%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO879^1 : 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 : n004.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 09:54:59 AM UTC 2026
% Result : Theorem 2.74s 1.86s
% Output : Refutation 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO879^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n004.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:49:56 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SYO879^1 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Syntactic
% 0.21/0.47 % Problem : ProofGold problem Random3_35_neg_th0
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Urb20]
% 0.21/0.47 % Names : Random3_35_neg_th0.p [Urb20]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.90 v8.2.0, 0.77 v8.1.0, 0.64 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.21/0.47 % Number of atoms : 489 ( 140 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 10 ( 4 avg)
% 0.21/0.47 % Number of connectives : 1142 ( 0 ~; 0 |; 0 &;1049 @)
% 0.21/0.47 % ( 0 <=>; 93 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 23 ( 2 avg)
% 0.21/0.47 % Number of types : 2 ( 0 usr)
% 0.21/0.47 % Number of type conns : 564 ( 564 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.21/0.47 % Number of variables : 419 ( 275 ^; 105 !; 39 ?; 419 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : See https://proofgold.org
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(c_Eps_i_tp,type,
% 0.21/0.47 c_Eps_i: ( $i > $o ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_False_tp,type,
% 0.21/0.47 c_False: $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_True_tp,type,
% 0.21/0.47 c_True: $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_not_tp,type,
% 0.21/0.47 c_not: $o > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_and_tp,type,
% 0.21/0.47 c_and: $o > $o > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_or_tp,type,
% 0.21/0.47 c_or: $o > $o > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_iff_tp,type,
% 0.21/0.47 c_iff: $o > $o > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_In_tp,type,
% 0.21/0.47 c_In: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_Subq_tp,type,
% 0.21/0.47 c_Subq: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_Empty_tp,type,
% 0.21/0.47 c_Empty: $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Union_tp,type,
% 0.21/0.47 c_Union: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Power_tp,type,
% 0.21/0.47 c_Power: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Repl_tp,type,
% 0.21/0.47 c_Repl: $i > ( $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_TransSet_tp,type,
% 0.21/0.47 c_TransSet: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_atleast2_tp,type,
% 0.21/0.47 c_atleast2: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_atleast3_tp,type,
% 0.21/0.47 c_atleast3: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_atleast4_tp,type,
% 0.21/0.47 c_atleast4: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_atleast5_tp,type,
% 0.21/0.47 c_atleast5: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_atleast6_tp,type,
% 0.21/0.47 c_atleast6: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_exactly2_tp,type,
% 0.21/0.47 c_exactly2: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_exactly3_tp,type,
% 0.21/0.47 c_exactly3: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_exactly4_tp,type,
% 0.21/0.47 c_exactly4: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_exactly5_tp,type,
% 0.21/0.47 c_exactly5: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_exu_i_tp,type,
% 0.21/0.47 c_exu_i: ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_reflexive_i_tp,type,
% 0.21/0.47 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_irreflexive_i_tp,type,
% 0.21/0.47 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_symmetric_i_tp,type,
% 0.21/0.47 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_antisymmetric_i_tp,type,
% 0.21/0.47 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_transitive_i_tp,type,
% 0.21/0.47 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_eqreln_i_tp,type,
% 0.21/0.47 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_per_i_tp,type,
% 0.21/0.47 c_per_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_linear_i_tp,type,
% 0.21/0.47 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_trichotomous_or_i_tp,type,
% 0.21/0.47 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_partialorder_i_tp,type,
% 0.21/0.47 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_totalorder_i_tp,type,
% 0.21/0.47 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_strictpartialorder_i_tp,type,
% 0.21/0.47 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_stricttotalorder_i_tp,type,
% 0.21/0.47 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_If_i_tp,type,
% 0.21/0.47 c_If_i: $o > $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_exactly1of2_tp,type,
% 0.21/0.47 c_exactly1of2: $o > $o > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_exactly1of3_tp,type,
% 0.21/0.47 c_exactly1of3: $o > $o > $o > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_nIn_tp,type,
% 0.21/0.47 c_nIn: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_nSubq_tp,type,
% 0.21/0.47 c_nSubq: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_UPair_tp,type,
% 0.21/0.47 c_UPair: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Sing_tp,type,
% 0.21/0.47 c_Sing: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_binunion_tp,type,
% 0.21/0.47 c_binunion: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_SetAdjoin_tp,type,
% 0.21/0.47 c_SetAdjoin: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_famunion_tp,type,
% 0.21/0.47 c_famunion: $i > ( $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Sep_tp,type,
% 0.21/0.47 c_Sep: $i > ( $i > $o ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_ReplSep_tp,type,
% 0.21/0.47 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_binintersect_tp,type,
% 0.21/0.47 c_binintersect: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_setminus_tp,type,
% 0.21/0.47 c_setminus: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_inj_tp,type,
% 0.21/0.47 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_bij_tp,type,
% 0.21/0.47 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_atleastp_tp,type,
% 0.21/0.47 c_atleastp: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_equip_tp,type,
% 0.21/0.47 c_equip: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_In_rec_poly_G_i_tp,type,
% 0.21/0.47 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_In_rec_poly_i_tp,type,
% 0.21/0.47 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_ordsucc_tp,type,
% 0.21/0.47 c_ordsucc: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_nat_p_tp,type,
% 0.21/0.47 c_nat_p: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_nat_primrec_tp,type,
% 0.21/0.47 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_add_nat_tp,type,
% 0.21/0.47 c_add_nat: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_mul_nat_tp,type,
% 0.21/0.47 c_mul_nat: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_ordinal_tp,type,
% 0.21/0.47 c_ordinal: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_V__tp,type,
% 0.21/0.47 c_V_: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Inj1_tp,type,
% 0.21/0.47 c_Inj1: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Inj0_tp,type,
% 0.21/0.47 c_Inj0: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Unj_tp,type,
% 0.21/0.47 c_Unj: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_combine_funcs_tp,type,
% 0.21/0.47 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_setsum_tp,type,
% 0.21/0.47 c_setsum: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_proj0_tp,type,
% 0.21/0.47 c_proj0: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_proj1_tp,type,
% 0.21/0.47 c_proj1: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_binrep_tp,type,
% 0.21/0.47 c_binrep: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_lam_tp,type,
% 0.21/0.47 c_lam: $i > ( $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_setprod_tp,type,
% 0.21/0.47 c_setprod: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_ap_tp,type,
% 0.21/0.47 c_ap: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_setsum_p_tp,type,
% 0.21/0.47 c_setsum_p: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_tuple_p_tp,type,
% 0.21/0.47 c_tuple_p: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_Pi_tp,type,
% 0.21/0.47 c_Pi: $i > ( $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_setexp_tp,type,
% 0.21/0.47 c_setexp: $i > $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_Sep2_tp,type,
% 0.21/0.47 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_set_of_pairs_tp,type,
% 0.21/0.47 c_set_of_pairs: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_lam2_tp,type,
% 0.21/0.47 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_PNoEq__tp,type,
% 0.21/0.47 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_PNoLt__tp,type,
% 0.21/0.47 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_PNoLt_tp,type,
% 0.21/0.47 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_PNoLe_tp,type,
% 0.21/0.47 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_PNo_downc_tp,type,
% 0.21/0.47 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_PNo_upc_tp,type,
% 0.21/0.47 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNoElts__tp,type,
% 0.21/0.47 c_SNoElts_: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNo__tp,type,
% 0.21/0.47 c_SNo_: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_PSNo_tp,type,
% 0.21/0.47 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNo_tp,type,
% 0.21/0.47 c_SNo: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNoLev_tp,type,
% 0.21/0.47 c_SNoLev: $i > $i ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNoEq__tp,type,
% 0.21/0.47 c_SNoEq_: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNoLt_tp,type,
% 0.21/0.47 c_SNoLt: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_SNoLe_tp,type,
% 0.21/0.47 c_SNoLe: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_binop_on_tp,type,
% 0.21/0.47 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_Loop_tp,type,
% 0.21/0.47 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_Loop_with_defs_tp,type,
% 0.21/0.47 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 ).
% 0.21/0.47
% 0.21/0.47 thf(c_Loop_with_defs_cex1_tp,type,
% 0.21/0.47 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 ).
% 0.21/0.47
% 0.21/0.47 thf(c_Loop_with_defs_cex2_tp,type,
% 0.21/0.47 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 ).
% 0.21/0.47
% 0.21/0.47 thf(c_combinator_tp,type,
% 0.21/0.47 c_combinator: $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_combinator_equiv_tp,type,
% 0.21/0.47 c_combinator_equiv: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(c_equip_mod_tp,type,
% 0.21/0.47 c_equip_mod: $i > $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(ax1,axiom,
% 0.21/0.47 ! [X0: $i > $o,X1: $i] :
% 0.21/0.47 ( ( X0 @ X1 )
% 0.21/0.47 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax2,axiom,
% 0.21/0.47 ! [X0: $o] :
% 0.21/0.47 ( ( c_not @ ( c_not @ X0 ) )
% 0.21/0.47 => X0 ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax3,axiom,
% 0.21/0.47 ! [X0: $o,X1: $o] :
% 0.21/0.47 ( ( c_iff @ X0 @ X1 )
% 0.21/0.47 => ( X0 = X1 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax4,axiom,
% 0.21/0.47 ! [X0: $i,X1: $i] :
% 0.21/0.47 ( ( c_Subq @ X0 @ X1 )
% 0.21/0.47 => ( ( c_Subq @ X1 @ X0 )
% 0.21/0.47 => ( X0 = X1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax5,axiom,
% 0.21/0.47 ( c_not
% 0.21/0.47 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax6,axiom,
% 0.21/0.47 ! [X0: $i,X1: $i] :
% 0.21/0.47 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.21/0.47 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax7,axiom,
% 0.21/0.47 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax8,axiom,
% 0.21/0.47 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.21/0.47 ( c_iff
% 0.21/0.47 @ ( c_In @ X2
% 0.21/0.47 @ ( c_Repl @ X0
% 0.21/0.47 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.21/0.47 @ ? [X3: $i] :
% 0.21/0.47 ( c_and @ ( c_In @ X3 @ X0 )
% 0.21/0.47 @ ( X2
% 0.21/0.47 = ( X1 @ X3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax9,axiom,
% 0.21/0.47 ! [X0: $i > $o] :
% 0.21/0.47 ( ! [X1: $i] :
% 0.21/0.47 ( ( X0 @ X1 )
% 0.21/0.47 => ! [X2: $i] :
% 0.21/0.47 ( ( c_In @ X2 @ X1 )
% 0.21/0.47 => ( X0 @ X2 ) ) )
% 0.21/0.47 => ( ( X0 @ c_Empty )
% 0.21/0.47 => ( ! [X1: $i] :
% 0.21/0.47 ( ( X0 @ X1 )
% 0.21/0.47 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.21/0.47 => ( ! [X1: $i] :
% 0.21/0.47 ( ( X0 @ X1 )
% 0.21/0.47 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.21/0.47 => ( ! [X1: $i] :
% 0.21/0.47 ( ( X0 @ X1 )
% 0.21/0.47 => ! [X2: $i > $i] :
% 0.21/0.47 ( ! [X3: $i] :
% 0.21/0.47 ( ( c_In @ X3 @ X1 )
% 0.21/0.47 => ( X0 @ ( X2 @ X3 ) ) )
% 0.21/0.47 => ( X0
% 0.21/0.47 @ ( c_Repl @ X1
% 0.21/0.47 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.21/0.47 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax10,axiom,
% 0.21/0.47 ! [X0: $i > $o] :
% 0.21/0.47 ( ! [X1: $i] :
% 0.21/0.47 ( ! [X2: $i] :
% 0.21/0.47 ( ( c_In @ X2 @ X1 )
% 0.21/0.47 => ( X0 @ X2 ) )
% 0.21/0.47 => ( X0 @ X1 ) )
% 0.21/0.47 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax11,axiom,
% 0.21/0.47 ( c_False
% 0.21/0.47 = ( ! [X0: $o] : X0 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax12,axiom,
% 0.21/0.47 ( c_True
% 0.21/0.47 = ( ! [X0: $o] :
% 0.21/0.47 ( X0
% 0.21/0.47 => X0 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax13,axiom,
% 0.21/0.47 ( c_not
% 0.21/0.47 = ( ^ [X0: $o] :
% 0.21/0.47 ( X0
% 0.21/0.47 => c_False ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax14,axiom,
% 0.21/0.47 ( c_and
% 0.21/0.47 = ( ^ [X0: $o,X1: $o] :
% 0.21/0.47 ! [X2: $o] :
% 0.21/0.47 ( ( X0
% 0.21/0.47 => ( X1
% 0.21/0.47 => X2 ) )
% 0.21/0.47 => X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax15,axiom,
% 0.21/0.47 ( c_or
% 0.21/0.47 = ( ^ [X0: $o,X1: $o] :
% 0.21/0.47 ! [X2: $o] :
% 0.21/0.47 ( ( X0
% 0.21/0.47 => X2 )
% 0.21/0.47 => ( ( X1
% 0.21/0.47 => X2 )
% 0.21/0.47 => X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax16,axiom,
% 0.21/0.47 ( c_iff
% 0.21/0.47 = ( ^ [X0: $o,X1: $o] :
% 0.21/0.47 ( c_and
% 0.21/0.47 @ ( X0
% 0.21/0.47 => X1 )
% 0.21/0.47 @ ( X1
% 0.21/0.47 => X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax17,axiom,
% 0.21/0.47 ( c_Subq
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ! [X2: $i] :
% 0.21/0.47 ( ( c_In @ X2 @ X0 )
% 0.21/0.47 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax18,axiom,
% 0.21/0.47 ( c_TransSet
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ! [X1: $i] :
% 0.21/0.47 ( ( c_In @ X1 @ X0 )
% 0.21/0.47 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax19,axiom,
% 0.21/0.47 ( c_atleast2
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax20,axiom,
% 0.21/0.47 ( c_atleast3
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax21,axiom,
% 0.21/0.47 ( c_atleast4
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax22,axiom,
% 0.21/0.47 ( c_atleast5
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax23,axiom,
% 0.21/0.47 ( c_atleast6
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax24,axiom,
% 0.21/0.47 ( c_exactly2
% 0.21/0.47 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax25,axiom,
% 0.21/0.47 ( c_exactly3
% 0.21/0.47 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax26,axiom,
% 0.21/0.47 ( c_exactly4
% 0.21/0.47 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax27,axiom,
% 0.21/0.47 ( c_exactly5
% 0.21/0.47 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax28,axiom,
% 0.21/0.47 ( c_exu_i
% 0.21/0.47 = ( ^ [X0: $i > $o] :
% 0.21/0.47 ( c_and
% 0.21/0.47 @ ? [X1: $i] : ( X0 @ X1 )
% 0.21/0.47 @ ! [X1: $i,X2: $i] :
% 0.21/0.47 ( ( X0 @ X1 )
% 0.21/0.47 => ( ( X0 @ X2 )
% 0.21/0.47 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax29,axiom,
% 0.21/0.47 ( c_reflexive_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax30,axiom,
% 0.21/0.47 ( c_irreflexive_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax31,axiom,
% 0.21/0.47 ( c_symmetric_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i,X2: $i] :
% 0.21/0.47 ( ( X0 @ X1 @ X2 )
% 0.21/0.47 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax32,axiom,
% 0.21/0.47 ( c_antisymmetric_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i,X2: $i] :
% 0.21/0.47 ( ( X0 @ X1 @ X2 )
% 0.21/0.47 => ( ( X0 @ X2 @ X1 )
% 0.21/0.47 => ( X1 = X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax33,axiom,
% 0.21/0.47 ( c_transitive_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i,X2: $i,X3: $i] :
% 0.21/0.47 ( ( X0 @ X1 @ X2 )
% 0.21/0.47 => ( ( X0 @ X2 @ X3 )
% 0.21/0.47 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax34,axiom,
% 0.21/0.47 ( c_eqreln_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax35,axiom,
% 0.21/0.47 ( c_per_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax36,axiom,
% 0.21/0.47 ( c_linear_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax37,axiom,
% 0.21/0.47 ( c_trichotomous_or_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] :
% 0.21/0.47 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax38,axiom,
% 0.21/0.47 ( c_partialorder_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax39,axiom,
% 0.21/0.47 ( c_totalorder_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax40,axiom,
% 0.21/0.47 ( c_strictpartialorder_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax41,axiom,
% 0.21/0.47 ( c_stricttotalorder_i
% 0.21/0.47 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax42,axiom,
% 0.21/0.47 ( c_If_i
% 0.21/0.47 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.21/0.47 ( c_Eps_i
% 0.21/0.47 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax43,axiom,
% 0.21/0.47 ( c_exactly1of2
% 0.21/0.47 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax44,axiom,
% 0.21/0.47 ( c_exactly1of3
% 0.21/0.47 = ( ^ [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 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax45,axiom,
% 0.21/0.47 ( c_nIn
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax46,axiom,
% 0.21/0.47 ( c_nSubq
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax47,axiom,
% 0.21/0.47 ( c_UPair
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.21/0.47 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax48,axiom,
% 0.21/0.47 ( c_Sing
% 0.21/0.47 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax49,axiom,
% 0.21/0.47 ( c_binunion
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax50,axiom,
% 0.21/0.47 ( c_SetAdjoin
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax51,axiom,
% 0.21/0.47 ( c_famunion
% 0.21/0.47 = ( ^ [X0: $i,X1: $i > $i] :
% 0.21/0.47 ( c_Union
% 0.21/0.47 @ ( c_Repl @ X0
% 0.21/0.47 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax52,axiom,
% 0.21/0.47 ( c_Sep
% 0.21/0.47 = ( ^ [X0: $i,X1: $i > $o] :
% 0.21/0.47 ( c_If_i
% 0.21/0.47 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.21/0.47 @ ( c_Repl @ X0
% 0.21/0.47 @ ^ [X2: $i] :
% 0.21/0.47 ( ^ [X3: $i] :
% 0.21/0.47 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.21/0.47 @ ( c_Eps_i
% 0.21/0.47 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.21/0.47 @ X2 ) )
% 0.21/0.47 @ c_Empty ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax53,axiom,
% 0.21/0.47 ( c_ReplSep
% 0.21/0.47 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.21/0.47 ( c_Repl
% 0.21/0.47 @ ( c_Sep @ X0
% 0.21/0.47 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.21/0.47 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax54,axiom,
% 0.21/0.47 ( c_binintersect
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_Sep @ X0
% 0.21/0.47 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax55,axiom,
% 0.21/0.47 ( c_setminus
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_Sep @ X0
% 0.21/0.47 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax56,axiom,
% 0.21/0.47 ( c_inj
% 0.21/0.47 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.21/0.47 ( c_and
% 0.21/0.47 @ ! [X3: $i] :
% 0.21/0.47 ( ( c_In @ X3 @ X0 )
% 0.21/0.47 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.21/0.47 @ ! [X3: $i] :
% 0.21/0.47 ( ( c_In @ X3 @ X0 )
% 0.21/0.47 => ! [X4: $i] :
% 0.21/0.47 ( ( c_In @ X4 @ X0 )
% 0.21/0.47 => ( ( ( X2 @ X3 )
% 0.21/0.47 = ( X2 @ X4 ) )
% 0.21/0.47 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax57,axiom,
% 0.21/0.47 ( c_bij
% 0.21/0.47 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.21/0.47 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.21/0.47 @ ! [X3: $i] :
