63, type, c_V_: $i > $i).
% 9.57/2.74 thf(func_def_64, type, c_Inj1: $i > $i).
% 9.57/2.74 thf(func_def_65, type, c_Inj0: $i > $i).
% 9.57/2.74 thf(func_def_66, type, c_Unj: $i > $i).
% 9.57/2.74 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 9.57/2.74 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 9.57/2.74 thf(func_def_69, type, c_proj0: $i > $i).
% 9.57/2.74 thf(func_def_70, type, c_proj1: $i > $i).
% 9.57/2.74 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 9.57/2.74 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 9.57/2.74 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 9.57/2.74 thf(func_def_74, type, c_ap: $i > $i > $i).
% 9.57/2.74 thf(func_def_75, type, c_setsum_p: $i > $o).
% 9.57/2.74 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 9.57/2.74 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 9.57/2.74 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 9.57/2.74 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 9.57/2.74 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 9.57/2.74 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 9.57/2.74 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 9.57/2.74 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 9.57/2.74 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 9.57/2.74 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 9.57/2.74 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 9.57/2.74 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 9.57/2.74 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 9.57/2.74 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 9.57/2.74 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 9.57/2.74 thf(func_def_91, type, c_SNo: $i > $o).
% 9.57/2.74 thf(func_def_92, type, c_SNoLev: $i > $i).
% 9.57/2.74 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 9.57/2.74 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 9.57/2.74 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 9.57/2.74 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 9.57/2.74 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 9.57/2.74 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).
% 9.57/2.74 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).
% 9.57/2.74 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).
% 9.57/2.74 thf(func_def_101, type, c_combinator: $i > $o).
% 9.57/2.74 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 9.57/2.74 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 9.57/2.74 thf(func_def_133, type, ph1: !>[X0: $tType]:(X0)).
% 9.57/2.74 thf(f581,plain,(
% 9.57/2.74 $false),
% 9.57/2.74 inference(avatar_sat_refutation,[status(thm)],[f479,f489,f497,f572])).
% 9.57/2.74 thf(f572,plain,(
% 9.57/2.74 ~spl0_5),
% 9.57/2.74 inference(avatar_contradiction_clause,[status(thm)],[f571])).
% 9.57/2.74 thf(f571,plain,(
% 9.57/2.74 $false | ~spl0_5),
% 9.57/2.74 inference(trivial_inequality_removal,[status(thm)],[f570])).
% 9.57/2.74 thf(f570,plain,(
% 9.57/2.74 ($true = $false) | ~spl0_5),
% 9.57/2.74 inference(beta_eta_normalization,[status(thm)],[f499])).
% 9.57/2.74 thf(f499,plain,(
% 9.57/2.74 ( ! [X2 : $i > $i] : ((((^[Y0 : $i]: ($true)) @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) = $false)) ) | ~spl0_5),
% 9.57/2.74 inference(primitive_instantiation,[status(thm)],[f474])).
% 9.57/2.74 thf(f474,plain,(
% 9.57/2.74 ( ! [X2 : $i > $i,X1 : $i > $o] : (((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) = $false)) ) | ~spl0_5),
% 9.57/2.74 inference(avatar_component_clause,[status(thm)],[f473])).
% 9.57/2.74 thf(f473,definition,(
% 9.57/2.74 spl0_5 <=> ! [X2 : $i > $i,X1 : $i > $o] : ((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) = $false)),
% 9.57/2.74 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 9.57/2.74 thf(f497,plain,(
% 9.57/2.74 ~spl0_6),
% 9.57/2.74 inference(avatar_contradiction_clause,[status(thm)],[f496])).
% 9.57/2.74 thf(f496,plain,(
% 9.57/2.74 $false | ~spl0_6),
% 9.57/2.74 inference(trivial_inequality_removal,[status(thm)],[f493])).
% 9.57/2.74 thf(f493,plain,(
% 9.57/2.74 ($true = $false) | ~spl0_6),
% 9.57/2.74 inference(superposition,[status(thm)],[f433,f478])).
% 9.57/2.74 thf(f478,plain,(
% 9.57/2.74 (c_False = $true) | ~spl0_6),
% 9.57/2.74 inference(avatar_component_clause,[status(thm)],[f476])).
% 9.57/2.74 thf(f476,definition,(
% 9.57/2.74 spl0_6 <=> (c_False = $true)),
% 9.57/2.74 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 9.57/2.74 thf(f433,plain,(
% 9.57/2.74 (c_False = $false)),
% 9.57/2.74 inference(binary_proxy_clausification,[status(thm)],[f432])).
% 9.57/2.74 thf(f432,plain,(
% 9.57/2.74 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $o @ (^[Y2 : $o]: (((((Y0 @ (Y1 @ (c_Eps_i @ (^[Y3 : $i]: (c_or @ (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => (((c_Repl @ (Y1 @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_or @ (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y5 = Y6) => Y7)) => Y7))) @ (!! @ $o @ (^[Y7 : $o]: ((((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((c_In @ Y8 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y8 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y9)) => Y9))))) = Y6) => Y7)) => Y7)))))))) = Y3) => Y4)) => Y4))) @ (!! @ $o @ (^[Y4 : $o]: ((((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => c_False) => ((c_Empty = Y3) => Y4)) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y1 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y1 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y0 @ (c_lam @ Y5 @ (^[Y9 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_binunion @ Y5 @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_SetAdjoin @ Y9 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (c_or @ (!! @ $o @ (^[Y9 : $o]: (((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y9)) => Y9))) @ (!! @ $o @ (^[Y9 : $o]: ((((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y9)) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y0 @ (Y1 @ (Y1 @ (Y1 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y2)) => Y2))))))) => c_False) = $false)),
% 9.57/2.74 inference(not_proxy_clausification,[status(thm)],[f431])).
% 9.57/2.74 thf(f431,plain,(
% 9.57/2.74 ((~ ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $o @ (^[Y2 : $o]: (((((Y0 @ (Y1 @ (c_Eps_i @ (^[Y3 : $i]: (c_or @ (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => (((c_Repl @ (Y1 @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_or @ (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y5 = Y6) => Y7)) => Y7))) @ (!! @ $o @ (^[Y7 : $o]: ((((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((c_In @ Y8 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y8 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y9)) => Y9))))) = Y6) => Y7)) => Y7)))))))) = Y3) => Y4)) => Y4))) @ (!! @ $o @ (^[Y4 : $o]: ((((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => c_False) => ((c_Empty = Y3) => Y4)) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y1 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y1 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y0 @ (c_lam @ Y5 @ (^[Y9 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_binunion @ Y5 @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_SetAdjoin @ Y9 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (c_or @ (!! @ $o @ (^[Y9 : $o]: (((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y9)) => Y9))) @ (!! @ $o @ (^[Y9 : $o]: ((((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y9)) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y0 @ (Y1 @ (Y1 @ (Y1 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y2)) => Y2))))))) => c_False)) = $true)),
% 9.57/2.74 inference(beta_eta_normalization,[status(thm)],[f418])).
