%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO881^1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:54:59 AM UTC 2026
% Result : Theorem 8.06s 2.48s
% Output : Refutation 8.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO881^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:48:41 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SYO881^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : ProofGold problem Random3_48_neg_th0
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Urb20]
% 0.30/0.45 % Names : Random3_48_neg_th0.p [Urb20]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.78 v9.1.0, 0.75 v9.0.0, 0.80 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.30/0.45 % Number of atoms : 481 ( 136 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 5 ( 4 avg)
% 0.30/0.45 % Number of connectives : 1203 ( 0 ~; 0 |; 0 &;1114 @)
% 0.30/0.45 % ( 0 <=>; 89 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 15 ( 2 avg)
% 0.30/0.45 % Number of types : 2 ( 0 usr)
% 0.30/0.45 % Number of type conns : 564 ( 564 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.30/0.45 % Number of variables : 413 ( 275 ^; 101 !; 37 ?; 413 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : See https://proofgold.org
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(c_Eps_i_tp,type,
% 0.30/0.45 c_Eps_i: ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_False_tp,type,
% 0.30/0.45 c_False: $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_True_tp,type,
% 0.30/0.45 c_True: $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_not_tp,type,
% 0.30/0.45 c_not: $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_and_tp,type,
% 0.30/0.45 c_and: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_or_tp,type,
% 0.30/0.45 c_or: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_iff_tp,type,
% 0.30/0.45 c_iff: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_In_tp,type,
% 0.30/0.45 c_In: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Subq_tp,type,
% 0.30/0.45 c_Subq: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Empty_tp,type,
% 0.30/0.45 c_Empty: $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Union_tp,type,
% 0.30/0.45 c_Union: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Power_tp,type,
% 0.30/0.45 c_Power: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Repl_tp,type,
% 0.30/0.45 c_Repl: $i > ( $i > $i ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_TransSet_tp,type,
% 0.30/0.45 c_TransSet: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_atleast2_tp,type,
% 0.30/0.45 c_atleast2: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_atleast3_tp,type,
% 0.30/0.45 c_atleast3: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_atleast4_tp,type,
% 0.30/0.45 c_atleast4: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_atleast5_tp,type,
% 0.30/0.45 c_atleast5: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_atleast6_tp,type,
% 0.30/0.45 c_atleast6: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_exactly2_tp,type,
% 0.30/0.45 c_exactly2: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_exactly3_tp,type,
% 0.30/0.45 c_exactly3: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_exactly4_tp,type,
% 0.30/0.45 c_exactly4: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_exactly5_tp,type,
% 0.30/0.45 c_exactly5: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_exu_i_tp,type,
% 0.30/0.45 c_exu_i: ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_reflexive_i_tp,type,
% 0.30/0.45 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_irreflexive_i_tp,type,
% 0.30/0.45 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_symmetric_i_tp,type,
% 0.30/0.45 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_antisymmetric_i_tp,type,
% 0.30/0.45 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_transitive_i_tp,type,
% 0.30/0.45 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_eqreln_i_tp,type,
% 0.30/0.45 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_per_i_tp,type,
% 0.30/0.45 c_per_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_linear_i_tp,type,
% 0.30/0.45 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_trichotomous_or_i_tp,type,
% 0.30/0.45 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_partialorder_i_tp,type,
% 0.30/0.45 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_totalorder_i_tp,type,
% 0.30/0.45 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_strictpartialorder_i_tp,type,
% 0.30/0.45 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_stricttotalorder_i_tp,type,
% 0.30/0.45 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_If_i_tp,type,
% 0.30/0.45 c_If_i: $o > $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_exactly1of2_tp,type,
% 0.30/0.45 c_exactly1of2: $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_exactly1of3_tp,type,
% 0.30/0.45 c_exactly1of3: $o > $o > $o > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_nIn_tp,type,
% 0.30/0.45 c_nIn: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_nSubq_tp,type,
% 0.30/0.45 c_nSubq: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_UPair_tp,type,
% 0.30/0.45 c_UPair: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Sing_tp,type,
% 0.30/0.45 c_Sing: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_binunion_tp,type,
% 0.30/0.45 c_binunion: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_SetAdjoin_tp,type,