% 0.21/0.47 ( ( c_In @ X3 @ X1 )
% 0.21/0.47 => ? [X4: $i] :
% 0.21/0.47 ( c_and @ ( c_In @ X4 @ X0 )
% 0.21/0.47 @ ( ( X2 @ X4 )
% 0.21/0.47 = X3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax58,axiom,
% 0.21/0.47 ( c_atleastp
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax59,axiom,
% 0.21/0.47 ( c_equip
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax60,axiom,
% 0.21/0.47 ( c_In_rec_poly_G_i
% 0.21/0.47 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.21/0.47 ! [X3: $i > $i > $o] :
% 0.21/0.47 ( ! [X4: $i,X5: $i > $i] :
% 0.21/0.47 ( ! [X6: $i] :
% 0.21/0.47 ( ( c_In @ X6 @ X4 )
% 0.21/0.47 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.21/0.47 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.21/0.47 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax61,axiom,
% 0.21/0.47 ( c_In_rec_poly_i
% 0.21/0.47 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.21/0.47 ( c_Eps_i
% 0.21/0.47 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax62,axiom,
% 0.21/0.47 ( c_ordsucc
% 0.21/0.47 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax63,axiom,
% 0.21/0.47 ( c_nat_p
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ! [X1: $i > $o] :
% 0.21/0.47 ( ( X1 @ c_Empty )
% 0.21/0.47 => ( ! [X2: $i] :
% 0.21/0.47 ( ( X1 @ X2 )
% 0.21/0.47 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.21/0.47 => ( X1 @ X0 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax64,axiom,
% 0.21/0.47 ( c_nat_primrec
% 0.21/0.47 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.21/0.47 ( c_In_rec_poly_i
% 0.21/0.47 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax65,axiom,
% 0.21/0.47 ( c_add_nat
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_nat_primrec @ X0
% 0.21/0.47 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.21/0.47 @ X1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax66,axiom,
% 0.21/0.47 ( c_mul_nat
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_nat_primrec @ c_Empty
% 0.21/0.47 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.21/0.47 @ X1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax67,axiom,
% 0.21/0.47 ( c_ordinal
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ( c_and @ ( c_TransSet @ X0 )
% 0.21/0.47 @ ! [X1: $i] :
% 0.21/0.47 ( ( c_In @ X1 @ X0 )
% 0.21/0.47 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax68,axiom,
% 0.21/0.47 ( c_V_
% 0.21/0.47 = ( c_In_rec_poly_i
% 0.21/0.47 @ ^ [X0: $i,X1: $i > $i] :
% 0.21/0.47 ( c_famunion @ X0
% 0.21/0.47 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax69,axiom,
% 0.21/0.47 ( c_Inj1
% 0.21/0.47 = ( c_In_rec_poly_i
% 0.21/0.47 @ ^ [X0: $i,X1: $i > $i] :
% 0.21/0.47 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.21/0.47 @ ( c_Repl @ X0
% 0.21/0.47 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax70,axiom,
% 0.21/0.47 ( c_Inj0
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ( c_Repl @ X0
% 0.21/0.47 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax71,axiom,
% 0.21/0.47 ( c_Unj
% 0.21/0.47 = ( c_In_rec_poly_i
% 0.21/0.47 @ ^ [X0: $i,X1: $i > $i] :
% 0.21/0.47 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.21/0.47 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax72,axiom,
% 0.21/0.47 ( c_combine_funcs
% 0.21/0.47 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.21/0.47 ( c_If_i
% 0.21/0.47 @ ( X4
% 0.21/0.47 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.21/0.47 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.21/0.47 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax73,axiom,
% 0.21/0.47 ( c_setsum
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_binunion
% 0.21/0.47 @ ( c_Repl @ X0
% 0.21/0.47 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.21/0.47 @ ( c_Repl @ X1
% 0.21/0.47 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax74,axiom,
% 0.21/0.47 ( c_proj0
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ( c_ReplSep @ X0
% 0.21/0.47 @ ^ [X1: $i] :
% 0.21/0.47 ? [X2: $i] :
% 0.21/0.47 ( ( c_Inj0 @ X2 )
% 0.21/0.47 = X1 )
% 0.21/0.47 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax75,axiom,
% 0.21/0.47 ( c_proj1
% 0.21/0.47 = ( ^ [X0: $i] :
% 0.21/0.47 ( c_ReplSep @ X0
% 0.21/0.47 @ ^ [X1: $i] :
% 0.21/0.47 ? [X2: $i] :
% 0.21/0.47 ( ( c_Inj1 @ X2 )
% 0.21/0.47 = X1 )
% 0.21/0.47 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax76,axiom,
% 0.21/0.47 ( c_binrep
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax77,axiom,
% 0.21/0.47 ( c_lam
% 0.21/0.47 = ( ^ [X0: $i,X1: $i > $i] :
% 0.21/0.47 ( c_famunion @ X0
% 0.21/0.47 @ ^ [X2: $i] :
% 0.21/0.47 ( c_Repl @ ( X1 @ X2 )
% 0.21/0.47 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax78,axiom,
% 0.21/0.47 ( c_setprod
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_lam @ X0
% 0.21/0.47 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(ax79,axiom,
% 0.21/0.47 ( c_ap
% 0.21/0.47 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.47 ( c_ReplSep @ X0
% 0.21/0.47 @ ^ [X2: $i] :
% 0.21/0.47 ? [X3: $i] :
% 0.21/0.47 ( X2
% 0.21/0.47 = ( c_setsum @ X1 @ X3 ) )
% 0.21/0.47 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax80,axiom,
% 0.21/0.48 ( c_setsum_p
% 0.21/0.48 = ( ^ [X0: $i] :
% 0.21/0.48 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.21/0.48 = X0 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax81,axiom,
% 0.21/0.48 ( c_tuple_p
% 0.21/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.48 ! [X2: $i] :
% 0.21/0.48 ( ( c_In @ X2 @ X1 )
% 0.21/0.48 => ? [X3: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X3 @ X0 )
% 0.21/0.48 @ ? [X4: $i] :
% 0.21/0.48 ( X2
% 0.21/0.48 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax82,axiom,
% 0.21/0.48 ( c_Pi
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $i] :
% 0.21/0.48 ( c_Sep
% 0.21/0.48 @ ( c_Power
% 0.21/0.48 @ ( c_lam @ X0
% 0.21/0.48 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.21/0.48 @ ^ [X2: $i] :
% 0.21/0.48 ! [X3: $i] :
% 0.21/0.48 ( ( c_In @ X3 @ X0 )
% 0.21/0.48 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax83,axiom,
% 0.21/0.48 ( c_setexp
% 0.21/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.48 ( c_Pi @ X1
% 0.21/0.48 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax84,axiom,
% 0.21/0.48 ( c_Sep2
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.21/0.48 ( c_Sep
% 0.21/0.48 @ ( c_lam @ X0
% 0.21/0.48 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.21/0.48 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax85,axiom,
% 0.21/0.48 ( c_set_of_pairs
% 0.21/0.48 = ( ^ [X0: $i] :
% 0.21/0.48 ! [X1: $i] :
% 0.21/0.48 ( ( c_In @ X1 @ X0 )
% 0.21/0.48 => ? [X2: $i,X3: $i] :
% 0.21/0.48 ( X1
% 0.21/0.48 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.21/0.48 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax86,axiom,
% 0.21/0.48 ( c_lam2
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.21/0.48 ( c_lam @ X0
% 0.21/0.48 @ ^ [X3: $i] :
% 0.21/0.48 ( c_lam @ ( X1 @ X3 )
% 0.21/0.48 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax87,axiom,
% 0.21/0.48 ( c_PNoEq_
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.21/0.48 ! [X3: $i] :
% 0.21/0.48 ( ( c_In @ X3 @ X0 )
% 0.21/0.48 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax88,axiom,
% 0.21/0.48 ( c_PNoLt_
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.21/0.48 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax89,axiom,
% 0.21/0.48 ( c_PNoLt
% 0.21/0.48 = ( ^ [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 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax90,axiom,
% 0.21/0.48 ( c_PNoLe
% 0.21/0.48 = ( ^ [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 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax91,axiom,
% 0.21/0.48 ( c_PNo_downc
% 0.21/0.48 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.21/0.48 ? [X3: $i] :
% 0.21/0.48 ( c_and @ ( c_ordinal @ X3 )
% 0.21/0.48 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax92,axiom,
% 0.21/0.48 ( c_PNo_upc
% 0.21/0.48 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.21/0.48 ? [X3: $i] :
% 0.21/0.48 ( c_and @ ( c_ordinal @ X3 )
% 0.21/0.48 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax93,axiom,
% 0.21/0.48 ( c_SNoElts_
% 0.21/0.48 = ( ^ [X0: $i] :
% 0.21/0.48 ( c_binunion @ X0
% 0.21/0.48 @ ( c_Repl @ X0
% 0.21/0.48 @ ^ [X1: $i] :
% 0.21/0.48 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.21/0.48 @ X1 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax94,axiom,
% 0.21/0.48 ( c_SNo_
% 0.21/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.48 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.21/0.48 @ ! [X2: $i] :
% 0.21/0.48 ( ( c_In @ X2 @ X0 )
% 0.21/0.48 => ( c_exactly1of2
% 0.21/0.48 @ ( c_In
% 0.21/0.48 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.21/0.48 @ X2 )
% 0.21/0.48 @ X1 )
% 0.21/0.48 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax95,axiom,
% 0.21/0.48 ( c_PSNo
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $o] :
% 0.21/0.48 ( c_binunion
% 0.21/0.48 @ ( c_Sep @ X0
% 0.21/0.48 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.21/0.48 @ ( c_ReplSep @ X0
% 0.21/0.48 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.21/0.48 @ ^ [X2: $i] :
% 0.21/0.48 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.21/0.48 @ X2 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax96,axiom,
% 0.21/0.48 ( c_SNo
% 0.21/0.48 = ( ^ [X0: $i] :
% 0.21/0.48 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax97,axiom,
% 0.21/0.48 ( c_SNoLev
% 0.21/0.48 = ( ^ [X0: $i] :
% 0.21/0.48 ( c_Eps_i
% 0.21/0.48 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax98,axiom,
% 0.21/0.48 ( c_SNoEq_
% 0.21/0.48 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.21/0.48 ( c_PNoEq_ @ X0
% 0.21/0.48 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.21/0.48 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax99,axiom,
% 0.21/0.48 ( c_SNoLt
% 0.21/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.48 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.21/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.21/0.48 @ ( c_SNoLev @ X1 )
% 0.21/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax100,axiom,
% 0.21/0.48 ( c_SNoLe
% 0.21/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.48 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.21/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.21/0.48 @ ( c_SNoLev @ X1 )
% 0.21/0.48 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax101,axiom,
% 0.21/0.48 ( c_binop_on
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.21/0.48 ! [X2: $i] :
% 0.21/0.48 ( ( c_In @ X2 @ X0 )
% 0.21/0.48 => ! [X3: $i] :
% 0.21/0.48 ( ( c_In @ X3 @ X0 )
% 0.21/0.48 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax102,axiom,
% 0.21/0.48 ( c_Loop
% 0.21/0.48 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.21/0.48 ( c_and
% 0.21/0.48 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.21/0.48 @ ! [X5: $i] :
% 0.21/0.48 ( ( c_In @ X5 @ X0 )
% 0.21/0.48 => ( c_and
% 0.21/0.48 @ ( ( X1 @ X4 @ X5 )
% 0.21/0.48 = X5 )
% 0.21/0.48 @ ( ( X1 @ X5 @ X4 )
% 0.21/0.48 = X5 ) ) ) )
% 0.21/0.48 @ ! [X5: $i] :
% 0.21/0.48 ( ( c_In @ X5 @ X0 )
% 0.21/0.48 => ! [X6: $i] :
% 0.21/0.48 ( ( c_In @ X6 @ X0 )
% 0.21/0.48 => ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.21/0.48 = X6 )
% 0.21/0.48 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.21/0.48 = X6 ) )
% 0.21/0.48 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.21/0.48 = X5 ) )
% 0.21/0.48 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.21/0.48 = X5 ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax103,axiom,
% 0.21/0.48 ( c_Loop_with_defs
% 0.21/0.48 = ( ^ [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] :
% 0.21/0.48 ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.21/0.48 @ ! [X14: $i] :
% 0.21/0.48 ( ( c_In @ X14 @ X0 )
% 0.21/0.48 => ! [X15: $i] :
% 0.21/0.48 ( ( c_In @ X15 @ X0 )
% 0.21/0.48 => ( ( X5 @ X14 @ X15 )
% 0.21/0.48 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.21/0.48 @ ! [X14: $i] :
% 0.21/0.48 ( ( c_In @ X14 @ X0 )
% 0.21/0.48 => ! [X15: $i] :
% 0.21/0.48 ( ( c_In @ X15 @ X0 )
% 0.21/0.48 => ! [X16: $i] :
% 0.21/0.48 ( ( c_In @ X16 @ X0 )
% 0.21/0.48 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.21/0.48 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.21/0.48 @ ! [X14: $i] :
% 0.21/0.48 ( ( c_In @ X14 @ X0 )
% 0.21/0.48 => ! [X15: $i] :
% 0.21/0.48 ( ( c_In @ X15 @ X0 )
% 0.21/0.48 => ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( c_and
% 0.21/0.48 @ ( ( X7 @ X14 @ X15 )
% 0.21/0.48 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.21/0.48 @ ( ( X10 @ X14 @ X15 )
% 0.21/0.48 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.21/0.48 @ ( ( X11 @ X14 @ X15 )
% 0.21/0.48 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.21/0.48 @ ( ( X12 @ X14 @ X15 )
% 0.21/0.48 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.21/0.48 @ ( ( X13 @ X14 @ X15 )
% 0.21/0.48 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.21/0.48 @ ! [X14: $i] :
% 0.21/0.48 ( ( c_In @ X14 @ X0 )
% 0.21/0.48 => ! [X15: $i] :
% 0.21/0.48 ( ( c_In @ X15 @ X0 )
% 0.21/0.48 => ! [X16: $i] :
% 0.21/0.48 ( ( c_In @ X16 @ X0 )
% 0.21/0.48 => ( c_and
% 0.21/0.48 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.21/0.48 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.21/0.48 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.21/0.48 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax104,axiom,
% 0.21/0.48 ( c_Loop_with_defs_cex1
% 0.21/0.48 = ( ^ [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] :
% 0.21/0.48 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.21/0.48 @ ? [X14: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X14 @ X0 )
% 0.21/0.48 @ ? [X15: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X15 @ X0 )
% 0.21/0.48 @ ? [X16: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X16 @ X0 )
% 0.21/0.48 @ ? [X17: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X17 @ X0 )
% 0.21/0.48 @ ( c_not
% 0.21/0.48 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.21/0.48 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax105,axiom,
% 0.21/0.48 ( c_Loop_with_defs_cex2
% 0.21/0.48 = ( ^ [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] :
% 0.21/0.48 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.21/0.48 @ ? [X14: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X14 @ X0 )
% 0.21/0.48 @ ? [X15: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X15 @ X0 )
% 0.21/0.48 @ ? [X16: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X16 @ X0 )
% 0.21/0.48 @ ? [X17: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X17 @ X0 )
% 0.21/0.48 @ ? [X18: $i] :
% 0.21/0.48 ( c_and @ ( c_In @ X18 @ X0 )
% 0.21/0.48 @ ( c_not
% 0.21/0.48 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.21/0.48 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax106,axiom,
% 0.21/0.48 ( c_combinator
% 0.21/0.48 = ( ^ [X0: $i] :
% 0.21/0.48 ! [X1: $i > $o] :
% 0.21/0.48 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.21/0.48 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.21/0.48 => ( ! [X2: $i,X3: $i] :
% 0.21/0.48 ( ( X1 @ X2 )
% 0.21/0.48 => ( ( X1 @ X3 )
% 0.21/0.48 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.21/0.48 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax107,axiom,
% 0.21/0.48 ( c_combinator_equiv
% 0.21/0.48 = ( ^ [X0: $i,X1: $i] :
% 0.21/0.48 ! [X2: $i > $i > $o] :
% 0.21/0.48 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.21/0.48 ( ( c_per_i @ X2 )
% 0.21/0.48 => ( ! [X6: $i] :
% 0.21/0.48 ( ( c_combinator @ X6 )
% 0.21/0.48 => ( X2 @ X6 @ X6 ) )
% 0.21/0.48 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.21/0.48 ( ( c_combinator @ X6 )
% 0.21/0.48 => ( ( c_combinator @ X7 )
% 0.21/0.48 => ( ( c_combinator @ X8 )
% 0.21/0.48 => ( ( c_combinator @ X9 )
% 0.21/0.48 => ( ( X2 @ X6 @ X8 )
% 0.21/0.48 => ( ( X2 @ X7 @ X9 )
% 0.21/0.48 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.21/0.48 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.21/0.48 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.21/0.48 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.21/0.48 @ ( c_Inj0 @ c_Empty )
% 0.21/0.48 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.21/0.48 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(ax108,axiom,
% 0.21/0.48 ( c_equip_mod
% 0.21/0.48 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.21/0.48 ? [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 ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(conj,conjecture,
% 0.21/0.48 ( c_not
% 0.21/0.48 @ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.21/0.48 ( ( c_and
% 0.21/0.48 @ ! [X10: $i] :
% 0.21/0.48 ( ( ( X4 @ X9 )
% 0.21/0.48 = X10 )
% 0.21/0.48 => ( ( c_and @ ( X2 @ X10 )
% 0.21/0.48 @ ( ( X7 = X5 )
% 0.21/0.48 => ( c_and
% 0.21/0.48 @ ! [X11: $i] : ( X9 = X8 )
% 0.21/0.48 @ ? [X11: $i] : ( X3 @ X10 ) ) ) )
% 0.21/0.48 => ? [X11: $i] : ( X7 = X7 ) ) )
% 0.21/0.48 @ ( c_not @ ( X3 @ ( X4 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) ) )
% 0.21/0.48 => ( X6 = X9 ) ) ) ).
% 0.21/0.48
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 ------------------------
% 2.62/1.64 ---- Embedded in THF ---
% 2.62/1.64 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.62/1.64 %%% Generated on Tue Feb 24 14:49:57 EST 2026
% 2.62/1.64 %%% using '$$dhol' embedding, version 1.3.0.
% 2.62/1.64 %%% Logic specification used:
% 2.62/1.64 %%% thf(spec, logic, $$dhol).
% 2.62/1.64
% 2.62/1.64 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2DTF1961.p
% 2.62/1.64 thf(c_Eps_i_tp, type, c_Eps_i: (($i > $o) > $i)).
% 2.62/1.64 thf(c_False_tp, type, c_False: $o).
% 2.62/1.64 thf(c_True_tp, type, c_True: $o).
% 2.62/1.64 thf(c_not_tp, type, c_not: ($o > $o)).
% 2.62/1.64 thf(c_and_tp, type, c_and: ($o > ($o > $o))).
% 2.62/1.64 thf(c_or_tp, type, c_or: ($o > ($o > $o))).
% 2.62/1.64 thf(c_iff_tp, type, c_iff: ($o > ($o > $o))).
% 2.62/1.64 thf(c_In_tp, type, c_In: ($i > ($i > $o))).
% 2.62/1.64 thf(c_Subq_tp, type, c_Subq: ($i > ($i > $o))).
% 2.62/1.64 thf(c_Empty_tp, type, c_Empty: $i).
% 2.62/1.64 thf(c_Union_tp, type, c_Union: ($i > $i)).
% 2.62/1.64 thf(c_Power_tp, type, c_Power: ($i > $i)).
% 2.62/1.64 thf(c_Repl_tp, type, c_Repl: ($i > (($i > $i) > $i))).
% 2.62/1.64 thf(c_TransSet_tp, type, c_TransSet: ($i > $o)).
% 2.62/1.64 thf(c_atleast2_tp, type, c_atleast2: ($i > $o)).
% 2.62/1.64 thf(c_atleast3_tp, type, c_atleast3: ($i > $o)).
% 2.62/1.64 thf(c_atleast4_tp, type, c_atleast4: ($i > $o)).
% 2.62/1.64 thf(c_atleast5_tp, type, c_atleast5: ($i > $o)).
% 2.62/1.64 thf(c_atleast6_tp, type, c_atleast6: ($i > $o)).
% 2.62/1.64 thf(c_exactly2_tp, type, c_exactly2: ($i > $o)).
% 2.62/1.64 thf(c_exactly3_tp, type, c_exactly3: ($i > $o)).
% 2.62/1.64 thf(c_exactly4_tp, type, c_exactly4: ($i > $o)).
% 2.62/1.64 thf(c_exactly5_tp, type, c_exactly5: ($i > $o)).
% 2.62/1.64 thf(c_exu_i_tp, type, c_exu_i: (($i > $o) > $o)).
% 2.62/1.64 thf(c_reflexive_i_tp, type, c_reflexive_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_irreflexive_i_tp, type, c_irreflexive_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_symmetric_i_tp, type, c_symmetric_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_antisymmetric_i_tp, type, c_antisymmetric_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_transitive_i_tp, type, c_transitive_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_eqreln_i_tp, type, c_eqreln_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_per_i_tp, type, c_per_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_linear_i_tp, type, c_linear_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_trichotomous_or_i_tp, type, c_trichotomous_or_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_partialorder_i_tp, type, c_partialorder_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_totalorder_i_tp, type, c_totalorder_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_strictpartialorder_i_tp, type, c_strictpartialorder_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_stricttotalorder_i_tp, type, c_stricttotalorder_i: (($i > ($i > $o)) > $o)).
% 2.62/1.64 thf(c_If_i_tp, type, c_If_i: ($o > ($i > ($i > $i)))).
% 2.62/1.64 thf(c_exactly1of2_tp, type, c_exactly1of2: ($o > ($o > $o))).
% 2.62/1.64 thf(c_exactly1of3_tp, type, c_exactly1of3: ($o > ($o > ($o > $o)))).
% 2.62/1.64 thf(c_nIn_tp, type, c_nIn: ($i > ($i > $o))).
% 2.62/1.64 thf(c_nSubq_tp, type, c_nSubq: ($i > ($i > $o))).
% 2.62/1.64 thf(c_UPair_tp, type, c_UPair: ($i > ($i > $i))).
% 2.62/1.64 thf(c_Sing_tp, type, c_Sing: ($i > $i)).
% 2.62/1.64 thf(c_binunion_tp, type, c_binunion: ($i > ($i > $i))).
% 2.62/1.64 thf(c_SetAdjoin_tp, type, c_SetAdjoin: ($i > ($i > $i))).