% 9.57/2.74 thf(f418,plain,(
% 9.57/2.74 ((~ ((^[Y0 : $o]: (Y0 => c_False)) @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (((Y0 @ (Y1 @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (c_or @ ((^[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 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y4) @ (Y5 @ Y6)))) @ (c_Repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (c_or @ ((^[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 => c_False)) @ Y8) @ (Y10 = Y11)))))))))) @ (Y5 @ Y7) @ Y7 @ (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ (c_In @ Y8 @ Y4) @ (Y5 @ Y8)))))) @ Y6))) @ c_Empty)))) @ Y2 @ (^[Y4 : $i]: (c_In @ Y4 @ Y3)))))) @ (Y1 @ (c_Power @ c_Empty)) @ (Y1 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_setsum @ Y2 @ (c_Power @ Y3))))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => (((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2))))) @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2) @ ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y5) @ ((^[Y7 : $o]: (Y7 => c_False)) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y5 @ (c_Power @ Y6))))))) @ Y4) @ ((^[Y5 : $o]: (Y5 => c_False)) @ ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y6 @ Y5) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => c_False)) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y5 @ Y6)) @ ((^[Y7 : $i]: (?? @ $i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ (c_In @ Y8 @ Y7) @ ((^[Y9 : $o]: (Y9 => c_False)) @ ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y9) => (c_In @ Y11 @ Y10))))))) @ Y7 @ (c_Power @ Y8))))))) @ Y6)))))) @ Y4)))) @ ((^[Y4 : $i]: (c_binunion @ Y4 @ (c_Sing @ Y4))) @ (Y1 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2) @ (((Y1 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y4 @ Y2) @ ((^[Y5 : $o]: (Y5 => c_False)) @ (Y0 @ ((^[Y5 : $i]: ((^[Y6 : $i]: (c_lam @ Y5 @ (^[Y7 : $i]: (Y6)))))) @ Y3 @ ((^[Y5 : $i]: ((^[Y6 : $i]: (c_setsum @ Y5 @ (c_Power @ Y6))))) @ (c_Power @ ((^[Y5 : $i]: ((^[Y6 : $i]: (c_setsum @ Y5 @ (c_Power @ Y6))))) @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => ((^[Y8 : $i]: ((^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y8) => (c_In @ Y10 @ Y9))))))) @ Y7 @ Y6))))) @ Y5) @ (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => ((^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y9) => (c_In @ Y11 @ Y10))))))) @ Y8 @ Y7))))) @ Y6)))))) @ Y4) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y8))))))) @ Y6 @ ((^[Y7 : $i]: (c_binunion @ Y7 @ (c_Repl @ Y7 @ (^[Y8 : $i]: ((^[Y9 : $i]: (c_SetAdjoin @ Y9 @ (c_Sing @ ((^[Y10 : $i]: (c_binunion @ Y10 @ (c_Sing @ Y10))) @ c_Empty)))) @ Y8))))) @ Y5)) @ (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => ((^[Y8 : $o]: ((^[Y9 : $o]: (c_or @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y8 @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y8) @ Y9))))) @ (c_In @ ((^[Y8 : $i]: (c_SetAdjoin @ Y8 @ (c_Sing @ ((^[Y9 : $i]: (c_binunion @ Y9 @ (c_Sing @ Y9))) @ c_Empty)))) @ Y7) @ Y6) @ (c_In @ Y7 @ Y6))))))))) @ Y4 @ Y3))))) @ Y2)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_setsum @ Y2 @ (c_Power @ Y3))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_setsum @ Y2 @ (c_Power @ Y3))))) @ (c_Power @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_setsum @ Y2 @ (c_Power @ Y3))))) @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))))))) = $true)),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f326,f302,f306,f382,f293,f363,f306,f318,f369,f357,f306,f306,f318,f306,f318,f302,f311,f293,f293,f302,f408,f302,f293,f293,f293])).
% 9.57/2.74 thf(f408,plain,(
% 9.57/2.74 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y4 @ Y3))))) @ Y2) @ (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y4) => ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ Y7))))))) @ Y5 @ Y4))))) @ Y3)))))) @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ ((^[Y4 : $i]: (c_binunion @ Y4 @ (c_Repl @ Y4 @ (^[Y5 : $i]: ((^[Y6 : $i]: (c_SetAdjoin @ Y6 @ (c_Sing @ ((^[Y7 : $i]: (c_binunion @ Y7 @ (c_Sing @ Y7))) @ c_Empty)))) @ Y5))))) @ Y2)) @ (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => ((^[Y5 : $o]: ((^[Y6 : $o]: (c_or @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ Y5 @ ((^[Y7 : $o]: (Y7 => c_False)) @ Y6)) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => c_False)) @ Y5) @ Y6))))) @ (c_In @ ((^[Y5 : $i]: (c_SetAdjoin @ Y5 @ (c_Sing @ ((^[Y6 : $i]: (c_binunion @ Y6 @ (c_Sing @ Y6))) @ c_Empty)))) @ Y4) @ Y3) @ (c_In @ Y4 @ Y3))))))))) @ Y1 @ Y0))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f309,f306,f390,f406])).
% 9.57/2.74 thf(f406,plain,(
% 9.57/2.74 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ ((^[Y2 : $i]: (c_binunion @ Y2 @ (c_Repl @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (c_SetAdjoin @ Y4 @ (c_Sing @ ((^[Y5 : $i]: (c_binunion @ Y5 @ (c_Sing @ Y5))) @ c_Empty)))) @ Y3))))) @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => ((^[Y3 : $o]: ((^[Y4 : $o]: (c_or @ ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ Y3 @ ((^[Y5 : $o]: (Y5 => c_False)) @ Y4)) @ ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ ((^[Y5 : $o]: (Y5 => c_False)) @ Y3) @ Y4))))) @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ ((^[Y4 : $i]: (c_binunion @ Y4 @ (c_Sing @ Y4))) @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f308,f306,f318,f405,f376,f357])).
% 9.57/2.74 thf(f376,plain,(
% 9.57/2.74 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ Y0 @ ((^[Y2 : $o]: (Y2 => c_False)) @ Y1)) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ Y0) @ Y1))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f319,f306,f302,f306,f302])).
% 9.57/2.74 thf(f319,plain,(
% 9.57/2.74 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ (c_and @ Y0 @ (c_not @ Y1)) @ (c_and @ (c_not @ Y0) @ Y1))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f189])).
% 9.57/2.74 thf(f189,plain,(
% 9.57/2.74 (c_exactly1of2 = (^[Y0 : $o]: ((^[Y1 : $o]: (c_or @ (c_and @ Y0 @ (c_not @ Y1)) @ (c_and @ (c_not @ Y0) @ Y1))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f43])).
% 9.57/2.74 thf(f43,axiom,(
% 9.57/2.74 ((^[X0 : $o, X1 : $o] : (c_or @ (c_and @ X0 @ (c_not @ X1)) @ (c_and @ (c_not @ X0) @ X1))) = c_exactly1of2)),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax43)).
% 9.57/2.74 thf(f405,plain,(
% 9.57/2.74 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ ((^[Y3 : $i]: (c_binunion @ Y3 @ (c_Sing @ Y3))) @ c_Empty)))) @ Y1))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f316,f357])).
% 9.57/2.74 thf(f316,plain,(
% 9.57/2.74 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y1))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f231])).
% 9.57/2.74 thf(f231,plain,(
% 9.57/2.74 (c_SNoElts_ = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i]: (c_SetAdjoin @ Y2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y1))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f93])).
% 9.57/2.74 thf(f93,axiom,(
% 9.57/2.74 (c_SNoElts_ = (^[X0 : $i] : (c_binunion @ X0 @ (c_Repl @ X0 @ (^[X1 : $i] : ((^[X2 : $i] : (c_SetAdjoin @ X2 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ X1))))))),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax93)).