% 2.62/1.64 thf(c_famunion_tp, type, c_famunion: ($i > (($i > $i) > $i))).
% 2.62/1.64 thf(c_Sep_tp, type, c_Sep: ($i > (($i > $o) > $i))).
% 2.62/1.64 thf(c_ReplSep_tp, type, c_ReplSep: ($i > (($i > $o) > (($i > $i) > $i)))).
% 2.62/1.64 thf(c_binintersect_tp, type, c_binintersect: ($i > ($i > $i))).
% 2.62/1.64 thf(c_setminus_tp, type, c_setminus: ($i > ($i > $i))).
% 2.62/1.64 thf(c_inj_tp, type, c_inj: ($i > ($i > (($i > $i) > $o)))).
% 2.62/1.64 thf(c_bij_tp, type, c_bij: ($i > ($i > (($i > $i) > $o)))).
% 2.62/1.64 thf(c_atleastp_tp, type, c_atleastp: ($i > ($i > $o))).
% 2.62/1.64 thf(c_equip_tp, type, c_equip: ($i > ($i > $o))).
% 2.62/1.64 thf(c_In_rec_poly_G_i_tp, type, c_In_rec_poly_G_i: (($i > (($i > $i) > $i)) > ($i > ($i > $o)))).
% 2.62/1.64 thf(c_In_rec_poly_i_tp, type, c_In_rec_poly_i: (($i > (($i > $i) > $i)) > ($i > $i))).
% 2.62/1.64 thf(c_ordsucc_tp, type, c_ordsucc: ($i > $i)).
% 2.62/1.64 thf(c_nat_p_tp, type, c_nat_p: ($i > $o)).
% 2.62/1.64 thf(c_nat_primrec_tp, type, c_nat_primrec: ($i > (($i > ($i > $i)) > ($i > $i)))).
% 2.62/1.64 thf(c_add_nat_tp, type, c_add_nat: ($i > ($i > $i))).
% 2.62/1.64 thf(c_mul_nat_tp, type, c_mul_nat: ($i > ($i > $i))).
% 2.62/1.64 thf(c_ordinal_tp, type, c_ordinal: ($i > $o)).
% 2.62/1.64 thf(c_V__tp, type, c_V_: ($i > $i)).
% 2.62/1.64 thf(c_Inj1_tp, type, c_Inj1: ($i > $i)).
% 2.62/1.64 thf(c_Inj0_tp, type, c_Inj0: ($i > $i)).
% 2.62/1.64 thf(c_Unj_tp, type, c_Unj: ($i > $i)).
% 2.62/1.64 thf(c_combine_funcs_tp, type, c_combine_funcs: ($i > ($i > (($i > $i) > (($i > $i) > ($i > $i)))))).
% 2.62/1.64 thf(c_setsum_tp, type, c_setsum: ($i > ($i > $i))).
% 2.62/1.64 thf(c_proj0_tp, type, c_proj0: ($i > $i)).
% 2.62/1.64 thf(c_proj1_tp, type, c_proj1: ($i > $i)).
% 2.62/1.64 thf(c_binrep_tp, type, c_binrep: ($i > ($i > $i))).
% 2.62/1.64 thf(c_lam_tp, type, c_lam: ($i > (($i > $i) > $i))).
% 2.62/1.64 thf(c_setprod_tp, type, c_setprod: ($i > ($i > $i))).
% 2.62/1.64 thf(c_ap_tp, type, c_ap: ($i > ($i > $i))).
% 2.62/1.64 thf(c_setsum_p_tp, type, c_setsum_p: ($i > $o)).
% 2.62/1.64 thf(c_tuple_p_tp, type, c_tuple_p: ($i > ($i > $o))).
% 2.62/1.64 thf(c_Pi_tp, type, c_Pi: ($i > (($i > $i) > $i))).
% 2.62/1.64 thf(c_setexp_tp, type, c_setexp: ($i > ($i > $i))).
% 2.62/1.64 thf(c_Sep2_tp, type, c_Sep2: ($i > (($i > $i) > (($i > ($i > $o)) > $i)))).
% 2.62/1.64 thf(c_set_of_pairs_tp, type, c_set_of_pairs: ($i > $o)).
% 2.62/1.64 thf(c_lam2_tp, type, c_lam2: ($i > (($i > $i) > (($i > ($i > $i)) > $i)))).
% 2.62/1.64 thf(c_PNoEq__tp, type, c_PNoEq_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 2.62/1.64 thf(c_PNoLt__tp, type, c_PNoLt_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 2.62/1.64 thf(c_PNoLt_tp, type, c_PNoLt: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 2.62/1.64 thf(c_PNoLe_tp, type, c_PNoLe: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 2.62/1.64 thf(c_PNo_downc_tp, type, c_PNo_downc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 2.62/1.64 thf(c_PNo_upc_tp, type, c_PNo_upc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 2.62/1.64 thf(c_SNoElts__tp, type, c_SNoElts_: ($i > $i)).
% 2.62/1.64 thf(c_SNo__tp, type, c_SNo_: ($i > ($i > $o))).
% 2.62/1.64 thf(c_PSNo_tp, type, c_PSNo: ($i > (($i > $o) > $i))).
% 2.62/1.64 thf(c_SNo_tp, type, c_SNo: ($i > $o)).
% 2.62/1.64 thf(c_SNoLev_tp, type, c_SNoLev: ($i > $i)).
% 2.62/1.64 thf(c_SNoEq__tp, type, c_SNoEq_: ($i > ($i > ($i > $o)))).
% 2.62/1.64 thf(c_SNoLt_tp, type, c_SNoLt: ($i > ($i > $o))).
% 2.62/1.64 thf(c_SNoLe_tp, type, c_SNoLe: ($i > ($i > $o))).
% 2.62/1.64 thf(c_binop_on_tp, type, c_binop_on: ($i > (($i > ($i > $i)) > $o))).
% 2.62/1.64 thf(c_Loop_tp, type, c_Loop: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > $o)))))).
% 2.62/1.64 thf(c_Loop_with_defs_tp, type, c_Loop_with_defs: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.62/1.64 thf(c_Loop_with_defs_cex1_tp, type, c_Loop_with_defs_cex1: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.62/1.64 thf(c_Loop_with_defs_cex2_tp, type, c_Loop_with_defs_cex2: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.62/1.64 thf(c_combinator_tp, type, c_combinator: ($i > $o)).
% 2.62/1.64 thf(c_combinator_equiv_tp, type, c_combinator_equiv: ($i > ($i > $o))).
% 2.62/1.64 thf(c_equip_mod_tp, type, c_equip_mod: ($i > ($i > ($i > $o)))).
% 2.62/1.64 thf(ax1, axiom, (! [X0:($i > $o),X1:$i]: (((X0 @ X1) => (X0 @ (c_Eps_i @ X0)))))).
% 2.62/1.64 thf(ax2, axiom, (! [X0:$o]: (((c_not @ (c_not @ X0)) => X0)))).
% 2.62/1.64 thf(ax3, axiom, (! [X0:$o,X1:$o]: ((((c_iff @ X0) @ X1) => (X0 = X1))))).
% 2.62/1.64 thf(ax4, axiom, (! [X0:$i,X1:$i]: ((((c_Subq @ X0) @ X1) => (((c_Subq @ X1) @ X0) => (X0 = X1)))))).
% 2.62/1.64 thf(ax5, axiom, (c_not @ (? [X0:$i]: (((c_In @ X0) @ c_Empty))))).
% 2.62/1.64 thf(ax6, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ (? [X2:$i]: (((c_and @ ((c_In @ X1) @ X2)) @ ((c_In @ X2) @ X0)))))))).
% 2.62/1.64 thf(ax7, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))))).
% 2.62/1.64 thf(ax8, axiom, (! [X0:$i,X1:($i > $i),X2:$i]: (((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ (^ [X3:$i]: ((X1 @ X3)))))) @ (? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ (X2 = (X1 @ X3))))))))).
% 2.62/1.64 thf(ax9, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((X0 @ X1) => (! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2))))))) => ((X0 @ c_Empty) => ((! [X1:$i]: (((X0 @ X1) => (X0 @ (c_Union @ X1))))) => ((! [X1:$i]: (((X0 @ X1) => (X0 @ (c_Power @ X1))))) => ((! [X1:$i]: (((X0 @ X1) => (! [X2:($i > $i)]: (((! [X3:$i]: ((((c_In @ X3) @ X1) => (X0 @ (X2 @ X3))))) => (X0 @ ((c_Repl @ X1) @ (^ [X3:$i]: ((X2 @ X3))))))))))) => (! [X1:$i]: ((X0 @ X1))))))))))).
% 2.62/1.64 thf(ax10, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2)))) => (X0 @ X1)))) => (! [X1:$i]: ((X0 @ X1))))))).
% 2.62/1.64 thf(ax11, axiom, (c_False = (! [X0:$o]: (X0)))).
% 2.62/1.64 thf(ax12, axiom, (c_True = (! [X0:$o]: ((X0 => X0))))).
% 2.62/1.64 thf(ax13, axiom, (c_not = (^ [X0:$o]: ((X0 => c_False))))).
% 2.62/1.64 thf(ax14, axiom, (c_and = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => (X1 => X2)) => X2))))))).
% 2.62/1.64 thf(ax15, axiom, (c_or = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => X2) => ((X1 => X2) => X2)))))))).
% 2.62/1.64 thf(ax16, axiom, (c_iff = (^ [X0:$o,X1:$o]: (((c_and @ (X0 => X1)) @ (X1 => X0)))))).
% 2.62/1.64 thf(ax17, axiom, (c_Subq = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax18, axiom, (c_TransSet = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => ((c_Subq @ X1) @ X0)))))))).
% 2.62/1.64 thf(ax19, axiom, (c_atleast2 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_In @ X1) @ X0)) @ (c_not @ ((c_Subq @ X0) @ (c_Power @ X1)))))))))).
% 2.62/1.64 thf(ax20, axiom, (c_atleast3 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast2 @ X1))))))))).
% 2.62/1.64 thf(ax21, axiom, (c_atleast4 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast3 @ X1))))))))).
% 2.62/1.64 thf(ax22, axiom, (c_atleast5 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast4 @ X1))))))))).
% 2.62/1.64 thf(ax23, axiom, (c_atleast6 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast5 @ X1))))))))).
% 2.62/1.64 thf(ax24, axiom, (c_exactly2 = (^ [X0:$i]: (((c_and @ (c_atleast2 @ X0)) @ (c_not @ (c_atleast3 @ X0))))))).
% 2.62/1.64 thf(ax25, axiom, (c_exactly3 = (^ [X0:$i]: (((c_and @ (c_atleast3 @ X0)) @ (c_not @ (c_atleast4 @ X0))))))).
% 2.62/1.64 thf(ax26, axiom, (c_exactly4 = (^ [X0:$i]: (((c_and @ (c_atleast4 @ X0)) @ (c_not @ (c_atleast5 @ X0))))))).
% 2.62/1.64 thf(ax27, axiom, (c_exactly5 = (^ [X0:$i]: (((c_and @ (c_atleast5 @ X0)) @ (c_not @ (c_atleast6 @ X0))))))).
% 2.62/1.64 thf(ax28, axiom, (c_exu_i = (^ [X0:($i > $o)]: (((c_and @ (? [X1:$i]: ((X0 @ X1)))) @ (! [X1:$i,X2:$i]: (((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))))))).
% 2.62/1.64 thf(ax29, axiom, (c_reflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: (((X0 @ X1) @ X1))))))).
% 2.62/1.64 thf(ax30, axiom, (c_irreflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: ((c_not @ ((X0 @ X1) @ X1)))))))).
% 2.62/1.64 thf(ax31, axiom, (c_symmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => ((X0 @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax32, axiom, (c_antisymmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X1) => (X1 = X2))))))))).
% 2.62/1.64 thf(ax33, axiom, (c_transitive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i,X3:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X3) => ((X0 @ X1) @ X3))))))))).
% 2.62/1.64 thf(ax34, axiom, (c_eqreln_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_symmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 2.62/1.64 thf(ax35, axiom, (c_per_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_symmetric_i @ X0)) @ (c_transitive_i @ X0)))))).
% 2.62/1.64 thf(ax36, axiom, (c_linear_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((X0 @ X1) @ X2)) @ ((X0 @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax37, axiom, (c_trichotomous_or_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((c_or @ ((X0 @ X1) @ X2)) @ (X1 = X2))) @ ((X0 @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax38, axiom, (c_partialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_antisymmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 2.62/1.64 thf(ax39, axiom, (c_totalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_partialorder_i @ X0)) @ (c_linear_i @ X0)))))).
% 2.62/1.64 thf(ax40, axiom, (c_strictpartialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_irreflexive_i @ X0)) @ (c_transitive_i @ X0)))))).
% 2.62/1.64 thf(ax41, axiom, (c_stricttotalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_strictpartialorder_i @ X0)) @ (c_trichotomous_or_i @ X0)))))).
% 2.62/1.64 thf(ax42, axiom, (c_If_i = (^ [X0:$o,X1:$i,X2:$i]: ((c_Eps_i @ (^ [X3:$i]: (((c_or @ ((c_and @ X0) @ (X3 = X1))) @ ((c_and @ (c_not @ X0)) @ (X3 = X2)))))))))).
% 2.62/1.64 thf(ax43, axiom, (c_exactly1of2 = (^ [X0:$o,X1:$o]: (((c_or @ ((c_and @ X0) @ (c_not @ X1))) @ ((c_and @ (c_not @ X0)) @ X1)))))).
% 2.62/1.64 thf(ax44, axiom, (c_exactly1of3 = (^ [X0:$o,X1:$o,X2:$o]: (((c_or @ ((c_and @ ((c_exactly1of2 @ X0) @ X1)) @ (c_not @ X2))) @ ((c_and @ ((c_and @ (c_not @ X0)) @ (c_not @ X1))) @ X2)))))).
% 2.62/1.64 thf(ax45, axiom, (c_nIn = (^ [X0:$i,X1:$i]: ((c_not @ ((c_In @ X0) @ X1)))))).
% 2.62/1.64 thf(ax46, axiom, (c_nSubq = (^ [X0:$i,X1:$i]: ((c_not @ ((c_Subq @ X0) @ X1)))))).
% 2.62/1.64 thf(ax47, axiom, (c_UPair = (^ [X0:$i,X1:$i]: (((c_Repl @ (c_Power @ (c_Power @ c_Empty))) @ (^ [X2:$i]: ((((c_If_i @ ((c_In @ c_Empty) @ X2)) @ X0) @ X1)))))))).
% 2.62/1.64 thf(ax48, axiom, (c_Sing = (^ [X0:$i]: (((c_UPair @ X0) @ X0))))).
% 2.62/1.64 thf(ax49, axiom, (c_binunion = (^ [X0:$i,X1:$i]: ((c_Union @ ((c_UPair @ X0) @ X1)))))).
% 2.62/1.64 thf(ax50, axiom, (c_SetAdjoin = (^ [X0:$i,X1:$i]: (((c_binunion @ X0) @ (c_Sing @ X1)))))).
% 2.62/1.64 thf(ax51, axiom, (c_famunion = (^ [X0:$i,X1:($i > $i)]: ((c_Union @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 2.62/1.64 thf(ax52, axiom, (c_Sep = (^ [X0:$i,X1:($i > $o)]: ((((c_If_i @ (? [X2:$i]: (((c_and @ ((c_In @ X2) @ X0)) @ (X1 @ X2))))) @ ((c_Repl @ X0) @ (^ [X2:$i]: (((^ [X3:$i]: ((((c_If_i @ (X1 @ X3)) @ X3) @ (c_Eps_i @ (^ [X4:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ (X1 @ X4)))))))) @ X2))))) @ c_Empty))))).
% 2.62/1.64 thf(ax53, axiom, (c_ReplSep = (^ [X0:$i,X1:($i > $o),X2:($i > $i)]: (((c_Repl @ ((c_Sep @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: ((X2 @ X3)))))))).
% 2.62/1.64 thf(ax54, axiom, (c_binintersect = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax55, axiom, (c_setminus = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_nIn @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax56, axiom, (c_inj = (^ [X0:$i,X1:$i,X2:($i > $i)]: (((c_and @ (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ (X2 @ X3)) @ X1))))) @ (! [X3:$i]: ((((c_In @ X3) @ X0) => (! [X4:$i]: ((((c_In @ X4) @ X0) => (((X2 @ X3) = (X2 @ X4)) => (X3 = X4))))))))))))).
% 2.62/1.64 thf(ax57, axiom, (c_bij = (^ [X0:$i,X1:$i,X2:($i > $i)]: (((c_and @ (((c_inj @ X0) @ X1) @ X2)) @ (! [X3:$i]: ((((c_In @ X3) @ X1) => (? [X4:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ ((X2 @ X4) = X3)))))))))))).
% 2.62/1.64 thf(ax58, axiom, (c_atleastp = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_inj @ X0) @ X1) @ X2))))))).
% 2.62/1.64 thf(ax59, axiom, (c_equip = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_bij @ X0) @ X1) @ X2))))))).
% 2.62/1.64 thf(ax60, axiom, (c_In_rec_poly_G_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i,X2:$i]: ((! [X3:($i > ($i > $o))]: (((! [X4:$i,X5:($i > $i)]: (((! [X6:$i]: ((((c_In @ X6) @ X4) => ((X3 @ X6) @ (X5 @ X6))))) => ((X3 @ X4) @ ((X0 @ X4) @ X5))))) => ((X3 @ X1) @ X2)))))))).
% 2.62/1.64 thf(ax61, axiom, (c_In_rec_poly_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i]: ((c_Eps_i @ (^ [X2:$i]: ((((c_In_rec_poly_G_i @ X0) @ X1) @ X2)))))))).
% 2.62/1.64 thf(ax62, axiom, (c_ordsucc = (^ [X0:$i]: (((c_binunion @ X0) @ (c_Sing @ X0)))))).
% 2.62/1.64 thf(ax63, axiom, (c_nat_p = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ c_Empty) => ((! [X2:$i]: (((X1 @ X2) => (X1 @ (c_ordsucc @ X2))))) => (X1 @ X0))))))))).
% 2.62/1.64 thf(ax64, axiom, (c_nat_primrec = (^ [X0:$i,X1:($i > ($i > $i))]: ((c_In_rec_poly_i @ (^ [X2:$i,X3:($i > $i)]: ((((c_If_i @ ((c_In @ (c_Union @ X2)) @ X2)) @ ((X1 @ (c_Union @ X2)) @ (X3 @ (c_Union @ X2)))) @ X0)))))))).
% 2.62/1.64 thf(ax65, axiom, (c_add_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ X0) @ (^ [X2:$i,X3:$i]: ((c_ordsucc @ X3)))) @ X1))))).
% 2.62/1.64 thf(ax66, axiom, (c_mul_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ c_Empty) @ (^ [X2:$i,X3:$i]: (((c_add_nat @ X0) @ X3)))) @ X1))))).
% 2.62/1.64 thf(ax67, axiom, (c_ordinal = (^ [X0:$i]: (((c_and @ (c_TransSet @ X0)) @ (! [X1:$i]: ((((c_In @ X1) @ X0) => (c_TransSet @ X1))))))))).
% 2.62/1.64 thf(ax68, axiom, (c_V_ = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: ((c_Power @ (X1 @ X2)))))))))).
% 2.62/1.64 thf(ax69, axiom, (c_Inj1 = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_binunion @ (c_Sing @ c_Empty)) @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2)))))))))).
% 2.62/1.64 thf(ax70, axiom, (c_Inj0 = (^ [X0:$i]: (((c_Repl @ X0) @ (^ [X1:$i]: ((c_Inj1 @ X1)))))))).
% 2.62/1.64 thf(ax71, axiom, (c_Unj = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_Repl @ ((c_setminus @ X0) @ (c_Sing @ c_Empty))) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 2.62/1.64 thf(ax72, axiom, (c_combine_funcs = (^ [X0:$i,X1:$i,X2:($i > $i),X3:($i > $i),X4:$i]: ((((c_If_i @ (X4 = (c_Inj0 @ (c_Unj @ X4)))) @ (X2 @ (c_Unj @ X4))) @ (X3 @ (c_Unj @ X4))))))).
% 2.62/1.64 thf(ax73, axiom, (c_setsum = (^ [X0:$i,X1:$i]: (((c_binunion @ ((c_Repl @ X0) @ (^ [X2:$i]: ((c_Inj0 @ X2))))) @ ((c_Repl @ X1) @ (^ [X2:$i]: ((c_Inj1 @ X2))))))))).
% 2.62/1.64 thf(ax74, axiom, (c_proj0 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj0 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 2.62/1.64 thf(ax75, axiom, (c_proj1 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj1 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 2.62/1.64 thf(ax76, axiom, (c_binrep = (^ [X0:$i,X1:$i]: (((c_setsum @ X0) @ (c_Power @ X1)))))).
% 2.62/1.64 thf(ax77, axiom, (c_lam = (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: (((c_Repl @ (X1 @ X2)) @ (^ [X3:$i]: (((c_setsum @ X2) @ X3))))))))))).