% 9.57/2.74 thf(f308,plain,(
% 9.57/2.74 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ (c_SNoElts_ @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_exactly1of2 @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f132])).
% 9.57/2.74 thf(f132,plain,(
% 9.57/2.74 (c_SNo_ = (^[Y0 : $i]: ((^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ (c_SNoElts_ @ Y0)) @ (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_exactly1of2 @ (c_In @ ((^[Y3 : $i]: (c_SetAdjoin @ Y3 @ (c_Sing @ (c_ordsucc @ c_Empty)))) @ Y2) @ Y1) @ (c_In @ Y2 @ Y1))))))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f131])).
% 9.57/2.74 thf(f131,plain,(
% 9.57/2.74 ((^[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))))) = c_SNo_)),
% 9.57/2.74 inference(rectify,[status(thm)],[f94])).
% 9.57/2.74 thf(f94,axiom,(
% 9.57/2.74 ((^[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))))) = c_SNo_)),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax94)).
% 9.57/2.74 thf(f390,plain,(
% 9.57/2.74 (c_ordinal = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y1) => ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y2 @ Y1))))) @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y3 @ Y2))))) @ Y1)))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f346,f306,f363,f363])).
% 9.57/2.74 thf(f346,plain,(
% 9.57/2.74 (c_ordinal = (^[Y0 : $i]: (c_and @ (c_TransSet @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_TransSet @ Y1)))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f211])).
% 9.57/2.74 thf(f211,plain,(
% 9.57/2.74 (c_ordinal = (^[Y0 : $i]: (c_and @ (c_TransSet @ Y0) @ (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_TransSet @ Y1)))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f210])).
% 9.57/2.74 thf(f210,plain,(
% 9.57/2.74 (c_ordinal = (^[X0 : $i] : (c_and @ (c_TransSet @ X0) @ ! [X1 : $i] : ((c_In @ X1 @ X0) => (c_TransSet @ X1)))))),
% 9.57/2.74 inference(rectify,[status(thm)],[f67])).
% 9.57/2.74 thf(f67,axiom,(
% 9.57/2.74 (c_ordinal = (^[X0 : $i] : (c_and @ (c_TransSet @ X0) @ ! [X1 : $i] : ((c_In @ X1 @ X0) => (c_TransSet @ X1)))))),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax67)).
% 9.57/2.74 thf(f309,plain,(
% 9.57/2.74 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_ordinal @ Y1) @ (c_SNo_ @ Y1 @ Y0))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f272])).
% 9.57/2.74 thf(f272,plain,(
% 9.57/2.74 (c_SNo = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_ordinal @ Y1) @ (c_SNo_ @ Y1 @ Y0))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f271])).
% 9.57/2.74 thf(f271,plain,(
% 9.57/2.74 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_ordinal @ X1) @ (c_SNo_ @ X1 @ X0)))) = c_SNo)),
% 9.57/2.74 inference(rectify,[status(thm)],[f96])).
% 9.57/2.74 thf(f96,axiom,(
% 9.57/2.74 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_ordinal @ X1) @ (c_SNo_ @ X1 @ X0)))) = c_SNo)),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax96)).
% 9.57/2.74 thf(f311,plain,(
% 9.57/2.74 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: (c_lam @ Y0 @ (^[Y2 : $i]: (Y1)))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f179])).
% 9.57/2.74 thf(f179,plain,(
% 9.57/2.74 (c_setprod = (^[Y0 : $i]: ((^[Y1 : $i]: (c_lam @ Y0 @ (^[Y2 : $i]: (Y1)))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f78])).
% 9.57/2.74 thf(f78,axiom,(
% 9.57/2.74 ((^[X0 : $i, X1 : $i] : (c_lam @ X0 @ (^[X2 : $i] : (X1)))) = c_setprod)),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax78)).
% 9.57/2.74 thf(f357,plain,(
% 9.57/2.74 (c_ordsucc = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y0))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f265])).
% 9.57/2.74 thf(f265,plain,(
% 9.57/2.74 (c_ordsucc = (^[Y0 : $i]: (c_binunion @ Y0 @ (c_Sing @ Y0))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f62])).
% 9.57/2.74 thf(f62,axiom,(
% 9.57/2.74 ((^[X0 : $i] : (c_binunion @ X0 @ (c_Sing @ X0))) = c_ordsucc)),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax62)).
% 9.57/2.74 thf(f369,plain,(
% 9.57/2.74 (c_exactly2 = (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (c_In @ Y2 @ Y1) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y1 @ (c_Power @ Y2))))))) @ Y0) @ ((^[Y1 : $o]: (Y1 => c_False)) @ ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y2 @ Y1) @ ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ ((^[Y3 : $o]: (Y3 => c_False)) @ ((^[Y3 : $i]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y4))))))) @ Y1 @ Y2)) @ ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y3) @ ((^[Y5 : $o]: (Y5 => c_False)) @ ((^[Y5 : $i]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y6))))))) @ Y3 @ (c_Power @ Y4))))))) @ Y2)))))) @ Y0)))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f320,f306,f364,f302,f365])).
% 9.57/2.74 thf(f365,plain,(
% 9.57/2.74 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0) @ ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ ((^[Y2 : $o]: (Y2 => c_False)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y0 @ Y1)) @ ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ (c_In @ Y3 @ Y2) @ ((^[Y4 : $o]: (Y4 => c_False)) @ ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y5))))))) @ Y2 @ (c_Power @ Y3))))))) @ Y1)))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f334,f306,f318,f306,f302,f318,f364])).
% 9.57/2.74 thf(f334,plain,(
% 9.57/2.74 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ Y0) @ (c_and @ (c_not @ (c_Subq @ Y0 @ Y1)) @ (c_atleast2 @ Y1)))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f149])).
% 9.57/2.74 thf(f149,plain,(
% 9.57/2.74 (c_atleast3 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_Subq @ Y1 @ Y0) @ (c_and @ (c_not @ (c_Subq @ Y0 @ Y1)) @ (c_atleast2 @ Y1)))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f148])).
% 9.57/2.74 thf(f148,plain,(
% 9.57/2.74 (c_atleast3 = (^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_Subq @ X1 @ X0) @ (c_and @ (c_not @ (c_Subq @ X0 @ X1)) @ (c_atleast2 @ X1))))))),
% 9.57/2.74 inference(rectify,[status(thm)],[f20])).
% 9.57/2.74 thf(f20,axiom,(
% 9.57/2.74 (c_atleast3 = (^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_Subq @ X1 @ X0) @ (c_and @ (c_not @ (c_Subq @ X0 @ X1)) @ (c_atleast2 @ X1))))))),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax20)).
% 9.57/2.74 thf(f364,plain,(
% 9.57/2.74 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (c_In @ Y1 @ Y0) @ ((^[Y2 : $o]: (Y2 => c_False)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y0 @ (c_Power @ Y1))))))))),
% 9.57/2.74 inference(definition_unfolding,[status(thm)],[f337,f306,f302,f318])).
% 9.57/2.74 thf(f337,plain,(
% 9.57/2.74 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_In @ Y1 @ Y0) @ (c_not @ (c_Subq @ Y0 @ (c_Power @ Y1))))))))),
% 9.57/2.74 inference(cnf_transformation,[status(thm)],[f285])).
% 9.57/2.74 thf(f285,plain,(
% 9.57/2.74 (c_atleast2 = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (c_and @ (c_In @ Y1 @ Y0) @ (c_not @ (c_Subq @ Y0 @ (c_Power @ Y1))))))))),
% 9.57/2.74 inference(fool_elimination,[status(thm)],[f284])).