% 2.62/1.64 thf(ax78, axiom, (c_setprod = (^ [X0:$i,X1:$i]: (((c_lam @ X0) @ (^ [X2:$i]: (X1))))))).
% 2.62/1.64 thf(ax79, axiom, (c_ap = (^ [X0:$i,X1:$i]: ((((c_ReplSep @ X0) @ (^ [X2:$i]: ((? [X3:$i]: ((X2 = ((c_setsum @ X1) @ X3))))))) @ (^ [X2:$i]: ((c_proj1 @ X2)))))))).
% 2.62/1.64 thf(ax80, axiom, (c_setsum_p = (^ [X0:$i]: ((((c_setsum @ ((c_ap @ X0) @ c_Empty)) @ ((c_ap @ X0) @ (c_ordsucc @ c_Empty))) = X0))))).
% 2.62/1.64 thf(ax81, axiom, (c_tuple_p = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X1) => (? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ (? [X4:$i]: ((X2 = ((c_setsum @ X3) @ X4)))))))))))))).
% 2.62/1.64 thf(ax82, axiom, (c_Pi = (^ [X0:$i,X1:($i > $i)]: (((c_Sep @ (c_Power @ ((c_lam @ X0) @ (^ [X2:$i]: ((c_Union @ (X1 @ X2))))))) @ (^ [X2:$i]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((c_ap @ X2) @ X3)) @ (X1 @ X3)))))))))))).
% 2.62/1.64 thf(ax83, axiom, (c_setexp = (^ [X0:$i,X1:$i]: (((c_Pi @ X1) @ (^ [X2:$i]: (X0))))))).
% 2.62/1.64 thf(ax84, axiom, (c_Sep2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $o))]: (((c_Sep @ ((c_lam @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: (((X2 @ ((c_ap @ X3) @ c_Empty)) @ ((c_ap @ X3) @ (c_ordsucc @ c_Empty)))))))))).
% 2.62/1.64 thf(ax85, axiom, (c_set_of_pairs = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => (? [X2:$i,X3:$i]: ((X1 = ((c_lam @ (c_ordsucc @ (c_ordsucc @ c_Empty))) @ (^ [X4:$i]: ((((c_If_i @ (X4 = c_Empty)) @ X2) @ X3)))))))))))))).
% 2.62/1.64 thf(ax86, axiom, (c_lam2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $i))]: (((c_lam @ X0) @ (^ [X3:$i]: (((c_lam @ (X1 @ X3)) @ (^ [X4:$i]: (((X2 @ X3) @ X4))))))))))).
% 2.62/1.64 thf(ax87, axiom, (c_PNoEq_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_iff @ (X1 @ X3)) @ (X2 @ X3))))))))).
% 2.62/1.64 thf(ax88, axiom, (c_PNoLt_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ ((c_and @ ((c_and @ (((c_PNoEq_ @ X3) @ X1) @ X2)) @ (c_not @ (X1 @ X3)))) @ (X2 @ X3))))))))).
% 2.62/1.64 thf(ax89, axiom, (c_PNoLt = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((c_or @ (((c_PNoLt_ @ ((c_binintersect @ X0) @ X2)) @ X1) @ X3)) @ ((c_and @ ((c_and @ ((c_In @ X0) @ X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))) @ (X3 @ X0)))) @ ((c_and @ ((c_and @ ((c_In @ X2) @ X0)) @ (((c_PNoEq_ @ X2) @ X1) @ X3))) @ (c_not @ (X1 @ X2)))))))).
% 2.62/1.64 thf(ax90, axiom, (c_PNoLe = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((((c_PNoLt @ X0) @ X1) @ X2) @ X3)) @ ((c_and @ (X0 = X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))))))).
% 2.62/1.64 thf(ax91, axiom, (c_PNo_downc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X1) @ X2) @ X3) @ X4))))))))))).
% 2.62/1.64 thf(ax92, axiom, (c_PNo_upc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X3) @ X4) @ X1) @ X2))))))))))).
% 2.62/1.64 thf(ax93, axiom, (c_SNoElts_ = (^ [X0:$i]: (((c_binunion @ X0) @ ((c_Repl @ X0) @ (^ [X1:$i]: (((^ [X2:$i]: (((c_SetAdjoin @ X2) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))).
% 2.62/1.64 thf(ax94, axiom, (c_SNo_ = (^ [X0:$i,X1:$i]: (((c_and @ ((c_Subq @ X1) @ (c_SNoElts_ @ X0))) @ (! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_exactly1of2 @ ((c_In @ ((^ [X3:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2)) @ X1)) @ ((c_In @ X2) @ X1)))))))))).
% 2.62/1.64 thf(ax95, axiom, (c_PSNo = (^ [X0:$i,X1:($i > $o)]: (((c_binunion @ ((c_Sep @ X0) @ (^ [X2:$i]: ((X1 @ X2))))) @ (((c_ReplSep @ X0) @ (^ [X2:$i]: ((c_not @ (X1 @ X2))))) @ (^ [X2:$i]: (((^ [X3:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2))))))))).
% 2.62/1.64 thf(ax96, axiom, (c_SNo = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0)))))))).
% 2.62/1.64 thf(ax97, axiom, (c_SNoLev = (^ [X0:$i]: ((c_Eps_i @ (^ [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0))))))))).
% 2.62/1.64 thf(ax98, axiom, (c_SNoEq_ = (^ [X0:$i,X1:$i,X2:$i]: ((((c_PNoEq_ @ X0) @ (^ [X3:$i]: (((c_In @ X3) @ X1)))) @ (^ [X3:$i]: (((c_In @ X3) @ X2)))))))).
% 2.62/1.64 thf(ax99, axiom, (c_SNoLt = (^ [X0:$i,X1:$i]: (((((c_PNoLt @ (c_SNoLev @ X0)) @ (^ [X2:$i]: (((c_In @ X2) @ X0)))) @ (c_SNoLev @ X1)) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax100, axiom, (c_SNoLe = (^ [X0:$i,X1:$i]: (((((c_PNoLe @ (c_SNoLev @ X0)) @ (^ [X2:$i]: (((c_In @ X2) @ X0)))) @ (c_SNoLev @ X1)) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.62/1.64 thf(ax101, axiom, (c_binop_on = (^ [X0:$i,X1:($i > ($i > $i))]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((X1 @ X2) @ X3)) @ X0))))))))))).
% 2.62/1.64 thf(ax102, axiom, (c_Loop = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i]: (((c_and @ ((c_and @ ((c_and @ ((c_and @ ((c_binop_on @ X0) @ X1)) @ ((c_binop_on @ X0) @ X2))) @ ((c_binop_on @ X0) @ X3))) @ (! [X5:$i]: ((((c_In @ X5) @ X0) => ((c_and @ (((X1 @ X4) @ X5) = X5)) @ (((X1 @ X5) @ X4) = X5))))))) @ (! [X5:$i]: ((((c_In @ X5) @ X0) => (! [X6:$i]: ((((c_In @ X6) @ X0) => ((c_and @ ((c_and @ ((c_and @ (((X2 @ X5) @ ((X1 @ X5) @ X6)) = X6)) @ (((X1 @ X5) @ ((X2 @ X5) @ X6)) = X6))) @ (((X3 @ ((X1 @ X5) @ X6)) @ X6) = X5))) @ (((X1 @ ((X3 @ X5) @ X6)) @ X6) = X5))))))))))))).
% 2.62/1.64 thf(ax103, axiom, (c_Loop_with_defs = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((c_and @ ((c_and @ ((c_and @ (((((c_Loop @ X0) @ X1) @ X2) @ X3) @ X4)) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (((X5 @ X14) @ X15) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X14) @ X15))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (! [X16:$i]: ((((c_In @ X16) @ X0) => ((((X6 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X14) @ ((X1 @ X15) @ X16))) @ ((X1 @ ((X1 @ X14) @ X15)) @ X16)))))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => ((c_and @ ((c_and @ ((c_and @ ((c_and @ (((X7 @ X14) @ X15) = ((X2 @ X14) @ ((X1 @ X15) @ X14)))) @ (((X10 @ X14) @ X15) = ((X1 @ X14) @ ((X1 @ X15) @ ((X2 @ X14) @ X4)))))) @ (((X11 @ X14) @ X15) = ((X1 @ ((X1 @ ((X3 @ X4) @ X14)) @ X15)) @ X14)))) @ (((X12 @ X14) @ X15) = ((X1 @ ((X2 @ X14) @ X15)) @ ((X2 @ ((X2 @ X14) @ X4)) @ X4))))) @ (((X13 @ X14) @ X15) = ((X1 @ ((X3 @ X4) @ ((X3 @ X4) @ X14))) @ ((X3 @ X15) @ X14)))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (! [X16:$i]: ((((c_In @ X16) @ X0) => ((c_and @ ((((X8 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X15) @ ((X1 @ X14) @ X16))))) @ ((((X9 @ X14) @ X15) @ X16) = ((X3 @ ((X1 @ ((X1 @ X16) @ X14)) @ X15)) @ ((X1 @ X14) @ X15)))))))))))))))))).
% 2.62/1.64 thf(ax104, axiom, (c_Loop_with_defs_cex1 = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((((((((((((((c_Loop_with_defs @ X0) @ X1) @ X2) @ X3) @ X4) @ X5) @ X6) @ X7) @ X8) @ X9) @ X10) @ X11) @ X12) @ X13)) @ (? [X14:$i]: (((c_and @ ((c_In @ X14) @ X0)) @ (? [X15:$i]: (((c_and @ ((c_In @ X15) @ X0)) @ (? [X16:$i]: (((c_and @ ((c_In @ X16) @ X0)) @ (? [X17:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (c_not @ (((X5 @ ((X1 @ ((X2 @ (((X8 @ X15) @ X16) @ X14)) @ X4)) @ X14)) @ X17) = X4))))))))))))))))))).
% 2.62/1.64 thf(ax105, axiom, (c_Loop_with_defs_cex2 = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((((((((((((((c_Loop_with_defs @ X0) @ X1) @ X2) @ X3) @ X4) @ X5) @ X6) @ X7) @ X8) @ X9) @ X10) @ X11) @ X12) @ X13)) @ (? [X14:$i]: (((c_and @ ((c_In @ X14) @ X0)) @ (? [X15:$i]: (((c_and @ ((c_In @ X15) @ X0)) @ (? [X16:$i]: (((c_and @ ((c_In @ X16) @ X0)) @ (? [X17:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (? [X18:$i]: (((c_and @ ((c_In @ X18) @ X0)) @ (c_not @ ((((X6 @ X18) @ ((X1 @ ((X3 @ X4) @ X14)) @ (((X9 @ X15) @ X16) @ X14))) @ X17) = X4)))))))))))))))))))))).
% 2.62/1.64 thf(ax106, axiom, (c_combinator = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ (c_Inj0 @ c_Empty)) => ((X1 @ (c_Inj0 @ (c_Power @ c_Empty))) => ((! [X2:$i,X3:$i]: (((X1 @ X2) => ((X1 @ X3) => (X1 @ (c_Inj1 @ ((c_setsum @ X2) @ X3))))))) => (X1 @ X0)))))))))).
% 2.62/1.64 thf(ax107, axiom, (c_combinator_equiv = (^ [X0:$i,X1:$i]: ((! [X2:($i > ($i > $o))]: (((((^ [X3:$i,X4:$i,X5:($i > ($i > $i))]: (((c_per_i @ X2) => ((! [X6:$i]: (((c_combinator @ X6) => ((X2 @ X6) @ X6)))) => ((! [X6:$i,X7:$i,X8:$i,X9:$i]: (((c_combinator @ X6) => ((c_combinator @ X7) => ((c_combinator @ X8) => ((c_combinator @ X9) => (((X2 @ X6) @ X8) => (((X2 @ X7) @ X9) => ((X2 @ ((X5 @ X6) @ X7)) @ ((X5 @ X8) @ X9)))))))))) => ((! [X6:$i,X7:$i]: (((X2 @ ((X5 @ ((X5 @ X3) @ X6)) @ X7)) @ X6))) => ((! [X6:$i,X7:$i,X8:$i]: (((X2 @ ((X5 @ ((X5 @ ((X5 @ X4) @ X6)) @ X7)) @ X8)) @ ((X5 @ ((X5 @ X6) @ X8)) @ ((X5 @ X7) @ X8))))) => ((X2 @ X0) @ X1)))))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ (c_Power @ c_Empty))) @ (^ [X3:$i,X4:$i]: ((c_Inj1 @ ((c_setsum @ X3) @ X4))))))))))).
% 2.62/1.64 thf(ax108, axiom, (c_equip_mod = (^ [X0:$i,X1:$i,X2:$i]: ((? [X3:$i,X4:$i]: (((c_or @ ((c_and @ ((c_equip @ ((c_setsum @ X0) @ X3)) @ X1)) @ ((c_equip @ ((c_setprod @ X4) @ X3)) @ X2))) @ ((c_and @ ((c_equip @ ((c_setsum @ X1) @ X3)) @ X0)) @ ((c_equip @ ((c_setprod @ X4) @ X3)) @ X2))))))))).
% 2.62/1.64 thf(conj, conjecture, (c_not @ (! [X0:($i > ($i > $o)),X1:($i > ($i > $i)),X2:($i > $o),X3:($i > $o),X4:($i > $i),X5:$i,X6:$i,X7:$i,X8:$i,X9:$i]: ((((c_and @ (! [X10:$i]: ((((X4 @ X9) = X10) => (((c_and @ (X2 @ X10)) @ ((X7 = X5) => ((c_and @ (! [X11:$i]: ((X9 = X8)))) @ (? [X11:$i]: ((X3 @ X10)))))) => (? [X11:$i]: ((X7 = X7)))))))) @ (c_not @ (X3 @ (X4 @ (X4 @ ((X1 @ X7) @ X5)))))) => (X6 = X9)))))).
% 2.62/1.64 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2DTF1961.p
% 2.62/1.64 ------------------------
% 2.62/1.67 ---- Cleaned THF ---
% 2.62/1.67 thf(c_Eps_i_tp,type,
% 2.62/1.67 c_Eps_i: ( $i > $o ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_False_tp,type,
% 2.62/1.67 c_False: $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_True_tp,type,
% 2.62/1.67 c_True: $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_not_tp,type,
% 2.62/1.67 c_not: $o > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_and_tp,type,
% 2.62/1.67 c_and: $o > $o > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_or_tp,type,
% 2.62/1.67 c_or: $o > $o > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_iff_tp,type,
% 2.62/1.67 c_iff: $o > $o > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_In_tp,type,
% 2.62/1.67 c_In: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_Subq_tp,type,
% 2.62/1.67 c_Subq: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_Empty_tp,type,
% 2.62/1.67 c_Empty: $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Union_tp,type,
% 2.62/1.67 c_Union: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Power_tp,type,
% 2.62/1.67 c_Power: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Repl_tp,type,
% 2.62/1.67 c_Repl: $i > ( $i > $i ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_TransSet_tp,type,
% 2.62/1.67 c_TransSet: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_atleast2_tp,type,
% 2.62/1.67 c_atleast2: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_atleast3_tp,type,
% 2.62/1.67 c_atleast3: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_atleast4_tp,type,
% 2.62/1.67 c_atleast4: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_atleast5_tp,type,
% 2.62/1.67 c_atleast5: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_atleast6_tp,type,
% 2.62/1.67 c_atleast6: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_exactly2_tp,type,
% 2.62/1.67 c_exactly2: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_exactly3_tp,type,
% 2.62/1.67 c_exactly3: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_exactly4_tp,type,
% 2.62/1.67 c_exactly4: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_exactly5_tp,type,
% 2.62/1.67 c_exactly5: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_exu_i_tp,type,
% 2.62/1.67 c_exu_i: ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_reflexive_i_tp,type,
% 2.62/1.67 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_irreflexive_i_tp,type,
% 2.62/1.67 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_symmetric_i_tp,type,
% 2.62/1.67 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_antisymmetric_i_tp,type,
% 2.62/1.67 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_transitive_i_tp,type,
% 2.62/1.67 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_eqreln_i_tp,type,
% 2.62/1.67 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_per_i_tp,type,
% 2.62/1.67 c_per_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_linear_i_tp,type,
% 2.62/1.67 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_trichotomous_or_i_tp,type,
% 2.62/1.67 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_partialorder_i_tp,type,
% 2.62/1.67 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_totalorder_i_tp,type,
% 2.62/1.67 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_strictpartialorder_i_tp,type,
% 2.62/1.67 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_stricttotalorder_i_tp,type,
% 2.62/1.67 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_If_i_tp,type,
% 2.62/1.67 c_If_i: $o > $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_exactly1of2_tp,type,
% 2.62/1.67 c_exactly1of2: $o > $o > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_exactly1of3_tp,type,
% 2.62/1.67 c_exactly1of3: $o > $o > $o > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_nIn_tp,type,
% 2.62/1.67 c_nIn: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_nSubq_tp,type,
% 2.62/1.67 c_nSubq: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_UPair_tp,type,
% 2.62/1.67 c_UPair: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Sing_tp,type,
% 2.62/1.67 c_Sing: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_binunion_tp,type,
% 2.62/1.67 c_binunion: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_SetAdjoin_tp,type,
% 2.62/1.67 c_SetAdjoin: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_famunion_tp,type,
% 2.62/1.67 c_famunion: $i > ( $i > $i ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Sep_tp,type,
% 2.62/1.67 c_Sep: $i > ( $i > $o ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_ReplSep_tp,type,
% 2.62/1.67 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_binintersect_tp,type,
% 2.62/1.67 c_binintersect: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_setminus_tp,type,
% 2.62/1.67 c_setminus: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_inj_tp,type,
% 2.62/1.67 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_bij_tp,type,
% 2.62/1.67 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_atleastp_tp,type,
% 2.62/1.67 c_atleastp: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_equip_tp,type,
% 2.62/1.67 c_equip: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_In_rec_poly_G_i_tp,type,
% 2.62/1.67 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_In_rec_poly_i_tp,type,
% 2.62/1.67 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_ordsucc_tp,type,
% 2.62/1.67 c_ordsucc: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_nat_p_tp,type,
% 2.62/1.67 c_nat_p: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_nat_primrec_tp,type,
% 2.62/1.67 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_add_nat_tp,type,
% 2.62/1.67 c_add_nat: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_mul_nat_tp,type,
% 2.62/1.67 c_mul_nat: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_ordinal_tp,type,
% 2.62/1.67 c_ordinal: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_V__tp,type,
% 2.62/1.67 c_V_: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Inj1_tp,type,
% 2.62/1.67 c_Inj1: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Inj0_tp,type,
% 2.62/1.67 c_Inj0: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Unj_tp,type,
% 2.62/1.67 c_Unj: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_combine_funcs_tp,type,
% 2.62/1.67 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_setsum_tp,type,
% 2.62/1.67 c_setsum: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_proj0_tp,type,
% 2.62/1.67 c_proj0: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_proj1_tp,type,
% 2.62/1.67 c_proj1: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_binrep_tp,type,
% 2.62/1.67 c_binrep: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_lam_tp,type,
% 2.62/1.67 c_lam: $i > ( $i > $i ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_setprod_tp,type,
% 2.62/1.67 c_setprod: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_ap_tp,type,
% 2.62/1.67 c_ap: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_setsum_p_tp,type,
% 2.62/1.67 c_setsum_p: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_tuple_p_tp,type,
% 2.62/1.67 c_tuple_p: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_Pi_tp,type,
% 2.62/1.67 c_Pi: $i > ( $i > $i ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_setexp_tp,type,
% 2.62/1.67 c_setexp: $i > $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_Sep2_tp,type,
% 2.62/1.67 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_set_of_pairs_tp,type,
% 2.62/1.67 c_set_of_pairs: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_lam2_tp,type,
% 2.62/1.67 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_PNoEq__tp,type,
% 2.62/1.67 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_PNoLt__tp,type,
% 2.62/1.67 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_PNoLt_tp,type,
% 2.62/1.67 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_PNoLe_tp,type,
% 2.62/1.67 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_PNo_downc_tp,type,
% 2.62/1.67 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_PNo_upc_tp,type,
% 2.62/1.67 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNoElts__tp,type,
% 2.62/1.67 c_SNoElts_: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNo__tp,type,
% 2.62/1.67 c_SNo_: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_PSNo_tp,type,
% 2.62/1.67 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNo_tp,type,
% 2.62/1.67 c_SNo: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNoLev_tp,type,
% 2.62/1.67 c_SNoLev: $i > $i ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNoEq__tp,type,
% 2.62/1.67 c_SNoEq_: $i > $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNoLt_tp,type,
% 2.62/1.67 c_SNoLt: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_SNoLe_tp,type,
% 2.62/1.67 c_SNoLe: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_binop_on_tp,type,
% 2.62/1.67 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_Loop_tp,type,
% 2.62/1.67 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_Loop_with_defs_tp,type,
% 2.62/1.67 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 ).
% 2.62/1.67
% 2.62/1.67 thf(c_Loop_with_defs_cex1_tp,type,
% 2.62/1.67 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 ).
% 2.62/1.67
% 2.62/1.67 thf(c_Loop_with_defs_cex2_tp,type,
% 2.62/1.67 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 ).
% 2.62/1.67
% 2.62/1.67 thf(c_combinator_tp,type,
% 2.62/1.67 c_combinator: $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_combinator_equiv_tp,type,
% 2.62/1.67 c_combinator_equiv: $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(c_equip_mod_tp,type,
% 2.62/1.67 c_equip_mod: $i > $i > $i > $o ).
% 2.62/1.67
% 2.62/1.67 thf(ax1,axiom,
% 2.62/1.67 ! [X0: $i > $o,X1: $i] :
% 2.62/1.67 ( ( X0 @ X1 )
% 2.62/1.67 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax2,axiom,
% 2.62/1.67 ! [X0: $o] :
% 2.62/1.67 ( ( c_not @ ( c_not @ X0 ) )
% 2.62/1.67 => X0 ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax3,axiom,
% 2.62/1.67 ! [X0: $o,X1: $o] :
% 2.62/1.67 ( ( c_iff @ X0 @ X1 )
% 2.62/1.67 => ( X0 = X1 ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax4,axiom,
% 2.62/1.67 ! [X0: $i,X1: $i] :
% 2.62/1.67 ( ( c_Subq @ X0 @ X1 )
% 2.62/1.67 => ( ( c_Subq @ X1 @ X0 )
% 2.62/1.67 => ( X0 = X1 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax5,axiom,
% 2.62/1.67 ( c_not
% 2.62/1.67 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax6,axiom,
% 2.62/1.67 ! [X0: $i,X1: $i] :
% 2.62/1.67 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.62/1.67 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax7,axiom,
% 2.62/1.67 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax8,axiom,
% 2.62/1.67 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.62/1.67 ( c_iff
% 2.62/1.67 @ ( c_In @ X2
% 2.62/1.67 @ ( c_Repl @ X0
% 2.62/1.67 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.62/1.67 @ ? [X3: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X3 @ X0 )
% 2.62/1.67 @ ( X2
% 2.62/1.67 = ( X1 @ X3 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax9,axiom,
% 2.62/1.67 ! [X0: $i > $o] :
% 2.62/1.67 ( ! [X1: $i] :
% 2.62/1.67 ( ( X0 @ X1 )
% 2.62/1.67 => ! [X2: $i] :
% 2.62/1.67 ( ( c_In @ X2 @ X1 )
% 2.62/1.67 => ( X0 @ X2 ) ) )
% 2.62/1.67 => ( ( X0 @ c_Empty )
% 2.62/1.67 => ( ! [X1: $i] :
% 2.62/1.67 ( ( X0 @ X1 )
% 2.62/1.67 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.62/1.67 => ( ! [X1: $i] :
% 2.62/1.67 ( ( X0 @ X1 )
% 2.62/1.67 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.62/1.67 => ( ! [X1: $i] :
% 2.62/1.67 ( ( X0 @ X1 )
% 2.62/1.67 => ! [X2: $i > $i] :
% 2.62/1.67 ( ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X1 )
% 2.62/1.67 => ( X0 @ ( X2 @ X3 ) ) )
% 2.62/1.67 => ( X0
% 2.62/1.67 @ ( c_Repl @ X1
% 2.62/1.67 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.62/1.67 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax10,axiom,
% 2.62/1.67 ! [X0: $i > $o] :
% 2.62/1.67 ( ! [X1: $i] :
% 2.62/1.67 ( ! [X2: $i] :
% 2.62/1.67 ( ( c_In @ X2 @ X1 )
% 2.62/1.67 => ( X0 @ X2 ) )
% 2.62/1.67 => ( X0 @ X1 ) )
% 2.62/1.67 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax11,axiom,
% 2.62/1.67 ( c_False
% 2.62/1.67 = ( ! [X0: $o] : X0 ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax12,axiom,
% 2.62/1.67 ( c_True
% 2.62/1.67 = ( ! [X0: $o] :
% 2.62/1.67 ( X0
% 2.62/1.67 => X0 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax13,axiom,
% 2.62/1.67 ( c_not
% 2.62/1.67 = ( ^ [X0: $o] :
% 2.62/1.67 ( X0
% 2.62/1.67 => c_False ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax14,axiom,
% 2.62/1.67 ( c_and
% 2.62/1.67 = ( ^ [X0: $o,X1: $o] :
% 2.62/1.67 ! [X2: $o] :
% 2.62/1.67 ( ( X0
% 2.62/1.67 => ( X1
% 2.62/1.67 => X2 ) )
% 2.62/1.67 => X2 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax15,axiom,
% 2.62/1.67 ( c_or
% 2.62/1.67 = ( ^ [X0: $o,X1: $o] :
% 2.62/1.67 ! [X2: $o] :
% 2.62/1.67 ( ( X0
% 2.62/1.67 => X2 )
% 2.62/1.67 => ( ( X1
% 2.62/1.67 => X2 )
% 2.62/1.67 => X2 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax16,axiom,
% 2.62/1.67 ( c_iff
% 2.62/1.67 = ( ^ [X0: $o,X1: $o] :
% 2.62/1.67 ( c_and
% 2.62/1.67 @ ( X0
% 2.62/1.67 => X1 )
% 2.62/1.67 @ ( X1
% 2.62/1.67 => X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax17,axiom,
% 2.62/1.67 ( c_Subq
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ! [X2: $i] :
% 2.62/1.67 ( ( c_In @ X2 @ X0 )
% 2.62/1.67 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax18,axiom,
% 2.62/1.67 ( c_TransSet
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ! [X1: $i] :
% 2.62/1.67 ( ( c_In @ X1 @ X0 )
% 2.62/1.67 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax19,axiom,
% 2.62/1.67 ( c_atleast2
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax20,axiom,
% 2.62/1.67 ( c_atleast3
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax21,axiom,
% 2.62/1.67 ( c_atleast4
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax22,axiom,
% 2.62/1.67 ( c_atleast5
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax23,axiom,
% 2.62/1.67 ( c_atleast6
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax24,axiom,
% 2.62/1.67 ( c_exactly2
% 2.62/1.67 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax25,axiom,
% 2.62/1.67 ( c_exactly3
% 2.62/1.67 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax26,axiom,
% 2.62/1.67 ( c_exactly4
% 2.62/1.67 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax27,axiom,
% 2.62/1.67 ( c_exactly5
% 2.62/1.67 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax28,axiom,
% 2.62/1.67 ( c_exu_i
% 2.62/1.67 = ( ^ [X0: $i > $o] :
% 2.62/1.67 ( c_and
% 2.62/1.67 @ ? [X1: $i] : ( X0 @ X1 )
% 2.62/1.67 @ ! [X1: $i,X2: $i] :
% 2.62/1.67 ( ( X0 @ X1 )
% 2.62/1.67 => ( ( X0 @ X2 )
% 2.62/1.67 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax29,axiom,
% 2.62/1.67 ( c_reflexive_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax30,axiom,
% 2.62/1.67 ( c_irreflexive_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax31,axiom,
% 2.62/1.67 ( c_symmetric_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i,X2: $i] :
% 2.62/1.67 ( ( X0 @ X1 @ X2 )
% 2.62/1.67 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax32,axiom,
% 2.62/1.67 ( c_antisymmetric_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i,X2: $i] :
% 2.62/1.67 ( ( X0 @ X1 @ X2 )
% 2.62/1.67 => ( ( X0 @ X2 @ X1 )
% 2.62/1.67 => ( X1 = X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax33,axiom,
% 2.62/1.67 ( c_transitive_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i,X2: $i,X3: $i] :
% 2.62/1.67 ( ( X0 @ X1 @ X2 )
% 2.62/1.67 => ( ( X0 @ X2 @ X3 )
% 2.62/1.67 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax34,axiom,
% 2.62/1.67 ( c_eqreln_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax35,axiom,
% 2.62/1.67 ( c_per_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax36,axiom,
% 2.62/1.67 ( c_linear_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax37,axiom,
% 2.62/1.67 ( c_trichotomous_or_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] :
% 2.62/1.67 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax38,axiom,
% 2.62/1.67 ( c_partialorder_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax39,axiom,
% 2.62/1.67 ( c_totalorder_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax40,axiom,
% 2.62/1.67 ( c_strictpartialorder_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax41,axiom,
% 2.62/1.67 ( c_stricttotalorder_i
% 2.62/1.67 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax42,axiom,
% 2.62/1.67 ( c_If_i
% 2.62/1.67 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.62/1.67 ( c_Eps_i
% 2.62/1.67 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax43,axiom,
% 2.62/1.67 ( c_exactly1of2
% 2.62/1.67 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax44,axiom,
% 2.62/1.67 ( c_exactly1of3
% 2.62/1.67 = ( ^ [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 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax45,axiom,
% 2.62/1.67 ( c_nIn
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax46,axiom,
% 2.62/1.67 ( c_nSubq
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax47,axiom,
% 2.62/1.67 ( c_UPair
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.62/1.67 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax48,axiom,
% 2.62/1.67 ( c_Sing
% 2.62/1.67 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax49,axiom,
% 2.62/1.67 ( c_binunion
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax50,axiom,
% 2.62/1.67 ( c_SetAdjoin
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax51,axiom,
% 2.62/1.67 ( c_famunion
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i] :
% 2.62/1.67 ( c_Union
% 2.62/1.67 @ ( c_Repl @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax52,axiom,
% 2.62/1.67 ( c_Sep
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $o] :
% 2.62/1.67 ( c_If_i
% 2.62/1.67 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.62/1.67 @ ( c_Repl @ X0
% 2.62/1.67 @ ^ [X2: $i] :
% 2.62/1.67 ( ^ [X3: $i] :
% 2.62/1.67 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.62/1.67 @ ( c_Eps_i
% 2.62/1.67 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.62/1.67 @ X2 ) )
% 2.62/1.67 @ c_Empty ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax53,axiom,
% 2.62/1.67 ( c_ReplSep
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.62/1.67 ( c_Repl
% 2.62/1.67 @ ( c_Sep @ X0
% 2.62/1.67 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.62/1.67 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax54,axiom,
% 2.62/1.67 ( c_binintersect
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_Sep @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax55,axiom,
% 2.62/1.67 ( c_setminus
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_Sep @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax56,axiom,
% 2.62/1.67 ( c_inj
% 2.62/1.67 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.62/1.67 ( c_and
% 2.62/1.67 @ ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X0 )
% 2.62/1.67 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.62/1.67 @ ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X0 )
% 2.62/1.67 => ! [X4: $i] :
% 2.62/1.67 ( ( c_In @ X4 @ X0 )
% 2.62/1.67 => ( ( ( X2 @ X3 )
% 2.62/1.67 = ( X2 @ X4 ) )
% 2.62/1.67 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax57,axiom,
% 2.62/1.67 ( c_bij
% 2.62/1.67 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.62/1.67 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.62/1.67 @ ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X1 )
% 2.62/1.67 => ? [X4: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X4 @ X0 )
% 2.62/1.67 @ ( ( X2 @ X4 )
% 2.62/1.67 = X3 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax58,axiom,
% 2.62/1.67 ( c_atleastp
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax59,axiom,
% 2.62/1.67 ( c_equip
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax60,axiom,
% 2.62/1.67 ( c_In_rec_poly_G_i
% 2.62/1.67 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.62/1.67 ! [X3: $i > $i > $o] :
% 2.62/1.67 ( ! [X4: $i,X5: $i > $i] :
% 2.62/1.67 ( ! [X6: $i] :
% 2.62/1.67 ( ( c_In @ X6 @ X4 )
% 2.62/1.67 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.62/1.67 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.62/1.67 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax61,axiom,
% 2.62/1.67 ( c_In_rec_poly_i
% 2.62/1.67 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.62/1.67 ( c_Eps_i
% 2.62/1.67 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax62,axiom,
% 2.62/1.67 ( c_ordsucc
% 2.62/1.67 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax63,axiom,
% 2.62/1.67 ( c_nat_p
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ! [X1: $i > $o] :
% 2.62/1.67 ( ( X1 @ c_Empty )
% 2.62/1.67 => ( ! [X2: $i] :
% 2.62/1.67 ( ( X1 @ X2 )
% 2.62/1.67 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.62/1.67 => ( X1 @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax64,axiom,
% 2.62/1.67 ( c_nat_primrec
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.62/1.67 ( c_In_rec_poly_i
% 2.62/1.67 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax65,axiom,
% 2.62/1.67 ( c_add_nat
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_nat_primrec @ X0
% 2.62/1.67 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.62/1.67 @ X1 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax66,axiom,
% 2.62/1.67 ( c_mul_nat
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_nat_primrec @ c_Empty
% 2.62/1.67 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.62/1.67 @ X1 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax67,axiom,
% 2.62/1.67 ( c_ordinal
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( c_and @ ( c_TransSet @ X0 )
% 2.62/1.67 @ ! [X1: $i] :
% 2.62/1.67 ( ( c_In @ X1 @ X0 )
% 2.62/1.67 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax68,axiom,
% 2.62/1.67 ( c_V_
% 2.62/1.67 = ( c_In_rec_poly_i
% 2.62/1.67 @ ^ [X0: $i,X1: $i > $i] :
% 2.62/1.67 ( c_famunion @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax69,axiom,
% 2.62/1.67 ( c_Inj1
% 2.62/1.67 = ( c_In_rec_poly_i
% 2.62/1.67 @ ^ [X0: $i,X1: $i > $i] :
% 2.62/1.67 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.62/1.67 @ ( c_Repl @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax70,axiom,
% 2.62/1.67 ( c_Inj0
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( c_Repl @ X0
% 2.62/1.67 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax71,axiom,
% 2.62/1.67 ( c_Unj
% 2.62/1.67 = ( c_In_rec_poly_i
% 2.62/1.67 @ ^ [X0: $i,X1: $i > $i] :
% 2.62/1.67 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.62/1.67 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax72,axiom,
% 2.62/1.67 ( c_combine_funcs
% 2.62/1.67 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.62/1.67 ( c_If_i
% 2.62/1.67 @ ( X4
% 2.62/1.67 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.62/1.67 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.62/1.67 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax73,axiom,
% 2.62/1.67 ( c_setsum
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_binunion
% 2.62/1.67 @ ( c_Repl @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.62/1.67 @ ( c_Repl @ X1
% 2.62/1.67 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax74,axiom,
% 2.62/1.67 ( c_proj0
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( c_ReplSep @ X0
% 2.62/1.67 @ ^ [X1: $i] :
% 2.62/1.67 ? [X2: $i] :
% 2.62/1.67 ( ( c_Inj0 @ X2 )
% 2.62/1.67 = X1 )
% 2.62/1.67 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax75,axiom,
% 2.62/1.67 ( c_proj1
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( c_ReplSep @ X0
% 2.62/1.67 @ ^ [X1: $i] :
% 2.62/1.67 ? [X2: $i] :
% 2.62/1.67 ( ( c_Inj1 @ X2 )
% 2.62/1.67 = X1 )
% 2.62/1.67 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax76,axiom,
% 2.62/1.67 ( c_binrep
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax77,axiom,
% 2.62/1.67 ( c_lam
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i] :
% 2.62/1.67 ( c_famunion @ X0
% 2.62/1.67 @ ^ [X2: $i] :
% 2.62/1.67 ( c_Repl @ ( X1 @ X2 )
% 2.62/1.67 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax78,axiom,
% 2.62/1.67 ( c_setprod
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_lam @ X0
% 2.62/1.67 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax79,axiom,
% 2.62/1.67 ( c_ap
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_ReplSep @ X0
% 2.62/1.67 @ ^ [X2: $i] :
% 2.62/1.67 ? [X3: $i] :
% 2.62/1.67 ( X2
% 2.62/1.67 = ( c_setsum @ X1 @ X3 ) )
% 2.62/1.67 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax80,axiom,
% 2.62/1.67 ( c_setsum_p
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.62/1.67 = X0 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax81,axiom,
% 2.62/1.67 ( c_tuple_p
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ! [X2: $i] :
% 2.62/1.67 ( ( c_In @ X2 @ X1 )
% 2.62/1.67 => ? [X3: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X3 @ X0 )
% 2.62/1.67 @ ? [X4: $i] :
% 2.62/1.67 ( X2
% 2.62/1.67 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax82,axiom,
% 2.62/1.67 ( c_Pi
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i] :
% 2.62/1.67 ( c_Sep
% 2.62/1.67 @ ( c_Power
% 2.62/1.67 @ ( c_lam @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.62/1.67 @ ^ [X2: $i] :
% 2.62/1.67 ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X0 )
% 2.62/1.67 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax83,axiom,
% 2.62/1.67 ( c_setexp
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_Pi @ X1
% 2.62/1.67 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax84,axiom,
% 2.62/1.67 ( c_Sep2
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.62/1.67 ( c_Sep
% 2.62/1.67 @ ( c_lam @ X0
% 2.62/1.67 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.62/1.67 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax85,axiom,
% 2.62/1.67 ( c_set_of_pairs
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ! [X1: $i] :
% 2.62/1.67 ( ( c_In @ X1 @ X0 )
% 2.62/1.67 => ? [X2: $i,X3: $i] :
% 2.62/1.67 ( X1
% 2.62/1.67 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.62/1.67 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax86,axiom,
% 2.62/1.67 ( c_lam2
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.62/1.67 ( c_lam @ X0
% 2.62/1.67 @ ^ [X3: $i] :
% 2.62/1.67 ( c_lam @ ( X1 @ X3 )
% 2.62/1.67 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax87,axiom,
% 2.62/1.67 ( c_PNoEq_
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.62/1.67 ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X0 )
% 2.62/1.67 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax88,axiom,
% 2.62/1.67 ( c_PNoLt_
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.62/1.67 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax89,axiom,
% 2.62/1.67 ( c_PNoLt
% 2.62/1.67 = ( ^ [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 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax90,axiom,
% 2.62/1.67 ( c_PNoLe
% 2.62/1.67 = ( ^ [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 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax91,axiom,
% 2.62/1.67 ( c_PNo_downc
% 2.62/1.67 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.62/1.67 ? [X3: $i] :
% 2.62/1.67 ( c_and @ ( c_ordinal @ X3 )
% 2.62/1.67 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax92,axiom,
% 2.62/1.67 ( c_PNo_upc
% 2.62/1.67 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.62/1.67 ? [X3: $i] :
% 2.62/1.67 ( c_and @ ( c_ordinal @ X3 )
% 2.62/1.67 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax93,axiom,
% 2.62/1.67 ( c_SNoElts_
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( c_binunion @ X0
% 2.62/1.67 @ ( c_Repl @ X0
% 2.62/1.67 @ ^ [X1: $i] :
% 2.62/1.67 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.62/1.67 @ X1 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax94,axiom,
% 2.62/1.67 ( c_SNo_
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.62/1.67 @ ! [X2: $i] :
% 2.62/1.67 ( ( c_In @ X2 @ X0 )
% 2.62/1.67 => ( c_exactly1of2
% 2.62/1.67 @ ( c_In
% 2.62/1.67 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.62/1.67 @ X2 )
% 2.62/1.67 @ X1 )
% 2.62/1.67 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax95,axiom,
% 2.62/1.67 ( c_PSNo
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $o] :
% 2.62/1.67 ( c_binunion
% 2.62/1.67 @ ( c_Sep @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.62/1.67 @ ( c_ReplSep @ X0
% 2.62/1.67 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.62/1.67 @ ^ [X2: $i] :
% 2.62/1.67 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.62/1.67 @ X2 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax96,axiom,
% 2.62/1.67 ( c_SNo
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax97,axiom,
% 2.62/1.67 ( c_SNoLev
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ( c_Eps_i
% 2.62/1.67 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax98,axiom,
% 2.62/1.67 ( c_SNoEq_
% 2.62/1.67 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.62/1.67 ( c_PNoEq_ @ X0
% 2.62/1.67 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.62/1.67 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax99,axiom,
% 2.62/1.67 ( c_SNoLt
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.62/1.67 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.62/1.67 @ ( c_SNoLev @ X1 )
% 2.62/1.67 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax100,axiom,
% 2.62/1.67 ( c_SNoLe
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.62/1.67 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.62/1.67 @ ( c_SNoLev @ X1 )
% 2.62/1.67 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax101,axiom,
% 2.62/1.67 ( c_binop_on
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.62/1.67 ! [X2: $i] :
% 2.62/1.67 ( ( c_In @ X2 @ X0 )
% 2.62/1.67 => ! [X3: $i] :
% 2.62/1.67 ( ( c_In @ X3 @ X0 )
% 2.62/1.67 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax102,axiom,
% 2.62/1.67 ( c_Loop
% 2.62/1.67 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.62/1.67 ( c_and
% 2.62/1.67 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.62/1.67 @ ! [X5: $i] :
% 2.62/1.67 ( ( c_In @ X5 @ X0 )
% 2.62/1.67 => ( c_and
% 2.62/1.67 @ ( ( X1 @ X4 @ X5 )
% 2.62/1.67 = X5 )
% 2.62/1.67 @ ( ( X1 @ X5 @ X4 )
% 2.62/1.67 = X5 ) ) ) )
% 2.62/1.67 @ ! [X5: $i] :
% 2.62/1.67 ( ( c_In @ X5 @ X0 )
% 2.62/1.67 => ! [X6: $i] :
% 2.62/1.67 ( ( c_In @ X6 @ X0 )
% 2.62/1.67 => ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.62/1.67 = X6 )
% 2.62/1.67 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.62/1.67 = X6 ) )
% 2.62/1.67 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.62/1.67 = X5 ) )
% 2.62/1.67 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.62/1.67 = X5 ) ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax103,axiom,
% 2.62/1.67 ( c_Loop_with_defs
% 2.62/1.67 = ( ^ [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] :
% 2.62/1.67 ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.62/1.67 @ ! [X14: $i] :
% 2.62/1.67 ( ( c_In @ X14 @ X0 )
% 2.62/1.67 => ! [X15: $i] :
% 2.62/1.67 ( ( c_In @ X15 @ X0 )
% 2.62/1.67 => ( ( X5 @ X14 @ X15 )
% 2.62/1.67 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.62/1.67 @ ! [X14: $i] :
% 2.62/1.67 ( ( c_In @ X14 @ X0 )
% 2.62/1.67 => ! [X15: $i] :
% 2.62/1.67 ( ( c_In @ X15 @ X0 )
% 2.62/1.67 => ! [X16: $i] :
% 2.62/1.67 ( ( c_In @ X16 @ X0 )
% 2.62/1.67 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.62/1.67 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.62/1.67 @ ! [X14: $i] :
% 2.62/1.67 ( ( c_In @ X14 @ X0 )
% 2.62/1.67 => ! [X15: $i] :
% 2.62/1.67 ( ( c_In @ X15 @ X0 )
% 2.62/1.67 => ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( c_and
% 2.62/1.67 @ ( ( X7 @ X14 @ X15 )
% 2.62/1.67 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.62/1.67 @ ( ( X10 @ X14 @ X15 )
% 2.62/1.67 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.62/1.67 @ ( ( X11 @ X14 @ X15 )
% 2.62/1.67 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.62/1.67 @ ( ( X12 @ X14 @ X15 )
% 2.62/1.67 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.62/1.67 @ ( ( X13 @ X14 @ X15 )
% 2.62/1.67 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.62/1.67 @ ! [X14: $i] :
% 2.62/1.67 ( ( c_In @ X14 @ X0 )
% 2.62/1.67 => ! [X15: $i] :
% 2.62/1.67 ( ( c_In @ X15 @ X0 )
% 2.62/1.67 => ! [X16: $i] :
% 2.62/1.67 ( ( c_In @ X16 @ X0 )
% 2.62/1.67 => ( c_and
% 2.62/1.67 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.62/1.67 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.62/1.67 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.62/1.67 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax104,axiom,
% 2.62/1.67 ( c_Loop_with_defs_cex1
% 2.62/1.67 = ( ^ [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] :
% 2.62/1.67 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.62/1.67 @ ? [X14: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X14 @ X0 )
% 2.62/1.67 @ ? [X15: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X15 @ X0 )
% 2.62/1.67 @ ? [X16: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X16 @ X0 )
% 2.62/1.67 @ ? [X17: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X17 @ X0 )
% 2.62/1.67 @ ( c_not
% 2.62/1.67 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.62/1.67 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax105,axiom,
% 2.62/1.67 ( c_Loop_with_defs_cex2
% 2.62/1.67 = ( ^ [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] :
% 2.62/1.67 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.62/1.67 @ ? [X14: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X14 @ X0 )
% 2.62/1.67 @ ? [X15: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X15 @ X0 )
% 2.62/1.67 @ ? [X16: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X16 @ X0 )
% 2.62/1.67 @ ? [X17: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X17 @ X0 )
% 2.62/1.67 @ ? [X18: $i] :
% 2.62/1.67 ( c_and @ ( c_In @ X18 @ X0 )
% 2.62/1.67 @ ( c_not
% 2.62/1.67 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.62/1.67 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax106,axiom,
% 2.62/1.67 ( c_combinator
% 2.62/1.67 = ( ^ [X0: $i] :
% 2.62/1.67 ! [X1: $i > $o] :
% 2.62/1.67 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.62/1.67 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.62/1.67 => ( ! [X2: $i,X3: $i] :
% 2.62/1.67 ( ( X1 @ X2 )
% 2.62/1.67 => ( ( X1 @ X3 )
% 2.62/1.67 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.62/1.67 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax107,axiom,
% 2.62/1.67 ( c_combinator_equiv
% 2.62/1.67 = ( ^ [X0: $i,X1: $i] :
% 2.62/1.67 ! [X2: $i > $i > $o] :
% 2.62/1.67 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.62/1.67 ( ( c_per_i @ X2 )
% 2.62/1.67 => ( ! [X6: $i] :
% 2.62/1.67 ( ( c_combinator @ X6 )
% 2.62/1.67 => ( X2 @ X6 @ X6 ) )
% 2.62/1.67 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.62/1.67 ( ( c_combinator @ X6 )
% 2.62/1.67 => ( ( c_combinator @ X7 )
% 2.62/1.67 => ( ( c_combinator @ X8 )
% 2.62/1.67 => ( ( c_combinator @ X9 )
% 2.62/1.67 => ( ( X2 @ X6 @ X8 )
% 2.62/1.67 => ( ( X2 @ X7 @ X9 )
% 2.62/1.67 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.62/1.67 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.62/1.67 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.62/1.67 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.62/1.67 @ ( c_Inj0 @ c_Empty )
% 2.62/1.67 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.62/1.67 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(ax108,axiom,
% 2.62/1.67 ( c_equip_mod
% 2.62/1.67 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.62/1.67 ? [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 ) ) ) ) ) ).