% 9.57/2.74 thf(f284,plain,(
% 9.57/2.74 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_In @ X1 @ X0) @ (c_not @ (c_Subq @ X0 @ (c_Power @ X1)))))) = c_atleast2)),
% 9.57/2.74 inference(rectify,[status(thm)],[f19])).
% 9.57/2.74 thf(f19,axiom,(
% 9.57/2.74 ((^[X0 : $i] : (? [X1 : $i] : (c_and @ (c_In @ X1 @ X0) @ (c_not @ (c_Subq @ X0 @ (c_Power @ X1)))))) = c_atleast2)),
% 9.57/2.74 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax19)).
% 9.57/2.75 thf(f320,plain,(
% 9.57/2.75 (c_exactly2 = (^[Y0 : $i]: (c_and @ (c_atleast2 @ Y0) @ (c_not @ (c_atleast3 @ Y0)))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f205])).
% 9.57/2.75 thf(f205,plain,(
% 9.57/2.75 (c_exactly2 = (^[Y0 : $i]: (c_and @ (c_atleast2 @ Y0) @ (c_not @ (c_atleast3 @ Y0)))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f24])).
% 9.57/2.75 thf(f24,axiom,(
% 9.57/2.75 (c_exactly2 = (^[X0 : $i] : (c_and @ (c_atleast2 @ X0) @ (c_not @ (c_atleast3 @ X0)))))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax24)).
% 9.57/2.75 thf(f318,plain,(
% 9.57/2.75 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f182])).
% 9.57/2.75 thf(f182,plain,(
% 9.57/2.75 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f181])).
% 9.57/2.75 thf(f181,plain,(
% 9.57/2.75 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 9.57/2.75 inference(rectify,[status(thm)],[f17])).
% 9.57/2.75 thf(f17,axiom,(
% 9.57/2.75 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax17)).
% 9.57/2.75 thf(f363,plain,(
% 9.57/2.75 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y3))))))) @ Y1 @ Y0))))))),
% 9.57/2.75 inference(definition_unfolding,[status(thm)],[f307,f318])).
% 9.57/2.75 thf(f307,plain,(
% 9.57/2.75 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_Subq @ Y1 @ Y0))))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f230])).
% 9.57/2.75 thf(f230,plain,(
% 9.57/2.75 (c_TransSet = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_Subq @ Y1 @ Y0))))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f229])).
% 9.57/2.75 thf(f229,plain,(
% 9.57/2.75 (c_TransSet = (^[X0 : $i] : (! [X1 : $i] : ((c_In @ X1 @ X0) => (c_Subq @ X1 @ X0)))))),
% 9.57/2.75 inference(rectify,[status(thm)],[f18])).
% 9.57/2.75 thf(f18,axiom,(
% 9.57/2.75 (c_TransSet = (^[X0 : $i] : (! [X1 : $i] : ((c_In @ X1 @ X0) => (c_Subq @ X1 @ X0)))))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax18)).
% 9.57/2.75 thf(f293,plain,(
% 9.57/2.75 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ Y0 @ (c_Power @ Y1))))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f191])).
% 9.57/2.75 thf(f191,plain,(
% 9.57/2.75 (c_binrep = (^[Y0 : $i]: ((^[Y1 : $i]: (c_setsum @ Y0 @ (c_Power @ Y1))))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f76])).
% 9.57/2.75 thf(f76,axiom,(
% 9.57/2.75 (c_binrep = (^[X0 : $i, X1 : $i] : (c_setsum @ X0 @ (c_Power @ X1))))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax76)).
% 9.57/2.75 thf(f382,plain,(
% 9.57/2.75 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (c_or @ ((^[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 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y2) @ (Y3 @ Y4)))) @ (c_Repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: (c_or @ ((^[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 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (Y3 @ Y5) @ Y5 @ (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ (c_In @ Y6 @ Y2) @ (Y3 @ Y6)))))) @ Y4))) @ c_Empty)))) @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))),
% 9.57/2.75 inference(definition_unfolding,[status(thm)],[f297,f381])).
% 9.57/2.75 thf(f381,plain,(
% 9.57/2.75 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_or @ ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ Y2 @ (Y3 = Y5)) @ ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((^[Y6 : $o]: (Y6 => c_False)) @ Y2) @ (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: (!! @ $o @ (^[Y5 : $o]: ((Y3 => (Y4 => Y5)) => Y5)))))) @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (c_or @ ((^[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 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: (!! @ $o @ (^[Y7 : $o]: ((Y5 => (Y6 => Y7)) => Y7)))))) @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))),
% 9.57/2.75 inference(definition_unfolding,[status(thm)],[f295,f375,f306,f375,f306])).
% 9.57/2.75 thf(f375,plain,(
% 9.57/2.75 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ ((^[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 => c_False)) @ Y0) @ (Y2 = Y3)))))))))))),
% 9.57/2.75 inference(definition_unfolding,[status(thm)],[f349,f306,f306,f302])).
% 9.57/2.75 thf(f349,plain,(
% 9.57/2.75 (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)))))))))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f156])).
% 9.57/2.75 thf(f156,plain,(
% 9.57/2.75 (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)))))))))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f42])).
% 9.57/2.75 thf(f42,axiom,(
% 9.57/2.75 (c_If_i = (^[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)))))))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax42)).
% 9.57/2.75 thf(f295,plain,(
% 9.57/2.75 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (c_If_i @ (?? @ $i @ (^[Y2 : $i]: (c_and @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_If_i @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: (c_and @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f201])).
% 9.57/2.75 thf(f201,plain,(
% 9.57/2.75 (c_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (c_If_i @ (?? @ $i @ (^[Y2 : $i]: (c_and @ (c_In @ Y2 @ Y0) @ (Y1 @ Y2)))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_If_i @ (Y1 @ Y3) @ Y3 @ (c_Eps_i @ (^[Y4 : $i]: (c_and @ (c_In @ Y4 @ Y0) @ (Y1 @ Y4)))))) @ Y2))) @ c_Empty)))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f200])).
% 9.57/2.75 thf(f200,plain,(
% 9.57/2.75 (c_Sep = (^[X0 : $i, X1 : $i > $o] : (c_If_i @ ? [X2 : $i] : (c_and @ (c_In @ X2 @ X0) @ (X1 @ X2)) @ (c_Repl @ X0 @ (^[X3 : $i] : ((^[X4 : $i] : (c_If_i @ (X1 @ X4) @ X4 @ (c_Eps_i @ (^[X5 : $i] : (c_and @ (c_In @ X5 @ X0) @ (X1 @ X5)))))) @ X3))) @ c_Empty)))),
% 9.57/2.75 inference(rectify,[status(thm)],[f52])).
% 9.57/2.75 thf(f52,axiom,(
% 9.57/2.75 (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)))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax52)).
% 9.57/2.75 thf(f297,plain,(
% 9.57/2.75 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Sep @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f183])).
% 9.57/2.75 thf(f183,plain,(
% 9.57/2.75 (c_binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Sep @ Y0 @ (^[Y2 : $i]: (c_In @ Y2 @ Y1)))))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f54])).
% 9.57/2.75 thf(f54,axiom,(
% 9.57/2.75 ((^[X0 : $i, X1 : $i] : (c_Sep @ X0 @ (^[X2 : $i] : (c_In @ X2 @ X1)))) = c_binintersect)),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax54)).