% 2.62/1.67
% 2.62/1.67 thf(conj,conjecture,
% 2.62/1.67 ( c_not
% 2.62/1.67 @ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.62/1.67 ( ( c_and
% 2.62/1.67 @ ! [X10: $i] :
% 2.62/1.67 ( ( ( X4 @ X9 )
% 2.62/1.67 = X10 )
% 2.62/1.67 => ( ( c_and @ ( X2 @ X10 )
% 2.62/1.67 @ ( ( X7 = X5 )
% 2.62/1.67 => ( c_and
% 2.62/1.67 @ ! [X11: $i] : ( X9 = X8 )
% 2.62/1.67 @ ? [X11: $i] : ( X3 @ X10 ) ) ) )
% 2.62/1.67 => ? [X11: $i] : ( X7 = X7 ) ) )
% 2.62/1.67 @ ( c_not @ ( X3 @ ( X4 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) ) ) )
% 2.62/1.67 => ( X6 = X9 ) ) ) ).
% 2.62/1.67 ------------------------
% 2.74/1.70 % (2061)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_1961 for (2999ds/4Mi)
% 2.74/1.70 % (2060)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/183Mi)
% 2.74/1.70 % (2062)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_1961 for (2999ds/27Mi)
% 2.74/1.70 % (2063)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/2Mi)
% 2.74/1.70 % (2066)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/18Mi)
% 2.74/1.70 % (2064)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_1961 for (2999ds/2Mi)
% 2.74/1.70 % (2065)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_1961 for (2999ds/275Mi)
% 2.74/1.70 % (2063)Instruction limit reached!
% 2.74/1.70 % (2063)------------------------------
% 2.74/1.70 % (2063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.70 % (2063)Termination reason: Unknown
% 2.74/1.70 % (2063)Termination phase: shuffling
% 2.74/1.70 % (2064)Instruction limit reached!
% 2.74/1.70 % (2064)------------------------------
% 2.74/1.70 % (2064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.70 % (2064)Termination reason: Unknown
% 2.74/1.70 % (2064)Termination phase: shuffling
% 2.74/1.70
% 2.74/1.70 % (2064)Memory used [KB]: 1151
% 2.74/1.70 % (2064)Time elapsed: 0.003 s
% 2.74/1.70 % (2064)Instructions burned: 2 (million)
% 2.74/1.70 % (2064)------------------------------
% 2.74/1.70 % (2064)------------------------------
% 2.74/1.70
% 2.74/1.70 % (2063)Memory used [KB]: 1151
% 2.74/1.70 % (2063)Time elapsed: 0.003 s
% 2.74/1.70 % (2063)Instructions burned: 3 (million)
% 2.74/1.70 % (2063)------------------------------
% 2.74/1.70 % (2063)------------------------------
% 2.74/1.70 % (2061)Instruction limit reached!
% 2.74/1.70 % (2061)------------------------------
% 2.74/1.70 % (2061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.70 % (2061)Termination reason: Unknown
% 2.74/1.70 % (2061)Termination phase: shuffling
% 2.74/1.70
% 2.74/1.70 % (2061)Memory used [KB]: 1279
% 2.74/1.70 % (2061)Time elapsed: 0.004 s
% 2.74/1.70 % (2061)Instructions burned: 4 (million)
% 2.74/1.70 % (2061)------------------------------
% 2.74/1.70 % (2061)------------------------------
% 2.74/1.71 % (2066)Instruction limit reached!
% 2.74/1.71 % (2066)------------------------------
% 2.74/1.71 % (2066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.71 % (2066)Termination reason: Unknown
% 2.74/1.71 % (2066)Termination phase: shuffling
% 2.74/1.71
% 2.74/1.71 % (2066)Memory used [KB]: 1535
% 2.74/1.71 % (2066)Time elapsed: 0.010 s
% 2.74/1.71 % (2066)Instructions burned: 18 (million)
% 2.74/1.71 % (2066)------------------------------
% 2.74/1.71 % (2066)------------------------------
% 2.74/1.71 % (2062)Instruction limit reached!
% 2.74/1.71 % (2062)------------------------------
% 2.74/1.71 % (2062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.71 % (2062)Termination reason: Unknown
% 2.74/1.71 % (2062)Termination phase: Property scanning
% 2.74/1.71
% 2.74/1.71 % (2062)Memory used [KB]: 1535
% 2.74/1.71 % (2062)Time elapsed: 0.014 s
% 2.74/1.71 % (2062)Instructions burned: 27 (million)
% 2.74/1.71 % (2062)------------------------------
% 2.74/1.71 % (2062)------------------------------
% 2.74/1.72 % (2065)Refutation not found, incomplete strategy
% 2.74/1.72 % (2065)------------------------------
% 2.74/1.72 % (2065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.72 % (2065)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.72
% 2.74/1.72
% 2.74/1.72 % (2065)Memory used [KB]: 6012
% 2.74/1.72 % (2065)Time elapsed: 0.017 s
% 2.74/1.72 % (2065)Instructions burned: 34 (million)
% 2.74/1.72 % (2065)------------------------------
% 2.74/1.72 % (2065)------------------------------
% 2.74/1.72 % (2067)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/3Mi)
% 2.74/1.72 % (2068)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_1961 for (2999ds/37Mi)
% 2.74/1.72 % (2069)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_1961 for (2999ds/15Mi)
% 2.74/1.72 % (2067)Instruction limit reached!
% 2.74/1.72 % (2067)------------------------------
% 2.74/1.72 % (2067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.72 % (2067)Termination reason: Unknown
% 2.74/1.72 % (2067)Termination phase: shuffling
% 2.74/1.72
% 2.74/1.72 % (2067)Memory used [KB]: 1279
% 2.74/1.72 % (2067)Time elapsed: 0.003 s
% 2.74/1.72 % (2067)Instructions burned: 3 (million)
% 2.74/1.72 % (2067)------------------------------
% 2.74/1.72 % (2067)------------------------------
% 2.74/1.73 % (2070)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_1961 for (2999ds/3Mi)
% 2.74/1.73 % (2069)Instruction limit reached!
% 2.74/1.73 % (2069)------------------------------
% 2.74/1.73 % (2069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.73 % (2069)Termination reason: Unknown
% 2.74/1.73 % (2069)Termination phase: shuffling
% 2.74/1.73
% 2.74/1.73 % (2069)Memory used [KB]: 1535
% 2.74/1.73 % (2069)Time elapsed: 0.009 s
% 2.74/1.73 % (2069)Instructions burned: 16 (million)
% 2.74/1.73 % (2069)------------------------------
% 2.74/1.73 % (2069)------------------------------
% 2.74/1.73 % (2070)Instruction limit reached!
% 2.74/1.73 % (2070)------------------------------
% 2.74/1.73 % (2070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.73 % (2070)Termination reason: Unknown
% 2.74/1.73 % (2070)Termination phase: shuffling
% 2.74/1.73
% 2.74/1.73 % (2070)Memory used [KB]: 1151
% 2.74/1.73 % (2070)Time elapsed: 0.003 s
% 2.74/1.73 % (2070)Instructions burned: 3 (million)
% 2.74/1.73 % (2070)------------------------------
% 2.74/1.73 % (2070)------------------------------
% 2.74/1.73 % (2071)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_1961 for (2999ds/1041Mi)
% 2.74/1.73 % (2072)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/7Mi)
% 2.74/1.73 % (2068)Instruction limit reached!
% 2.74/1.73 % (2068)------------------------------
% 2.74/1.73 % (2068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.73 % (2068)Termination reason: Unknown
% 2.74/1.73 % (2068)Termination phase: Property scanning
% 2.74/1.73
% 2.74/1.73 % (2068)Memory used [KB]: 1535
% 2.74/1.73 % (2068)Time elapsed: 0.018 s
% 2.74/1.73 % (2068)Instructions burned: 37 (million)
% 2.74/1.73 % (2068)------------------------------
% 2.74/1.73 % (2068)------------------------------
% 2.74/1.74 % (2073)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/16Mi)
% 2.74/1.74 % (2072)Instruction limit reached!
% 2.74/1.74 % (2072)------------------------------
% 2.74/1.74 % (2072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (2072)Termination reason: Unknown
% 2.74/1.74 % (2072)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (2072)Memory used [KB]: 1279
% 2.74/1.74 % (2072)Time elapsed: 0.005 s
% 2.74/1.74 % (2072)Instructions burned: 8 (million)
% 2.74/1.74 % (2072)------------------------------
% 2.74/1.74 % (2072)------------------------------
% 2.74/1.74 % (2074)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_1961 for (2999ds/3Mi)
% 2.74/1.74 % (2075)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_1961 for (2999ds/3Mi)
% 2.74/1.74 % (2073)Instruction limit reached!
% 2.74/1.74 % (2073)------------------------------
% 2.74/1.74 % (2073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (2073)Termination reason: Unknown
% 2.74/1.74 % (2073)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (2073)Memory used [KB]: 1407
% 2.74/1.74 % (2073)Time elapsed: 0.009 s
% 2.74/1.74 % (2073)Instructions burned: 16 (million)
% 2.74/1.74 % (2073)------------------------------
% 2.74/1.74 % (2073)------------------------------
% 2.74/1.74 % (2074)Instruction limit reached!
% 2.74/1.74 % (2074)------------------------------
% 2.74/1.74 % (2074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (2074)Termination reason: Unknown
% 2.74/1.74 % (2074)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (2074)Memory used [KB]: 1151
% 2.74/1.74 % (2074)Time elapsed: 0.003 s
% 2.74/1.74 % (2074)Instructions burned: 3 (million)
% 2.74/1.74 % (2074)------------------------------
% 2.74/1.74 % (2074)------------------------------
% 2.74/1.74 % (2075)Instruction limit reached!
% 2.74/1.74 % (2075)------------------------------
% 2.74/1.74 % (2075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.74 % (2075)Termination reason: Unknown
% 2.74/1.74 % (2075)Termination phase: shuffling
% 2.74/1.74
% 2.74/1.74 % (2075)Memory used [KB]: 1279
% 2.74/1.74 % (2075)Time elapsed: 0.003 s
% 2.74/1.74 % (2075)Instructions burned: 3 (million)
% 2.74/1.74 % (2075)------------------------------
% 2.74/1.74 % (2075)------------------------------
% 2.74/1.75 % (2076)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/7Mi)
% 2.74/1.75 % (2077)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/3Mi)
% 2.74/1.75 % (2076)Instruction limit reached!
% 2.74/1.75 % (2076)------------------------------
% 2.74/1.75 % (2076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (2076)Termination reason: Unknown
% 2.74/1.75 % (2076)Termination phase: shuffling
% 2.74/1.75
% 2.74/1.75 % (2076)Memory used [KB]: 1279
% 2.74/1.75 % (2076)Time elapsed: 0.005 s
% 2.74/1.75 % (2076)Instructions burned: 7 (million)
% 2.74/1.75 % (2076)------------------------------
% 2.74/1.75 % (2076)------------------------------
% 2.74/1.75 % (2077)Instruction limit reached!
% 2.74/1.75 % (2077)------------------------------
% 2.74/1.75 % (2077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (2077)Termination reason: Unknown
% 2.74/1.75 % (2077)Termination phase: shuffling
% 2.74/1.75
% 2.74/1.75 % (2077)Memory used [KB]: 1279
% 2.74/1.75 % (2077)Time elapsed: 0.003 s
% 2.74/1.75 % (2077)Instructions burned: 3 (million)
% 2.74/1.75 % (2077)------------------------------
% 2.74/1.75 % (2077)------------------------------
% 2.74/1.76 % (2078)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/4Mi)
% 2.74/1.76 % (2079)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/18Mi)
% 2.74/1.76 % (2080)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/710Mi)
% 2.74/1.76 % (2078)Instruction limit reached!
% 2.74/1.76 % (2078)------------------------------
% 2.74/1.76 % (2078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.76 % (2078)Termination reason: Unknown
% 2.74/1.76 % (2078)Termination phase: shuffling
% 2.74/1.76
% 2.74/1.76 % (2078)Memory used [KB]: 1279
% 2.74/1.76 % (2078)Time elapsed: 0.004 s
% 2.74/1.76 % (2078)Instructions burned: 6 (million)
% 2.74/1.76 % (2078)------------------------------
% 2.74/1.76 % (2078)------------------------------
% 2.74/1.77 % (2079)Instruction limit reached!
% 2.74/1.77 % (2079)------------------------------
% 2.74/1.77 % (2079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.77 % (2079)Termination reason: Unknown
% 2.74/1.77 % (2079)Termination phase: Property scanning
% 2.74/1.77
% 2.74/1.77 % (2079)Memory used [KB]: 1535
% 2.74/1.77 % (2079)Time elapsed: 0.010 s
% 2.74/1.77 % (2079)Instructions burned: 18 (million)
% 2.74/1.77 % (2079)------------------------------
% 2.74/1.77 % (2079)------------------------------
% 2.74/1.77 % (2081)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/6Mi)
% 2.74/1.77 % (2082)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_1961 for (2999ds/902Mi)
% 2.74/1.77 % (2081)Instruction limit reached!
% 2.74/1.77 % (2081)------------------------------
% 2.74/1.77 % (2081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.77 % (2081)Termination reason: Unknown
% 2.74/1.77 % (2081)Termination phase: shuffling
% 2.74/1.77
% 2.74/1.77 % (2081)Memory used [KB]: 1279
% 2.74/1.77 % (2081)Time elapsed: 0.005 s
% 2.74/1.77 % (2081)Instructions burned: 8 (million)
% 2.74/1.77 % (2081)------------------------------
% 2.74/1.77 % (2081)------------------------------
% 2.74/1.78 % (2083)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_1961 for (2999ds/21Mi)
% 2.74/1.78 % (2084)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/5Mi)
% 2.74/1.79 % (2084)Instruction limit reached!
% 2.74/1.79 % (2084)------------------------------
% 2.74/1.79 % (2084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.79 % (2084)Termination reason: Unknown
% 2.74/1.79 % (2084)Termination phase: shuffling
% 2.74/1.79
% 2.74/1.79 % (2084)Memory used [KB]: 1279
% 2.74/1.79 % (2084)Time elapsed: 0.004 s
% 2.74/1.79 % (2084)Instructions burned: 5 (million)
% 2.74/1.79 % (2084)------------------------------
% 2.74/1.79 % (2084)------------------------------
% 2.74/1.79 % (2083)Instruction limit reached!
% 2.74/1.79 % (2083)------------------------------
% 2.74/1.79 % (2083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.79 % (2083)Termination reason: Unknown
% 2.74/1.79 % (2083)Termination phase: Property scanning
% 2.74/1.79
% 2.74/1.79 % (2083)Memory used [KB]: 1535
% 2.74/1.79 % (2083)Time elapsed: 0.011 s
% 2.74/1.79 % (2083)Instructions burned: 21 (million)
% 2.74/1.79 % (2083)------------------------------
% 2.74/1.79 % (2083)------------------------------
% 2.74/1.79 % (2060)Instruction limit reached!
% 2.74/1.79 % (2060)------------------------------
% 2.74/1.79 % (2060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.79 % (2060)Termination reason: Unknown
% 2.74/1.79 % (2060)Termination phase: Saturation
% 2.74/1.79
% 2.74/1.79 % (2060)Memory used [KB]: 7036
% 2.74/1.79 % (2060)Time elapsed: 0.089 s
% 2.74/1.79 % (2060)Instructions burned: 183 (million)
% 2.74/1.79 % (2060)------------------------------
% 2.74/1.79 % (2060)------------------------------
% 2.74/1.79 % (2085)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_1961 for (2999ds/6Mi)
% 2.74/1.79 % (2085)Instruction limit reached!