% 9.57/2.75 thf(f306,plain,(
% 9.57/2.75 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f174])).
% 9.57/2.75 thf(f174,plain,(
% 9.57/2.75 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f173])).
% 9.57/2.75 thf(f173,plain,(
% 9.57/2.75 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 9.57/2.75 inference(rectify,[status(thm)],[f14])).
% 9.57/2.75 thf(f14,axiom,(
% 9.57/2.75 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax14)).
% 9.57/2.75 thf(f302,plain,(
% 9.57/2.75 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f134])).
% 9.57/2.75 thf(f134,plain,(
% 9.57/2.75 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f133])).
% 9.57/2.75 thf(f133,plain,(
% 9.57/2.75 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 9.57/2.75 inference(rectify,[status(thm)],[f13])).
% 9.57/2.75 thf(f13,axiom,(
% 9.57/2.75 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',ax13)).
% 9.57/2.75 thf(f326,plain,(
% 9.57/2.75 ((~ (c_not @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (c_and @ (((Y0 @ (Y1 @ (c_binintersect @ (Y1 @ (c_Power @ c_Empty)) @ (Y1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (c_exactly2 @ (c_ordsucc @ (Y1 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: (c_and @ (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (((Y1 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: (c_and @ (c_Subq @ Y4 @ Y2) @ (c_not @ (Y0 @ (c_setprod @ Y3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ (c_not @ (c_SNo @ Y2)))))) @ (c_not @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))))))) = $true)),
% 9.57/2.75 inference(cnf_transformation,[status(thm)],[f274])).
% 9.57/2.75 thf(f274,plain,(
% 9.57/2.75 ((~ (c_not @ (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (c_and @ (((Y0 @ (Y1 @ (c_binintersect @ (Y1 @ (c_Power @ c_Empty)) @ (Y1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (c_exactly2 @ (c_ordsucc @ (Y1 @ Y3))))))))))) => (?? @ $i @ (^[Y2 : $i]: (c_and @ (?? @ $i @ (^[Y3 : $i]: (c_and @ (c_Subq @ Y3 @ Y2) @ (((Y1 @ Y2) = Y2) => (?? @ $i @ (^[Y4 : $i]: (c_and @ (c_Subq @ Y4 @ Y2) @ (c_not @ (Y0 @ (c_setprod @ Y3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty))))))))))))) @ (c_not @ (c_SNo @ Y2)))))) @ (c_not @ (Y0 @ (Y1 @ (Y1 @ (Y1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))))))) = $true)),
% 9.57/2.75 inference(fool_elimination,[status(thm)],[f273])).
% 9.57/2.75 thf(f273,plain,(
% 9.57/2.75 ~(c_not @ ! [X0 : $i > $i,X1 : $i > $o] : (c_and @ ((X1 @ (X0 @ (c_binintersect @ (X0 @ (c_Power @ c_Empty)) @ (X0 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X0 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X0 @ X3))))))) => ? [X4 : $i] : (c_and @ ? [X5 : $i] : (c_and @ (c_Subq @ X5 @ X4) @ ((X0 @ X4) = X4) => ? [X6 : $i] : (c_and @ (c_Subq @ X6 @ X4) @ (c_not @ (X1 @ (c_setprod @ X5 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X4))) @ (c_not @ (X1 @ (X0 @ (X0 @ (X0 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))),
% 9.57/2.75 inference(rectify,[status(thm)],[f110])).
% 9.57/2.75 thf(f110,negated_conjecture,(
% 9.57/2.75 ~(c_not @ ! [X1 : $i > $i,X0 : $i > $o] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X2 : $i] : (c_and @ ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ ((X1 @ X2) = X2) => ? [X4 : $i] : (c_and @ (c_Subq @ X4 @ X2) @ (c_not @ (X0 @ (c_setprod @ X3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X2))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))),
% 9.57/2.75 inference(negated_conjecture,[status(cth)],[f109])).
% 9.57/2.75 thf(f109,conjecture,(
% 9.57/2.75 (c_not @ ! [X1 : $i > $i,X0 : $i > $o] : (c_and @ ((X0 @ (X1 @ (c_binintersect @ (X1 @ (c_Power @ c_Empty)) @ (X1 @ (c_binrep @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ c_Empty))))) => ((c_TransSet @ (X1 @ c_Empty)) => ! [X2 : $i] : ((c_In @ X2 @ c_Empty) => ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ (c_exactly2 @ (c_ordsucc @ (X1 @ X3))))))) => ? [X2 : $i] : (c_and @ ? [X3 : $i] : (c_and @ (c_Subq @ X3 @ X2) @ ((X1 @ X2) = X2) => ? [X4 : $i] : (c_and @ (c_Subq @ X4 @ X2) @ (c_not @ (X0 @ (c_setprod @ X3 @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ (c_Power @ c_Empty)))))))) @ (c_not @ (c_SNo @ X2))) @ (c_not @ (X0 @ (X1 @ (X1 @ (X1 @ (c_binrep @ (c_binrep @ (c_Power @ (c_binrep @ (c_Power @ (c_Power @ c_Empty)) @ c_Empty)) @ (c_Power @ c_Empty)) @ c_Empty))))))))),
% 9.57/2.75 file('/export/starexec/sandbox/tmp/tmp.BqcgKr7QEt/DTF2THF_2340.p',conj)).
% 9.57/2.75 thf(f489,plain,(
% 9.57/2.75 ~spl0_2),
% 9.57/2.75 inference(avatar_contradiction_clause,[status(thm)],[f488])).
% 9.57/2.75 thf(f488,plain,(
% 9.57/2.75 $false | ~spl0_2),
% 9.57/2.75 inference(trivial_inequality_removal,[status(thm)],[f481])).
% 9.57/2.75 thf(f481,plain,(
% 9.57/2.75 ($true = $false) | ~spl0_2),
% 9.57/2.75 inference(superposition,[status(thm)],[f433,f459])).
% 9.57/2.75 thf(f459,plain,(
% 9.57/2.75 ( ! [X3 : $o] : (($true = X3)) ) | ~spl0_2),
% 9.57/2.75 inference(avatar_component_clause,[status(thm)],[f458])).
% 9.57/2.75 thf(f458,definition,(
% 9.57/2.75 spl0_2 <=> ! [X3 : $o] : ($true = X3)),
% 9.57/2.75 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 9.57/2.75 thf(f479,plain,(
% 9.57/2.75 spl0_5 | spl0_6 | spl0_2),
% 9.57/2.75 inference(avatar_split_clause,[status(thm)],[f471,f458,f476,f473])).
% 9.57/2.75 thf(f471,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X3 : $o,X1 : $i > $o] : (($true = X3) | ((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) = $false) | (c_False = $true)) )),
% 9.57/2.75 inference(binary_proxy_clausification,[status(thm)],[f470])).
% 9.57/2.75 thf(f470,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X3 : $o,X1 : $i > $o] : (($true = X3) | (((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) = $true)) )),
% 9.57/2.75 inference(binary_proxy_clausification,[status(thm)],[f447])).
% 9.57/2.75 thf(f447,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X3 : $o,X1 : $i > $o] : (($true = X3) | ((((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => X3) = $false)) )),
% 9.57/2.75 inference(binary_proxy_clausification,[status(thm)],[f446])).