% 2.74/1.79 % (2085)------------------------------
% 2.74/1.79 % (2085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.79 % (2085)Termination reason: Unknown
% 2.74/1.79 % (2085)Termination phase: shuffling
% 2.74/1.79
% 2.74/1.79 % (2085)Memory used [KB]: 1279
% 2.74/1.79 % (2085)Time elapsed: 0.005 s
% 2.74/1.79 % (2085)Instructions burned: 8 (million)
% 2.74/1.79 % (2085)------------------------------
% 2.74/1.79 % (2085)------------------------------
% 2.74/1.80 % (2082)Refutation not found, incomplete strategy
% 2.74/1.80 % (2082)------------------------------
% 2.74/1.80 % (2082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.80 % (2082)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.80
% 2.74/1.80
% 2.74/1.80 % (2082)Memory used [KB]: 6140
% 2.74/1.80 % (2082)Time elapsed: 0.030 s
% 2.74/1.80 % (2082)Instructions burned: 61 (million)
% 2.74/1.80 % (2082)------------------------------
% 2.74/1.80 % (2082)------------------------------
% 2.74/1.80 % (2086)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1961 for (2999ds/377Mi)
% 2.74/1.80 % (2087)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_1961 for (2999ds/779Mi)
% 2.74/1.80 % (2088)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_1961 for (2999ds/19Mi)
% 2.74/1.81 % (2089)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1961 for (2998ds/879Mi)
% 2.74/1.81 % (2088)Instruction limit reached!
% 2.74/1.81 % (2088)------------------------------
% 2.74/1.81 % (2088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.81 % (2088)Termination reason: Unknown
% 2.74/1.81 % (2088)Termination phase: Property scanning
% 2.74/1.81
% 2.74/1.81 % (2088)Memory used [KB]: 1535
% 2.74/1.81 % (2088)Time elapsed: 0.011 s
% 2.74/1.81 % (2088)Instructions burned: 21 (million)
% 2.74/1.81 % (2088)------------------------------
% 2.74/1.81 % (2088)------------------------------
% 2.74/1.82 % (2090)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1961 for (2998ds/17Mi)
% 2.74/1.82 % (2090)Instruction limit reached!
% 2.74/1.82 % (2090)------------------------------
% 2.74/1.82 % (2090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.82 % (2090)Termination reason: Unknown
% 2.74/1.82 % (2090)Termination phase: shuffling
% 2.74/1.82
% 2.74/1.82 % (2090)Memory used [KB]: 1535
% 2.74/1.82 % (2090)Time elapsed: 0.010 s
% 2.74/1.82 % (2090)Instructions burned: 18 (million)
% 2.74/1.82 % (2090)------------------------------
% 2.74/1.82 % (2090)------------------------------
% 2.74/1.83 % (2091)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1961 for (2998ds/3Mi)
% 2.74/1.83 % (2091)Instruction limit reached!
% 2.74/1.83 % (2091)------------------------------
% 2.74/1.83 % (2091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.83 % (2091)Termination reason: Unknown
% 2.74/1.83 % (2091)Termination phase: shuffling
% 2.74/1.83
% 2.74/1.83 % (2091)Memory used [KB]: 1279
% 2.74/1.83 % (2091)Time elapsed: 0.003 s
% 2.74/1.83 % (2091)Instructions burned: 3 (million)
% 2.74/1.83 % (2091)------------------------------
% 2.74/1.83 % (2091)------------------------------
% 2.74/1.84 % (2092)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1961 for (2998ds/30Mi)
% 2.74/1.85 % (2093)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1961 for (2998ds/127Mi)
% 2.74/1.86 % (2092)Instruction limit reached!
% 2.74/1.86 % (2092)------------------------------
% 2.74/1.86 % (2092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.86 % (2092)Termination reason: Unknown
% 2.74/1.86 % (2092)Termination phase: Property scanning
% 2.74/1.86
% 2.74/1.86 % (2092)Memory used [KB]: 1535
% 2.74/1.86 % (2092)Time elapsed: 0.016 s
% 2.74/1.86 % (2092)Instructions burned: 31 (million)
% 2.74/1.86 % (2092)------------------------------
% 2.74/1.86 % (2092)------------------------------
% 2.74/1.86 % (2086)First to succeed.
% 2.74/1.86 % (2086)Refutation found. Thanks to Tanya!
% 2.74/1.86 % SZS status Theorem for DTF2THF_1961
% 2.74/1.86 % SZS output start Proof for DTF2THF_1961
% 2.74/1.86 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 2.74/1.86 thf(func_def_3, type, c_not: $o > $o).
% 2.74/1.86 thf(func_def_4, type, c_and: $o > $o > $o).
% 2.74/1.86 thf(func_def_5, type, c_or: $o > $o > $o).
% 2.74/1.86 thf(func_def_6, type, c_iff: $o > $o > $o).
% 2.74/1.86 thf(func_def_7, type, c_In: $i > $i > $o).
% 2.74/1.86 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 2.74/1.86 thf(func_def_10, type, c_Union: $i > $i).
% 2.74/1.86 thf(func_def_11, type, c_Power: $i > $i).
% 2.74/1.86 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 2.74/1.86 thf(func_def_13, type, c_TransSet: $i > $o).
% 2.74/1.86 thf(func_def_14, type, c_atleast2: $i > $o).
% 2.74/1.86 thf(func_def_15, type, c_atleast3: $i > $o).
% 2.74/1.86 thf(func_def_16, type, c_atleast4: $i > $o).
% 2.74/1.86 thf(func_def_17, type, c_atleast5: $i > $o).
% 2.74/1.86 thf(func_def_18, type, c_atleast6: $i > $o).
% 2.74/1.86 thf(func_def_19, type, c_exactly2: $i > $o).
% 2.74/1.86 thf(func_def_20, type, c_exactly3: $i > $o).
% 2.74/1.86 thf(func_def_21, type, c_exactly4: $i > $o).
% 2.74/1.86 thf(func_def_22, type, c_exactly5: $i > $o).
% 2.74/1.86 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 2.74/1.86 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 2.74/1.86 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 2.74/1.86 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 2.74/1.86 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 2.74/1.86 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 2.74/1.86 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 2.74/1.86 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 2.74/1.86 thf(func_def_43, type, c_Sing: $i > $i).
% 2.74/1.86 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 2.74/1.86 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 2.74/1.86 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 2.74/1.86 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 2.74/1.86 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 2.74/1.86 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 2.74/1.86 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 2.74/1.86 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 2.74/1.86 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 2.74/1.86 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 2.74/1.86 thf(func_def_54, type, c_equip: $i > $i > $o).
% 2.74/1.86 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 2.74/1.86 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 2.74/1.86 thf(func_def_57, type, c_ordsucc: $i > $i).
% 2.74/1.86 thf(func_def_58, type, c_nat_p: $i > $o).
% 2.74/1.86 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 2.74/1.86 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 2.74/1.86 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 2.74/1.86 thf(func_def_62, type, c_ordinal: $i > $o).
% 2.74/1.86 thf(func_def_63, type, c_V_: $i > $i).
% 2.74/1.86 thf(func_def_64, type, c_Inj1: $i > $i).
% 2.74/1.86 thf(func_def_65, type, c_Inj0: $i > $i).
% 2.74/1.86 thf(func_def_66, type, c_Unj: $i > $i).
% 2.74/1.86 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 2.74/1.86 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 2.74/1.86 thf(func_def_69, type, c_proj0: $i > $i).
% 2.74/1.86 thf(func_def_70, type, c_proj1: $i > $i).
% 2.74/1.86 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 2.74/1.86 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 2.74/1.86 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 2.74/1.86 thf(func_def_74, type, c_ap: $i > $i > $i).
% 2.74/1.86 thf(func_def_75, type, c_setsum_p: $i > $o).
% 2.74/1.86 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 2.74/1.86 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 2.74/1.86 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 2.74/1.86 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 2.74/1.86 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 2.74/1.86 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 2.74/1.86 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 2.74/1.86 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 2.74/1.86 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 2.74/1.86 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 2.74/1.86 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 2.74/1.86 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 2.74/1.86 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 2.74/1.86 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 2.74/1.86 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 2.74/1.86 thf(func_def_91, type, c_SNo: $i > $o).
% 2.74/1.86 thf(func_def_92, type, c_SNoLev: $i > $i).
% 2.74/1.86 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 2.74/1.86 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 2.74/1.86 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 2.74/1.86 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 2.74/1.86 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 2.74/1.87 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).
% 2.74/1.87 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).
% 2.74/1.87 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).
% 2.74/1.87 thf(func_def_101, type, c_combinator: $i > $o).
% 2.74/1.87 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 2.74/1.87 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 2.74/1.87 thf(func_def_131, type, sP0: ($i > $o) > $o).
% 2.74/1.87 thf(func_def_132, type, sP1: ($i > $o) > $o).
% 2.74/1.87 thf(func_def_133, type, sK2: ($i > $o) > $i).
% 2.74/1.87 thf(func_def_134, type, sK3: ($i > $o) > $i).
% 2.74/1.87 thf(func_def_135, type, sK4: ($i > $o) > $i).
% 2.74/1.87 thf(func_def_136, type, sK5: ($i > $o) > $i > $i).
% 2.74/1.87 thf(func_def_137, type, sK6: ($i > $o) > $i).
% 2.74/1.87 thf(func_def_138, type, sK7: ($i > $o) > $i).
% 2.74/1.87 thf(func_def_139, type, sK8: ($i > $o) > $i).
% 2.74/1.87 thf(func_def_142, type, sK11: $i > $i > ($i > $i) > $i).
% 2.74/1.87 thf(func_def_143, type, sK12: $i > ($i > $i) > $i > $i > $o).
% 2.74/1.87 thf(func_def_144, type, sK13: $i > $i > $i).
% 2.74/1.87 thf(func_def_145, type, sK14: $i > $i > $i).
% 2.74/1.87 thf(func_def_146, type, sK15: $i > $i > $i).
% 2.74/1.87 thf(func_def_147, type, sK16: $o > $o > $o).
% 2.74/1.87 thf(func_def_148, type, sK17: $i > $i > $i).
% 2.74/1.87 thf(func_def_149, type, sK18: ($i > $i) > $i > $i > ($i > $i > $i) > ($i > $o) > $o).
% 2.74/1.87 thf(func_def_153, type, sK22: $i > $i > $i).
% 2.74/1.87 thf(func_def_154, type, sK23: $i > $i > $i > $o).
% 2.74/1.87 thf(func_def_155, type, ph24: !>[X0: $tType]:(X0)).
% 2.74/1.87 thf(f992,plain,(
% 2.74/1.87 $false),
% 2.74/1.87 inference(avatar_sat_refutation,[status(thm)],[f708,f731,f743,f751,f809,f833,f988])).
% 2.74/1.87 thf(f988,plain,(
% 2.74/1.87 ~spl9_8 | ~spl9_11),
% 2.74/1.87 inference(avatar_contradiction_clause,[status(thm)],[f987])).
% 2.74/1.87 thf(f987,plain,(
% 2.74/1.87 $false | (~spl9_8 | ~spl9_11)),
% 2.74/1.87 inference(trivial_inequality_removal,[status(thm)],[f986])).
% 2.74/1.87 thf(f986,plain,(
% 2.74/1.87 ($true = $false) | (~spl9_8 | ~spl9_11)),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f984])).
% 2.74/1.87 thf(f984,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X6 : $i,X7 : $i] : ((((^[Y0 : $i]: ($false)) @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) = $true)) ) | (~spl9_8 | ~spl9_11)),
% 2.74/1.87 inference(primitive_instantiation,[status(thm)],[f842])).
% 2.74/1.87 thf(f842,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X6 : $i,X7 : $i,X5 : $i > $o] : (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) = $true)) ) | (~spl9_8 | ~spl9_11)),
% 2.74/1.87 inference(trivial_inequality_removal,[status(thm)],[f841])).
% 2.74/1.87 thf(f841,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X6 : $i,X7 : $i,X5 : $i > $o] : (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) = $true) | ($true = $false)) ) | (~spl9_8 | ~spl9_11)),
% 2.74/1.87 inference(forward_demodulation,[status(thm)],[f742,f730])).
% 2.74/1.87 thf(f730,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X6 : $i,X7 : $i,X5 : $i > $o] : (($false = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) ) | ~spl9_8),
% 2.74/1.87 inference(avatar_component_clause,[status(thm)],[f729])).
% 2.74/1.87 thf(f729,definition,(
% 2.74/1.87 spl9_8 <=> ! [X5 : $i > $o,X2 : $i > $i,X7 : $i,X6 : $i,X3 : $i > $i > $i] : ($false = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))),
% 2.74/1.87 introduced(definition,[new_symbols(naming,[spl9_8])],[avatar_definition])).
% 2.74/1.87 thf(f742,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X6 : $i,X7 : $i,X5 : $i > $o] : (($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)) | ((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) = $true)) ) | ~spl9_11),
% 2.74/1.87 inference(avatar_component_clause,[status(thm)],[f741])).
% 2.74/1.87 thf(f741,definition,(
% 2.74/1.87 spl9_11 <=> ! [X5 : $i > $o,X3 : $i > $i > $i,X7 : $i,X6 : $i,X2 : $i > $i] : (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) = $true) | ($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)))),
% 2.74/1.87 introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition])).
% 2.74/1.87 thf(f833,plain,(
% 2.74/1.87 ~spl9_1),
% 2.74/1.87 inference(avatar_contradiction_clause,[status(thm)],[f832])).
% 2.74/1.87 thf(f832,plain,(
% 2.74/1.87 $false | ~spl9_1),
% 2.74/1.87 inference(trivial_inequality_removal,[status(thm)],[f831])).
% 2.74/1.87 thf(f831,plain,(
% 2.74/1.87 ($true = $false) | ~spl9_1),
% 2.74/1.87 inference(superposition,[status(thm)],[f667,f704])).
% 2.74/1.87 thf(f704,plain,(
% 2.74/1.87 ( ! [X1 : $o] : (($true = X1)) ) | ~spl9_1),
% 2.74/1.87 inference(avatar_component_clause,[status(thm)],[f703])).
% 2.74/1.87 thf(f703,definition,(
% 2.74/1.87 spl9_1 <=> ! [X1 : $o] : ($true = X1)),
% 2.74/1.87 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 2.74/1.87 thf(f667,plain,(
% 2.74/1.87 (sK21 = $false)),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f666])).
% 2.74/1.87 thf(f666,plain,(
% 2.74/1.87 (((^[Y0 : $o]: (Y0)) @ sK21) = $false)),
% 2.74/1.87 inference(sigma_clausification,[status(thm)],[f631])).
% 2.74/1.87 thf(f631,plain,(
% 2.74/1.87 ($false = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f630])).
% 2.74/1.87 thf(f630,plain,(
% 2.74/1.87 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => Y9)) => Y9))) => (Y4 = Y0)))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) != $true)),
% 2.74/1.87 inference(boolean_simplification,[status(thm)],[f629])).
% 2.74/1.87 thf(f629,plain,(
% 2.74/1.87 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: (((Y2 @ Y0) = Y10) => $true))) => (((Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => Y9)) => Y9))) => (Y4 = Y0)))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))),
% 2.74/1.87 inference(boolean_simplification,[status(thm)],[f628])).
% 2.74/1.87 thf(f628,plain,(
% 2.74/1.87 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: (((Y2 @ Y0) = Y10) => ((!! @ $o @ (^[Y11 : $o]: (((Y8 @ Y10) => (((Y7 = Y6) => (!! @ $o @ (^[Y12 : $o]: (((Y1 = Y0) => ((Y5 @ Y10) => Y12)) => Y12)))) => Y11)) => Y11))) => $true)))) => (((Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => Y9)) => Y9))) => (Y4 = Y0)))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))),
% 2.74/1.87 inference(boolean_simplification,[status(thm)],[f627])).
% 2.74/1.87 thf(f627,plain,(
% 2.74/1.87 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: (((Y2 @ Y0) = Y10) => ((!! @ $o @ (^[Y11 : $o]: (((Y8 @ Y10) => (((Y7 = Y6) => (!! @ $o @ (^[Y12 : $o]: (((Y1 = Y0) => ((Y5 @ Y10) => Y12)) => Y12)))) => Y11)) => Y11))) => (Y6 = Y6))))) => (((Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => Y9)) => Y9))) => (Y4 = Y0)))))))))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f528])).
% 2.74/1.87 thf(f528,plain,(
% 2.74/1.87 (((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: (((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ (!! @ $i @ (^[Y9 : $i]: (((Y2 @ Y0) = Y9) => (((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ (Y8 @ Y9) @ ((Y7 = Y6) => ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ (Y1 = Y0) @ (Y5 @ Y9)))) => (Y6 = Y6))))) @ ((^[Y9 : $o]: (Y9 => (!! @ $o @ (^[Y10 : $o]: (Y10))))) @ (Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))))) => (Y4 = Y0))))))))))))))))))))) != $true)),
% 2.74/1.87 inference(definition_unfolding,[status(thm)],[f426,f435,f432,f432,f432,f435])).
% 2.74/1.87 thf(f432,plain,(
% 2.74/1.87 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f206])).
% 2.74/1.87 thf(f206,plain,(
% 2.74/1.87 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f205])).
% 2.74/1.87 thf(f205,plain,(
% 2.74/1.87 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 2.74/1.87 inference(rectify,[status(thm)],[f14])).
% 2.74/1.87 thf(f14,axiom,(
% 2.74/1.87 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax14)).
% 2.74/1.87 thf(f435,plain,(
% 2.74/1.87 (c_not = (^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))))),
% 2.74/1.87 inference(definition_unfolding,[status(thm)],[f406,f401])).
% 2.74/1.87 thf(f401,plain,(
% 2.74/1.87 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f190])).
% 2.74/1.87 thf(f190,plain,(
% 2.74/1.87 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f189])).
% 2.74/1.87 thf(f189,plain,(
% 2.74/1.87 (c_False = ! [X0 : $o] : X0)),
% 2.74/1.87 inference(rectify,[status(thm)],[f11])).
% 2.74/1.87 thf(f11,axiom,(
% 2.74/1.87 (c_False = ! [X0 : $o] : X0)),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax11)).
% 2.74/1.87 thf(f406,plain,(
% 2.74/1.87 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f188])).
% 2.74/1.87 thf(f188,plain,(
% 2.74/1.87 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f187])).
% 2.74/1.87 thf(f187,plain,(
% 2.74/1.87 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 2.74/1.87 inference(rectify,[status(thm)],[f13])).
% 2.74/1.87 thf(f13,axiom,(
% 2.74/1.87 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax13)).
% 2.74/1.87 thf(f426,plain,(
% 2.74/1.87 ((c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((c_and @ (!! @ $i @ (^[Y9 : $i]: (((Y2 @ Y0) = Y9) => ((c_and @ (Y8 @ Y9) @ ((Y7 = Y6) => (c_and @ (Y1 = Y0) @ (Y5 @ Y9)))) => (Y6 = Y6))))) @ (c_not @ (Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))))) => (Y4 = Y0))))))))))))))))))))) != $true)),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f288])).
% 2.74/1.87 thf(f288,plain,(
% 2.74/1.87 ((c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((c_and @ (!! @ $i @ (^[Y9 : $i]: (((Y2 @ Y0) = Y9) => ((c_and @ (Y8 @ Y9) @ ((Y7 = Y6) => (c_and @ (Y1 = Y0) @ (Y5 @ Y9)))) => (Y6 = Y6))))) @ (c_not @ (Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))))) => (Y4 = Y0))))))))))))))))))))) != $true)),
% 2.74/1.87 inference(flattening,[status(thm)],[f129])).
% 2.74/1.87 thf(f129,plain,(
% 2.74/1.87 ~((c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((c_and @ (!! @ $i @ (^[Y9 : $i]: (((Y2 @ Y0) = Y9) => ((c_and @ (Y8 @ Y9) @ ((Y7 = Y6) => (c_and @ (Y1 = Y0) @ (Y5 @ Y9)))) => (Y6 = Y6))))) @ (c_not @ (Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))))) => (Y4 = Y0))))))))))))))))))))) = $true)),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f128])).
% 2.74/1.87 thf(f128,plain,(
% 2.74/1.87 ~(c_not @ ! [X0 : $i > $o,X1 : $i,X2 : $i,X4 : $i > $o,X5 : $i,X6 : $i > $i > $i,X7 : $i > $i,X8 : $i,X9 : $i] : ((c_and @ ! [X10 : $i] : (((X7 @ X9) = X10) => ((c_and @ (X0 @ X10) @ (X1 = X2) => (c_and @ (X8 = X9) @ (X4 @ X10))) => (X2 = X2))) @ (c_not @ (X4 @ (X7 @ (X7 @ (X6 @ X2 @ X1)))))) => (X5 = X9)))),
% 2.74/1.87 inference(rectify,[status(thm)],[f110])).
% 2.74/1.87 thf(f110,negated_conjecture,(
% 2.74/1.87 ~(c_not @ ! [X2 : $i > $o,X5 : $i,X7 : $i,X0 : $i > $i > $o,X3 : $i > $o,X6 : $i,X1 : $i > $i > $i,X4 : $i > $i,X8 : $i,X9 : $i] : ((c_and @ ! [X10 : $i] : (((X4 @ X9) = X10) => ((c_and @ (X2 @ X10) @ (X5 = X7) => (c_and @ ! [X11 : $i] : (X8 = X9) @ ? [X11 : $i] : (X3 @ X10))) => ? [X11 : $i] : (X7 = X7))) @ (c_not @ (X3 @ (X4 @ (X4 @ (X1 @ X7 @ X5)))))) => (X6 = X9)))),
% 2.74/1.87 inference(negated_conjecture,[status(cth)],[f109])).
% 2.74/1.87 thf(f109,conjecture,(
% 2.74/1.87 (c_not @ ! [X2 : $i > $o,X5 : $i,X7 : $i,X0 : $i > $i > $o,X3 : $i > $o,X6 : $i,X1 : $i > $i > $i,X4 : $i > $i,X8 : $i,X9 : $i] : ((c_and @ ! [X10 : $i] : (((X4 @ X9) = X10) => ((c_and @ (X2 @ X10) @ (X5 = X7) => (c_and @ ! [X11 : $i] : (X8 = X9) @ ? [X11 : $i] : (X3 @ X10))) => ? [X11 : $i] : (X7 = X7))) @ (c_not @ (X3 @ (X4 @ (X4 @ (X1 @ X7 @ X5)))))) => (X6 = X9)))),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',conj)).
% 2.74/1.87 thf(f809,plain,(
% 2.74/1.87 ~spl9_2 | ~spl9_7 | ~spl9_13),
% 2.74/1.87 inference(avatar_contradiction_clause,[status(thm)],[f808])).
% 2.74/1.87 thf(f808,plain,(
% 2.74/1.87 $false | (~spl9_2 | ~spl9_7 | ~spl9_13)),
% 2.74/1.87 inference(trivial_inequality_removal,[status(thm)],[f807])).
% 2.74/1.87 thf(f807,plain,(
% 2.74/1.87 ($true = $false) | (~spl9_2 | ~spl9_7 | ~spl9_13)),
% 2.74/1.87 inference(forward_demodulation,[status(thm)],[f798,f783])).
% 2.74/1.87 thf(f783,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (((c_In @ X1 @ X0) = $false)) ) | (~spl9_2 | ~spl9_7)),
% 2.74/1.87 inference(superposition,[status(thm)],[f707,f727])).
% 2.74/1.87 thf(f727,plain,(
% 2.74/1.87 ( ! [X1 : $i,X4 : $i] : ((X1 = X4)) ) | ~spl9_7),
% 2.74/1.87 inference(avatar_component_clause,[status(thm)],[f726])).
% 2.74/1.87 thf(f726,definition,(
% 2.74/1.87 spl9_7 <=> ! [X4 : $i,X1 : $i] : (X1 = X4)),
% 2.74/1.87 introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition])).
% 2.74/1.87 thf(f707,plain,(
% 2.74/1.87 ( ! [X2 : $i] : (($false = (c_In @ X2 @ c_Empty))) ) | ~spl9_2),
% 2.74/1.87 inference(avatar_component_clause,[status(thm)],[f706])).
% 2.74/1.87 thf(f706,definition,(
% 2.74/1.87 spl9_2 <=> ! [X2 : $i] : ($false = (c_In @ X2 @ c_Empty))),
% 2.74/1.87 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 2.74/1.87 thf(f798,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (($true = (c_In @ X0 @ (c_Power @ X1)))) ) | (~spl9_2 | ~spl9_7 | ~spl9_13)),
% 2.74/1.87 inference(trivial_inequality_removal,[status(thm)],[f787])).
% 2.74/1.87 thf(f787,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (($true = (c_In @ X0 @ (c_Power @ X1))) | ($true = $false)) ) | (~spl9_2 | ~spl9_7 | ~spl9_13)),
% 2.74/1.87 inference(backward_demodulation,[status(thm)],[f750,f783])).
% 2.74/1.87 thf(f750,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (($true = (c_In @ X0 @ (c_Power @ X1))) | ((c_In @ (sK17 @ X1 @ X0) @ X0) = $true)) ) | ~spl9_13),
% 2.74/1.87 inference(avatar_component_clause,[status(thm)],[f749])).
% 2.74/1.87 thf(f749,definition,(
% 2.74/1.87 spl9_13 <=> ! [X0 : $i,X1 : $i] : (($true = (c_In @ X0 @ (c_Power @ X1))) | ((c_In @ (sK17 @ X1 @ X0) @ X0) = $true))),
% 2.74/1.87 introduced(definition,[new_symbols(naming,[spl9_13])],[avatar_definition])).
% 2.74/1.87 thf(f751,plain,(
% 2.74/1.87 spl9_1 | spl9_13),
% 2.74/1.87 inference(avatar_split_clause,[status(thm)],[f626,f749,f703])).
% 2.74/1.87 thf(f626,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (c_In @ X0 @ (c_Power @ X1))) | ((c_In @ (sK17 @ X1 @ X0) @ X0) = $true) | ($true = X2)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f624])).
% 2.74/1.87 thf(f624,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((c_In @ (sK17 @ X1 @ X0) @ X0) => (c_In @ (sK17 @ X1 @ X0) @ X1)) = $false) | ($true = X2) | ($true = (c_In @ X0 @ (c_Power @ X1)))) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f623])).
% 2.74/1.87 thf(f623,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (c_In @ X0 @ (c_Power @ X1))) | ($true = X2) | (((^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))) @ (sK17 @ X1 @ X0)) = $false)) )),
% 2.74/1.87 inference(sigma_clausification,[status(thm)],[f622])).
% 2.74/1.87 thf(f622,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) = $false) | ($true = X2) | ($true = (c_In @ X0 @ (c_Power @ X1)))) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f621])).
% 2.74/1.87 thf(f621,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) = $true) | ($true = X2)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f614])).
% 2.74/1.87 thf(f614,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2) = $false) | ($true = X2)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f613])).
% 2.74/1.87 thf(f613,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) = $false)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f612])).
% 2.74/1.87 thf(f612,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X0) => (c_In @ Y0 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => X2)) => X2))) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f611])).
% 2.74/1.87 thf(f611,plain,(
% 2.74/1.87 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((^[Y0 : $o]: ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => Y0)) => Y0)) @ X2))) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f610])).
% 2.74/1.87 thf(f610,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: ((((c_In @ X0 @ (c_Power @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X0) => (c_In @ Y1 @ X1)))) => (c_In @ X0 @ (c_Power @ X1))) => Y0)) => Y0))))) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f521])).
% 2.74/1.87 thf(f521,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))) @ (c_In @ X0 @ (c_Power @ X1)) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))) @ X0 @ X1)))) )),
% 2.74/1.87 inference(definition_unfolding,[status(thm)],[f330,f436,f397])).
% 2.74/1.87 thf(f397,plain,(
% 2.74/1.87 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f222])).
% 2.74/1.87 thf(f222,plain,(
% 2.74/1.87 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f221])).
% 2.74/1.87 thf(f221,plain,(
% 2.74/1.87 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 2.74/1.87 inference(rectify,[status(thm)],[f17])).
% 2.74/1.87 thf(f17,axiom,(
% 2.74/1.87 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax17)).
% 2.74/1.87 thf(f436,plain,(
% 2.74/1.87 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 2.74/1.87 inference(definition_unfolding,[status(thm)],[f323,f432])).
% 2.74/1.87 thf(f323,plain,(
% 2.74/1.87 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f220])).
% 2.74/1.87 thf(f220,plain,(
% 2.74/1.87 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f219])).
% 2.74/1.87 thf(f219,plain,(
% 2.74/1.87 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)),
% 2.74/1.87 inference(rectify,[status(thm)],[f16])).
% 2.74/1.87 thf(f16,axiom,(
% 2.74/1.87 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax16)).
% 2.74/1.87 thf(f330,plain,(
% 2.74/1.87 ( ! [X0 : $i,X1 : $i] : (($true = (c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1)))) )),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f147])).
% 2.74/1.87 thf(f147,plain,(
% 2.74/1.87 ! [X0 : $i,X1 : $i] : ($true = (c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1)))),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f146])).
% 2.74/1.87 thf(f146,plain,(
% 2.74/1.87 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X0 @ (c_Power @ X1)) @ (c_Subq @ X0 @ X1))),
% 2.74/1.87 inference(rectify,[status(thm)],[f7])).
% 2.74/1.87 thf(f7,axiom,(
% 2.74/1.87 ! [X1 : $i,X0 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax7)).
% 2.74/1.87 thf(f743,plain,(
% 2.74/1.87 spl9_7 | spl9_11),
% 2.74/1.87 inference(avatar_split_clause,[status(thm)],[f663,f741,f726])).
% 2.74/1.87 thf(f663,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) = $true) | (X1 = X4) | ($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f661])).
% 2.74/1.87 thf(f661,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((X1 = X4) | ($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)) | (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $false)) )),
% 2.74/1.87 inference(trivial_inequality_removal,[status(thm)],[f660])).
% 2.74/1.87 thf(f660,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((X1 = X4) | (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $false) | ($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)) | ($true = $false)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f659])).
% 2.74/1.87 thf(f659,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((((^[Y0 : $i]: ($true)) @ sK19) = $false) | (X1 = X4) | ($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)) | (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $false)) )),
% 2.74/1.87 inference(sigma_clausification,[status(thm)],[f658])).
% 2.74/1.87 thf(f658,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ($true))) = $false) | (X1 = X4) | (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $false) | ($true = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f657])).
% 2.74/1.87 thf(f657,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (($true = (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) => (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) | ((!! @ $i @ (^[Y0 : $i]: ($true))) = $false) | (X1 = X4)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f656])).
% 2.74/1.87 thf(f656,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((X1 = X4) | (((!! @ $i @ (^[Y0 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) => (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) = $true)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f654])).
% 2.74/1.87 thf(f654,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) => (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) => (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)) = $false) | (X1 = X4)) )),
% 2.74/1.87 inference(equality_proxy_clausification,[status(thm)],[f653])).
% 2.74/1.87 thf(f653,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((X4 = X1) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) => (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) => (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)) = $false)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f652])).
% 2.74/1.87 thf(f652,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((X4 = X1) = $true) | ($false = ((^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))) => Y0)) => Y0)) @ (sK18 @ X2 @ X6 @ X7 @ X3 @ X5)))) )),
% 2.74/1.87 inference(sigma_clausification,[status(thm)],[f651])).
% 2.74/1.87 thf(f651,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))) => Y0)) => Y0))) = $false) | ((X4 = X1) = $true)) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f650])).
% 2.74/1.87 thf(f650,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((((!! @ $o @ (^[Y0 : $o]: (((!! @ $i @ (^[Y1 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))) => Y0)) => Y0))) => (X4 = X1)) = $true)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f649])).
% 2.74/1.87 thf(f649,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X8 : $i > $o,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((!! @ $o @ (^[Y1 : $o]: (((!! @ $i @ (^[Y2 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y2 : $o]: (Y2)))) => Y1)) => Y1))) => (X4 = X1))) @ X8))) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f648])).
% 2.74/1.87 thf(f648,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $o @ (^[Y1 : $o]: (((!! @ $i @ (^[Y2 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ X7)))) => (!! @ $o @ (^[Y2 : $o]: (Y2)))) => Y1)) => Y1))) => (X4 = X1)))) = $true)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f647])).
% 2.74/1.87 thf(f647,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ Y0)))) => (!! @ $o @ (^[Y3 : $o]: (Y3)))) => Y2)) => Y2))) => (X4 = X1))))) @ X7) = $true)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f646])).
% 2.74/1.87 thf(f646,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $o @ (^[Y2 : $o]: (((!! @ $i @ (^[Y3 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ X6 @ Y0)))) => (!! @ $o @ (^[Y3 : $o]: (Y3)))) => Y2)) => Y2))) => (X4 = X1)))))) = $true)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f645])).
% 2.74/1.87 thf(f645,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ Y0 @ Y1)))) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => Y3)) => Y3))) => (X4 = X1))))))) @ X6) = $true)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f644])).
% 2.74/1.87 thf(f644,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X4 : $i,X5 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $o @ (^[Y3 : $o]: (((!! @ $i @ (^[Y4 : $i]: ($true))) => (((X5 @ (X2 @ (X2 @ (X3 @ Y0 @ Y1)))) => (!! @ $o @ (^[Y4 : $o]: (Y4)))) => Y3)) => Y3))) => (X4 = X1)))))))) = $true)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f643])).
% 2.74/1.87 thf(f643,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X4 : $i,X5 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ($true))) => (((Y0 @ (X2 @ (X2 @ (X3 @ Y1 @ Y2)))) => (!! @ $o @ (^[Y5 : $o]: (Y5)))) => Y4)) => Y4))) => (X4 = X1))))))))) @ X5) = $true)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f642])).
% 2.74/1.87 thf(f642,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X4 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $o @ (^[Y4 : $o]: (((!! @ $i @ (^[Y5 : $i]: ($true))) => (((Y0 @ (X2 @ (X2 @ (X3 @ Y1 @ Y2)))) => (!! @ $o @ (^[Y5 : $o]: (Y5)))) => Y4)) => Y4))) => (X4 = X1)))))))))))) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f641])).
% 2.74/1.87 thf(f641,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ($true))) => (((Y1 @ (X2 @ (X2 @ (X3 @ Y2 @ Y3)))) => (!! @ $o @ (^[Y6 : $o]: (Y6)))) => Y5)) => Y5))) => (Y0 = X1))))))))))) @ X4) = $true)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f640])).
% 2.74/1.87 thf(f640,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $o @ (^[Y5 : $o]: (((!! @ $i @ (^[Y6 : $i]: ($true))) => (((Y1 @ (X2 @ (X2 @ (X3 @ Y2 @ Y3)))) => (!! @ $o @ (^[Y6 : $o]: (Y6)))) => Y5)) => Y5))) => (Y0 = X1)))))))))))) = $true)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f639])).
% 2.74/1.87 thf(f639,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i] : ((((^[Y0 : $i > $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ($true))) => (((Y2 @ (X2 @ (X2 @ (Y0 @ Y3 @ Y4)))) => (!! @ $o @ (^[Y7 : $o]: (Y7)))) => Y6)) => Y6))) => (Y1 = X1))))))))))))) @ X3) = $true)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f638])).
% 2.74/1.87 thf(f638,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X1 : $i] : (((!! @ ($i > $i > $i) @ (^[Y0 : $i > $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: ((!! @ $o @ (^[Y6 : $o]: (((!! @ $i @ (^[Y7 : $i]: ($true))) => (((Y2 @ (X2 @ (X2 @ (Y0 @ Y3 @ Y4)))) => (!! @ $o @ (^[Y7 : $o]: (Y7)))) => Y6)) => Y6))) => (Y1 = X1)))))))))))))) = $true)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f637])).
% 2.74/1.87 thf(f637,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X1 : $i] : (($true = ((^[Y0 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ ($i > $o) @ (^[Y6 : $i > $o]: ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ($true))) => (((Y3 @ (Y0 @ (Y0 @ (Y1 @ Y4 @ Y5)))) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => Y7)) => Y7))) => (Y2 = X1))))))))))))))) @ X2))) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f636])).
% 2.74/1.87 thf(f636,plain,(
% 2.74/1.87 ( ! [X1 : $i] : (($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ ($i > $o) @ (^[Y6 : $i > $o]: ((!! @ $o @ (^[Y7 : $o]: (((!! @ $i @ (^[Y8 : $i]: ($true))) => (((Y3 @ (Y0 @ (Y0 @ (Y1 @ Y4 @ Y5)))) => (!! @ $o @ (^[Y8 : $o]: (Y8)))) => Y7)) => Y7))) => (Y2 = X1)))))))))))))))))) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f635])).
% 2.74/1.87 thf(f635,plain,(
% 2.74/1.87 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ ($i > $o) @ (^[Y7 : $i > $o]: ((!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ($true))) => (((Y4 @ (Y1 @ (Y1 @ (Y2 @ Y5 @ Y6)))) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => Y8)) => Y8))) => (Y3 = X1))))))))))))))))) @ X2) = $true)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f634])).
% 2.74/1.87 thf(f634,plain,(
% 2.74/1.87 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $o) @ (^[Y4 : $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ ($i > $o) @ (^[Y7 : $i > $o]: ((!! @ $o @ (^[Y8 : $o]: (((!! @ $i @ (^[Y9 : $i]: ($true))) => (((Y4 @ (Y1 @ (Y1 @ (Y2 @ Y5 @ Y6)))) => (!! @ $o @ (^[Y9 : $o]: (Y9)))) => Y8)) => Y8))) => (Y3 = X1)))))))))))))))))))) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f633])).
% 2.74/1.87 thf(f633,plain,(
% 2.74/1.87 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => Y9)) => Y9))) => (Y4 = Y0))))))))))))))))))) @ X1))) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f632])).
% 2.74/1.87 thf(f632,plain,(
% 2.74/1.87 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i) @ (^[Y2 : $i > $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $o) @ (^[Y5 : $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ ($i > $o) @ (^[Y8 : $i > $o]: ((!! @ $o @ (^[Y9 : $o]: (((!! @ $i @ (^[Y10 : $i]: ($true))) => (((Y5 @ (Y2 @ (Y2 @ (Y3 @ Y6 @ Y7)))) => (!! @ $o @ (^[Y10 : $o]: (Y10)))) => Y9)) => Y9))) => (Y4 = Y0)))))))))))))))))))))),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f630])).
% 2.74/1.87 thf(f731,plain,(
% 2.74/1.87 spl9_7 | spl9_8),
% 2.74/1.87 inference(avatar_split_clause,[status(thm)],[f655,f729,f726])).
% 2.74/1.87 thf(f655,plain,(
% 2.74/1.87 ( ! [X2 : $i > $i,X3 : $i > $i > $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i > $o] : ((X1 = X4) | ($false = (sK18 @ X2 @ X6 @ X7 @ X3 @ X5))) )),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f654])).
% 2.74/1.87 thf(f708,plain,(
% 2.74/1.87 spl9_1 | spl9_2),
% 2.74/1.87 inference(avatar_split_clause,[status(thm)],[f701,f706,f703])).
% 2.74/1.87 thf(f701,plain,(
% 2.74/1.87 ( ! [X2 : $i,X1 : $o] : (($false = (c_In @ X2 @ c_Empty)) | ($true = X1)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f700])).
% 2.74/1.87 thf(f700,plain,(
% 2.74/1.87 ( ! [X2 : $i,X1 : $o] : ((((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X2) = $false) | ($true = X1)) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f699])).
% 2.74/1.87 thf(f699,plain,(
% 2.74/1.87 ( ! [X1 : $o] : (($false = (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) | ($true = X1)) )),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f698])).
% 2.74/1.87 thf(f698,plain,(
% 2.74/1.87 ( ! [X1 : $o] : ((((^[Y0 : $o]: (Y0)) @ X1) = $true) | ($false = (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))) )),
% 2.74/1.87 inference(pi_clausification,[status(thm)],[f697])).
% 2.74/1.87 thf(f697,plain,(
% 2.74/1.87 ($true = (!! @ $o @ (^[Y0 : $o]: (Y0)))) | ($false = (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))),
% 2.74/1.87 inference(binary_proxy_clausification,[status(thm)],[f696])).
% 2.74/1.87 thf(f696,plain,(
% 2.74/1.87 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)),
% 2.74/1.87 inference(beta_eta_normalization,[status(thm)],[f527])).
% 2.74/1.87 thf(f527,plain,(
% 2.74/1.87 ($true = ((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 2.74/1.87 inference(definition_unfolding,[status(thm)],[f423,f435])).
% 2.74/1.87 thf(f423,plain,(
% 2.74/1.87 ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $true)),
% 2.74/1.87 inference(cnf_transformation,[status(thm)],[f231])).
% 2.74/1.87 thf(f231,plain,(
% 2.74/1.87 ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $true)),
% 2.74/1.87 inference(fool_elimination,[status(thm)],[f230])).
% 2.74/1.87 thf(f230,plain,(
% 2.74/1.87 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 2.74/1.87 inference(rectify,[status(thm)],[f5])).
% 2.74/1.87 thf(f5,axiom,(
% 2.74/1.87 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 2.74/1.87 file('/export/starexec/sandbox/tmp/tmp.4cTxUiGlDX/DTF2THF_1961.p',ax5)).
% 2.74/1.87 % SZS output end Proof for DTF2THF_1961
% 2.74/1.87 % (2086)------------------------------
% 2.74/1.87 % (2086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.87 % (2086)Termination reason: Refutation
% 2.74/1.87
% 2.74/1.87 % (2086)Memory used [KB]: 6652
% 2.74/1.87 % (2086)Time elapsed: 0.062 s
% 2.74/1.87 % (2086)Instructions burned: 118 (million)
% 2.74/1.87 % (2086)------------------------------
% 2.74/1.87 % (2086)------------------------------
% 2.74/1.87 % (2059)Success in time 0.193 s
%------------------------------------------------------------------------------