% 9.57/2.75 thf(f446,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X3 : $o,X1 : $i > $o] : (($true = X3) | ($false = ((((X1 @ (X2 @ (c_Eps_i @ (^[Y0 : $i]: (c_or @ (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((c_In @ Y2 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y3)) => Y3))))) => (((c_Repl @ (X2 @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y2 = Y3) => Y4)) => Y4))) @ (!! @ $o @ (^[Y4 : $o]: ((((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) = Y3) => Y4)) => Y4)))))))) = Y0) => Y1)) => Y1))) @ (!! @ $o @ (^[Y1 : $o]: ((((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((c_In @ Y2 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y3)) => Y3))))) => c_False) => ((c_Empty = Y0) => Y1)) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X2 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X2 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1)))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1)))) => (c_In @ Y6 @ (c_Power @ Y4))))) => c_False) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1)))) => (c_In @ Y7 @ Y4)))) => c_False) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => c_False) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X2 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X1 @ (c_lam @ Y2 @ (^[Y6 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y5)) => Y5)))))) => Y3)) => Y3))))) => (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_binunion @ Y2 @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_SetAdjoin @ Y6 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (c_or @ (!! @ $o @ (^[Y6 : $o]: (((c_In @ (c_SetAdjoin @ Y5 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y0) => (((c_In @ Y5 @ Y0) => c_False) => Y6)) => Y6))) @ (!! @ $o @ (^[Y6 : $o]: ((((c_In @ (c_SetAdjoin @ Y5 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y0) => c_False) => ((c_In @ Y5 @ Y0) => Y6)) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3))))) => c_False) => Y1)) => Y1)))))) => (((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => X3)))) )),
% 9.57/2.75 inference(binary_proxy_clausification,[status(thm)],[f445])).
% 9.57/2.75 thf(f445,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X3 : $o,X1 : $i > $o] : (($true = (((((X1 @ (X2 @ (c_Eps_i @ (^[Y0 : $i]: (c_or @ (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((c_In @ Y2 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y3)) => Y3))))) => (((c_Repl @ (X2 @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y2 = Y3) => Y4)) => Y4))) @ (!! @ $o @ (^[Y4 : $o]: ((((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) = Y3) => Y4)) => Y4)))))))) = Y0) => Y1)) => Y1))) @ (!! @ $o @ (^[Y1 : $o]: ((((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((c_In @ Y2 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y2 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y3)) => Y3))))) => c_False) => ((c_Empty = Y0) => Y1)) => Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ (X2 @ c_Empty)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ Y0) => (c_In @ Y1 @ (X2 @ c_Empty)))))))) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ c_Empty) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y1) => (c_In @ Y3 @ Y0)))) => ((!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1)))) => (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1)))) => (c_In @ Y6 @ (c_Power @ Y4))))) => c_False) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1))))))) => ((!! @ $o @ (^[Y6 : $o]: ((((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_binunion @ (X2 @ Y1) @ (c_Sing @ (X2 @ Y1)))) => (c_In @ Y7 @ Y4)))) => c_False) => ((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ Y4) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y4) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => Y6)) => Y6))) => Y5)) => Y5))))) => c_False) => Y3)) => Y3))) => Y2)) => Y2)))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y0)))) => ((((X2 @ Y0) = Y0) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y0)))) => (((X1 @ (c_lam @ Y2 @ (^[Y6 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y5)) => Y5)))))) => Y3)) => Y3))))) => (((?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (c_In @ Y6 @ Y2))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y5)))))))))) => Y4)) => Y4))) => ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y0) => (c_In @ Y5 @ (c_binunion @ Y2 @ (c_Repl @ Y2 @ (^[Y6 : $i]: (c_SetAdjoin @ Y6 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y2) => (c_or @ (!! @ $o @ (^[Y6 : $o]: (((c_In @ (c_SetAdjoin @ Y5 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y0) => (((c_In @ Y5 @ Y0) => c_False) => Y6)) => Y6))) @ (!! @ $o @ (^[Y6 : $o]: ((((c_In @ (c_SetAdjoin @ Y5 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y0) => c_False) => ((c_In @ Y5 @ Y0) => Y6)) => Y6))))))) => Y4)) => Y4))) => Y3)) => Y3))))) => c_False) => Y1)) => Y1)))))) => (((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => X3)) => X3))) )),
% 9.57/2.75 inference(beta_eta_normalization,[status(thm)],[f444])).
% 9.57/2.75 thf(f444,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X3 : $o,X1 : $i > $o] : ((((^[Y0 : $o]: (((((X1 @ (X2 @ (c_Eps_i @ (^[Y1 : $i]: (c_or @ (!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y4)) => Y4))))) => (((c_Repl @ (X2 @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (c_or @ (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y3 = Y4) => Y5)) => Y5))) @ (!! @ $o @ (^[Y5 : $o]: ((((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y6 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y7)) => Y7))))) = Y4) => Y5)) => Y5)))))))) = Y1) => Y2)) => Y2))) @ (!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y4)) => Y4))))) => c_False) => ((c_Empty = Y1) => Y2)) => Y2)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ (X2 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y1) => (c_In @ Y2 @ (X2 @ c_Empty)))))))) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ c_Empty) => (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y1)))) => ((!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2)))) => (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2)))) => (c_In @ Y7 @ (c_Power @ Y5))))) => c_False) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2))))))) => ((!! @ $o @ (^[Y7 : $o]: ((((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2)))) => (c_In @ Y8 @ Y5)))) => c_False) => ((?? @ $i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((c_In @ Y8 @ Y5) => (((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y5) => (c_In @ Y10 @ (c_Power @ Y8))))) => c_False) => Y9)) => Y9))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4))) => Y3)) => Y3)))))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y1)))) => ((((X2 @ Y1) = Y1) => (?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y1)))) => (((X1 @ (c_lam @ Y3 @ (^[Y7 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y6)) => Y6)))))) => Y4)) => Y4))))) => (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y3))))))) => ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (c_In @ Y8 @ Y6)))))))))) => Y5)) => Y5))) => ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y1) => (c_In @ Y6 @ (c_binunion @ Y3 @ (c_Repl @ Y3 @ (^[Y7 : $i]: (c_SetAdjoin @ Y7 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (c_or @ (!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_SetAdjoin @ Y6 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y1) => (((c_In @ Y6 @ Y1) => c_False) => Y7)) => Y7))) @ (!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_SetAdjoin @ Y6 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y1) => c_False) => ((c_In @ Y6 @ Y1) => Y7)) => Y7))))))) => Y5)) => Y5))) => Y4)) => Y4))))) => c_False) => Y2)) => Y2)))))) => (((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y0)) => Y0)) @ X3) = $true)) )),
% 9.57/2.75 inference(pi_clausification,[status(thm)],[f443])).
% 9.57/2.75 thf(f443,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X1 : $i > $o] : (($true = (!! @ $o @ (^[Y0 : $o]: (((((X1 @ (X2 @ (c_Eps_i @ (^[Y1 : $i]: (c_or @ (!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y4)) => Y4))))) => (((c_Repl @ (X2 @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: (c_or @ (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y3 = Y4) => Y5)) => Y5))) @ (!! @ $o @ (^[Y5 : $o]: ((((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y6 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y7)) => Y7))))) = Y4) => Y5)) => Y5)))))))) = Y1) => Y2)) => Y2))) @ (!! @ $o @ (^[Y2 : $o]: ((((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((c_In @ Y3 @ (X2 @ (c_Power @ c_Empty))) => ((c_In @ Y3 @ (X2 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y4)) => Y4))))) => c_False) => ((c_Empty = Y1) => Y2)) => Y2)))))))) => ((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ (X2 @ c_Empty)) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y1) => (c_In @ Y2 @ (X2 @ c_Empty)))))))) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ c_Empty) => (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y2) => (c_In @ Y4 @ Y1)))) => ((!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2)))) => (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2)))) => (c_In @ Y7 @ (c_Power @ Y5))))) => c_False) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2))))))) => ((!! @ $o @ (^[Y7 : $o]: ((((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ (c_binunion @ (X2 @ Y2) @ (c_Sing @ (X2 @ Y2)))) => (c_In @ Y8 @ Y5)))) => c_False) => ((?? @ $i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((c_In @ Y8 @ Y5) => (((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y5) => (c_In @ Y10 @ (c_Power @ Y8))))) => c_False) => Y9)) => Y9))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4))) => Y3)) => Y3)))))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y1)))) => ((((X2 @ Y1) = Y1) => (?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y1)))) => (((X1 @ (c_lam @ Y3 @ (^[Y7 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y6)) => Y6)))))) => Y4)) => Y4))))) => (((?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (c_In @ Y7 @ Y3))))))) => ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (c_In @ Y8 @ Y6)))))))))) => Y5)) => Y5))) => ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y1) => (c_In @ Y6 @ (c_binunion @ Y3 @ (c_Repl @ Y3 @ (^[Y7 : $i]: (c_SetAdjoin @ Y7 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y3) => (c_or @ (!! @ $o @ (^[Y7 : $o]: (((c_In @ (c_SetAdjoin @ Y6 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y1) => (((c_In @ Y6 @ Y1) => c_False) => Y7)) => Y7))) @ (!! @ $o @ (^[Y7 : $o]: ((((c_In @ (c_SetAdjoin @ Y6 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y1) => c_False) => ((c_In @ Y6 @ Y1) => Y7)) => Y7))))))) => Y5)) => Y5))) => Y4)) => Y4))))) => c_False) => Y2)) => Y2)))))) => (((X1 @ (X2 @ (X2 @ (X2 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y0)) => Y0))))) )),
% 9.57/2.75 inference(beta_eta_normalization,[status(thm)],[f442])).
% 9.57/2.75 thf(f442,plain,(
% 9.57/2.75 ( ! [X2 : $i > $i,X1 : $i > $o] : (($true = ((^[Y0 : $i > $i]: (!! @ $o @ (^[Y1 : $o]: (((((X1 @ (Y0 @ (c_Eps_i @ (^[Y2 : $i]: (c_or @ (!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (Y0 @ (c_Power @ c_Empty))) => ((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y5)) => Y5))))) => (((c_Repl @ (Y0 @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_or @ (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y4 = Y5) => Y6)) => Y6))) @ (!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (Y0 @ (c_Power @ c_Empty))) => ((c_In @ Y7 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y8)) => Y8))))) = Y5) => Y6)) => Y6)))))))) = Y2) => Y3)) => Y3))) @ (!! @ $o @ (^[Y3 : $o]: ((((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (Y0 @ (c_Power @ c_Empty))) => ((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y5)) => Y5))))) => c_False) => ((c_Empty = Y2) => Y3)) => Y3)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => (c_In @ Y3 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y2)))) => ((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3)))) => (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3)))) => (c_In @ Y8 @ (c_Power @ Y6))))) => c_False) => Y7)) => Y7))))) => (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3))))))) => ((!! @ $o @ (^[Y8 : $o]: ((((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3)))) => (c_In @ Y9 @ Y6)))) => c_False) => ((?? @ $i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((c_In @ Y9 @ Y6) => (((!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y6) => (c_In @ Y11 @ (c_Power @ Y9))))) => c_False) => Y10)) => Y10))))) => Y8)) => Y8))) => Y7)) => Y7))))) => c_False) => Y5)) => Y5))) => Y4)) => Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y2)))) => ((((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ Y2)))) => (((X1 @ (c_lam @ Y4 @ (^[Y8 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y7)) => Y7)))))) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (c_In @ Y8 @ Y4))))))) => ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y7)))))))))) => Y6)) => Y6))) => ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y2) => (c_In @ Y7 @ (c_binunion @ Y4 @ (c_Repl @ Y4 @ (^[Y8 : $i]: (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (c_or @ (!! @ $o @ (^[Y8 : $o]: (((c_In @ (c_SetAdjoin @ Y7 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y2) => (((c_In @ Y7 @ Y2) => c_False) => Y8)) => Y8))) @ (!! @ $o @ (^[Y8 : $o]: ((((c_In @ (c_SetAdjoin @ Y7 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y2) => c_False) => ((c_In @ Y7 @ Y2) => Y8)) => Y8))))))) => Y6)) => Y6))) => Y5)) => Y5))))) => c_False) => Y3)) => Y3)))))) => (((X1 @ (Y0 @ (Y0 @ (Y0 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y1)) => Y1)))) @ X2))) )),
% 9.57/2.75 inference(pi_clausification,[status(thm)],[f441])).
% 9.57/2.75 thf(f441,plain,(
% 9.57/2.75 ( ! [X1 : $i > $o] : (((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $o @ (^[Y1 : $o]: (((((X1 @ (Y0 @ (c_Eps_i @ (^[Y2 : $i]: (c_or @ (!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (Y0 @ (c_Power @ c_Empty))) => ((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y5)) => Y5))))) => (((c_Repl @ (Y0 @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: (c_or @ (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y4 = Y5) => Y6)) => Y6))) @ (!! @ $o @ (^[Y6 : $o]: ((((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (Y0 @ (c_Power @ c_Empty))) => ((c_In @ Y7 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y8)) => Y8))))) = Y5) => Y6)) => Y6)))))))) = Y2) => Y3)) => Y3))) @ (!! @ $o @ (^[Y3 : $o]: ((((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((c_In @ Y4 @ (Y0 @ (c_Power @ c_Empty))) => ((c_In @ Y4 @ (Y0 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y5)) => Y5))))) => c_False) => ((c_Empty = Y2) => Y3)) => Y3)))))))) => ((!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ (Y0 @ c_Empty)) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ Y2) => (c_In @ Y3 @ (Y0 @ c_Empty)))))))) => (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ c_Empty) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ((c_In @ Y5 @ Y3) => (c_In @ Y5 @ Y2)))) => ((!! @ $o @ (^[Y5 : $o]: (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y6 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3)))) => (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3)))) => (c_In @ Y8 @ (c_Power @ Y6))))) => c_False) => Y7)) => Y7))))) => (((?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3))))))) => ((!! @ $o @ (^[Y8 : $o]: ((((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_binunion @ (Y0 @ Y3) @ (c_Sing @ (Y0 @ Y3)))) => (c_In @ Y9 @ Y6)))) => c_False) => ((?? @ $i @ (^[Y9 : $i]: (!! @ $o @ (^[Y10 : $o]: (((c_In @ Y9 @ Y6) => (((!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y6) => (c_In @ Y11 @ (c_Power @ Y9))))) => c_False) => Y10)) => Y10))))) => Y8)) => Y8))) => Y7)) => Y7))))) => c_False) => Y5)) => Y5))) => Y4)) => Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y2)))) => ((((Y0 @ Y2) = Y2) => (?? @ $i @ (^[Y6 : $i]: (!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y6) => (c_In @ Y8 @ Y2)))) => (((X1 @ (c_lam @ Y4 @ (^[Y8 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y7)) => Y7)))))) => Y5)) => Y5))))) => (((?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (c_In @ Y8 @ Y4))))))) => ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y7) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y7)))))))))) => Y6)) => Y6))) => ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y2) => (c_In @ Y7 @ (c_binunion @ Y4 @ (c_Repl @ Y4 @ (^[Y8 : $i]: (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y4) => (c_or @ (!! @ $o @ (^[Y8 : $o]: (((c_In @ (c_SetAdjoin @ Y7 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y2) => (((c_In @ Y7 @ Y2) => c_False) => Y8)) => Y8))) @ (!! @ $o @ (^[Y8 : $o]: ((((c_In @ (c_SetAdjoin @ Y7 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y2) => c_False) => ((c_In @ Y7 @ Y2) => Y8)) => Y8))))))) => Y6)) => Y6))) => Y5)) => Y5))))) => c_False) => Y3)) => Y3)))))) => (((X1 @ (Y0 @ (Y0 @ (Y0 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y1)) => Y1))))) = $true)) )),
% 9.57/2.75 inference(beta_eta_normalization,[status(thm)],[f440])).
% 9.57/2.75 thf(f440,plain,(
% 9.57/2.75 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $o @ (^[Y2 : $o]: (((((Y0 @ (Y1 @ (c_Eps_i @ (^[Y3 : $i]: (c_or @ (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => (((c_Repl @ (Y1 @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_or @ (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y5 = Y6) => Y7)) => Y7))) @ (!! @ $o @ (^[Y7 : $o]: ((((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((c_In @ Y8 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y8 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y9)) => Y9))))) = Y6) => Y7)) => Y7)))))))) = Y3) => Y4)) => Y4))) @ (!! @ $o @ (^[Y4 : $o]: ((((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => c_False) => ((c_Empty = Y3) => Y4)) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y1 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y1 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y0 @ (c_lam @ Y5 @ (^[Y9 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_binunion @ Y5 @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_SetAdjoin @ Y9 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (c_or @ (!! @ $o @ (^[Y9 : $o]: (((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y9)) => Y9))) @ (!! @ $o @ (^[Y9 : $o]: ((((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y9)) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y0 @ (Y1 @ (Y1 @ (Y1 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y2)) => Y2)))))) @ X1))) )),
% 9.57/2.75 inference(pi_clausification,[status(thm)],[f434])).
% 9.57/2.75 thf(f434,plain,(
% 9.57/2.75 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $o @ (^[Y2 : $o]: (((((Y0 @ (Y1 @ (c_Eps_i @ (^[Y3 : $i]: (c_or @ (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => (((c_Repl @ (Y1 @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: (c_or @ (!! @ $o @ (^[Y7 : $o]: (((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => ((Y5 = Y6) => Y7)) => Y7))) @ (!! @ $o @ (^[Y7 : $o]: ((((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => c_False) => (((c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((c_In @ Y8 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y8 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y9)) => Y9))))) = Y6) => Y7)) => Y7)))))))) = Y3) => Y4)) => Y4))) @ (!! @ $o @ (^[Y4 : $o]: ((((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((c_In @ Y5 @ (Y1 @ (c_Power @ c_Empty))) => ((c_In @ Y5 @ (Y1 @ (c_setsum @ (c_Power @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))) => Y6)) => Y6))))) => c_False) => ((c_Empty = Y3) => Y4)) => Y4)))))))) => ((!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ (Y1 @ c_Empty)) => (!! @ $i @ (^[Y4 : $i]: ((c_In @ Y4 @ Y3) => (c_In @ Y4 @ (Y1 @ c_Empty)))))))) => (!! @ $i @ (^[Y3 : $i]: ((c_In @ Y3 @ c_Empty) => (?? @ $i @ (^[Y4 : $i]: (!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y4) => (c_In @ Y6 @ Y3)))) => ((!! @ $o @ (^[Y6 : $o]: (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((c_In @ Y7 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y9 @ (c_Power @ Y7))))) => c_False) => Y8)) => Y8))))) => (((?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4))))))) => ((!! @ $o @ (^[Y9 : $o]: ((((!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ (c_binunion @ (Y1 @ Y4) @ (c_Sing @ (Y1 @ Y4)))) => (c_In @ Y10 @ Y7)))) => c_False) => ((?? @ $i @ (^[Y10 : $i]: (!! @ $o @ (^[Y11 : $o]: (((c_In @ Y10 @ Y7) => (((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y7) => (c_In @ Y12 @ (c_Power @ Y10))))) => c_False) => Y11)) => Y11))))) => Y9)) => Y9))) => Y8)) => Y8))))) => c_False) => Y6)) => Y6))) => Y5)) => Y5)))))))))) => (?? @ $i @ (^[Y3 : $i]: (!! @ $o @ (^[Y4 : $o]: (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y5) => (c_In @ Y7 @ Y3)))) => ((((Y1 @ Y3) = Y3) => (?? @ $i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y7) => (c_In @ Y9 @ Y3)))) => (((Y0 @ (c_lam @ Y5 @ (^[Y9 : $i]: (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ (c_Power @ c_Empty))))))) => c_False) => Y8)) => Y8)))))) => Y6)) => Y6))))) => (((?? @ $i @ (^[Y5 : $i]: (!! @ $o @ (^[Y6 : $o]: (((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (c_In @ Y9 @ Y5))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (!! @ $i @ (^[Y10 : $i]: ((c_In @ Y10 @ Y9) => (c_In @ Y10 @ Y8)))))))))) => Y7)) => Y7))) => ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y3) => (c_In @ Y8 @ (c_binunion @ Y5 @ (c_Repl @ Y5 @ (^[Y9 : $i]: (c_SetAdjoin @ Y9 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty))))))))))) => ((!! @ $i @ (^[Y8 : $i]: ((c_In @ Y8 @ Y5) => (c_or @ (!! @ $o @ (^[Y9 : $o]: (((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => (((c_In @ Y8 @ Y3) => c_False) => Y9)) => Y9))) @ (!! @ $o @ (^[Y9 : $o]: ((((c_In @ (c_SetAdjoin @ Y8 @ (c_Sing @ (c_binunion @ c_Empty @ (c_Sing @ c_Empty)))) @ Y3) => c_False) => ((c_In @ Y8 @ Y3) => Y9)) => Y9))))))) => Y7)) => Y7))) => Y6)) => Y6))))) => c_False) => Y4)) => Y4)))))) => (((Y0 @ (Y1 @ (Y1 @ (Y1 @ (c_setsum @ (c_setsum @ (c_Power @ (c_setsum @ (c_Power @ (c_Power @ c_Empty)) @ (c_Power @ c_Empty))) @ (c_Power @ (c_Power @ c_Empty))) @ (c_Power @ c_Empty)))))) => c_False) => Y2)) => Y2))))))) = $true)),
% 9.57/2.75 inference(binary_proxy_clausification,[status(thm)],[f432])).
% 9.57/2.75 % SZS output end Proof for DTF2THF_2340
% 9.57/2.75 % (2731)------------------------------
% 9.57/2.75 % (2731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.57/2.75 % (2731)Termination reason: Refutation
% 9.57/2.75
% 9.57/2.75 % (2731)Memory used [KB]: 7803
% 9.57/2.75 % (2731)Time elapsed: 0.073 s
% 9.57/2.75 % (2731)Instructions burned: 238 (million)
% 9.57/2.75 % (2731)------------------------------
% 9.57/2.75 % (2731)------------------------------
% 9.57/2.75 % (2617)Success in time 1.323 s
%------------------------------------------------------------------------------