% 0.30/0.45 c_SetAdjoin: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_famunion_tp,type,
% 0.30/0.45 c_famunion: $i > ( $i > $i ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Sep_tp,type,
% 0.30/0.45 c_Sep: $i > ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_ReplSep_tp,type,
% 0.30/0.45 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_binintersect_tp,type,
% 0.30/0.45 c_binintersect: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_setminus_tp,type,
% 0.30/0.45 c_setminus: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_inj_tp,type,
% 0.30/0.45 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_bij_tp,type,
% 0.30/0.45 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_atleastp_tp,type,
% 0.30/0.45 c_atleastp: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_equip_tp,type,
% 0.30/0.45 c_equip: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_In_rec_poly_G_i_tp,type,
% 0.30/0.45 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_In_rec_poly_i_tp,type,
% 0.30/0.45 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_ordsucc_tp,type,
% 0.30/0.45 c_ordsucc: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_nat_p_tp,type,
% 0.30/0.45 c_nat_p: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_nat_primrec_tp,type,
% 0.30/0.45 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_add_nat_tp,type,
% 0.30/0.45 c_add_nat: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_mul_nat_tp,type,
% 0.30/0.45 c_mul_nat: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_ordinal_tp,type,
% 0.30/0.45 c_ordinal: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_V__tp,type,
% 0.30/0.45 c_V_: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Inj1_tp,type,
% 0.30/0.45 c_Inj1: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Inj0_tp,type,
% 0.30/0.45 c_Inj0: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Unj_tp,type,
% 0.30/0.45 c_Unj: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_combine_funcs_tp,type,
% 0.30/0.45 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_setsum_tp,type,
% 0.30/0.45 c_setsum: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_proj0_tp,type,
% 0.30/0.45 c_proj0: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_proj1_tp,type,
% 0.30/0.45 c_proj1: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_binrep_tp,type,
% 0.30/0.45 c_binrep: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_lam_tp,type,
% 0.30/0.45 c_lam: $i > ( $i > $i ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_setprod_tp,type,
% 0.30/0.45 c_setprod: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_ap_tp,type,
% 0.30/0.45 c_ap: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_setsum_p_tp,type,
% 0.30/0.45 c_setsum_p: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_tuple_p_tp,type,
% 0.30/0.45 c_tuple_p: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Pi_tp,type,
% 0.30/0.45 c_Pi: $i > ( $i > $i ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_setexp_tp,type,
% 0.30/0.45 c_setexp: $i > $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_Sep2_tp,type,
% 0.30/0.45 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_set_of_pairs_tp,type,
% 0.30/0.45 c_set_of_pairs: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_lam2_tp,type,
% 0.30/0.45 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_PNoEq__tp,type,
% 0.30/0.45 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_PNoLt__tp,type,
% 0.30/0.45 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_PNoLt_tp,type,
% 0.30/0.45 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_PNoLe_tp,type,
% 0.30/0.45 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_PNo_downc_tp,type,
% 0.30/0.45 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_PNo_upc_tp,type,
% 0.30/0.45 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNoElts__tp,type,
% 0.30/0.45 c_SNoElts_: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNo__tp,type,
% 0.30/0.45 c_SNo_: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_PSNo_tp,type,
% 0.30/0.45 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNo_tp,type,
% 0.30/0.45 c_SNo: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNoLev_tp,type,
% 0.30/0.45 c_SNoLev: $i > $i ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNoEq__tp,type,
% 0.30/0.45 c_SNoEq_: $i > $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNoLt_tp,type,
% 0.30/0.45 c_SNoLt: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_SNoLe_tp,type,
% 0.30/0.45 c_SNoLe: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_binop_on_tp,type,
% 0.30/0.45 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Loop_tp,type,
% 0.30/0.45 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Loop_with_defs_tp,type,
% 0.30/0.45 c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Loop_with_defs_cex1_tp,type,
% 0.30/0.45 c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_Loop_with_defs_cex2_tp,type,
% 0.30/0.45 c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_combinator_tp,type,
% 0.30/0.45 c_combinator: $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_combinator_equiv_tp,type,
% 0.30/0.45 c_combinator_equiv: $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(c_equip_mod_tp,type,
% 0.30/0.45 c_equip_mod: $i > $i > $i > $o ).
% 0.30/0.45
% 0.30/0.45 thf(ax1,axiom,
% 0.30/0.45 ! [X0: $i > $o,X1: $i] :
% 0.30/0.45 ( ( X0 @ X1 )
% 0.30/0.45 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax2,axiom,
% 0.30/0.45 ! [X0: $o] :
% 0.30/0.45 ( ( c_not @ ( c_not @ X0 ) )
% 0.30/0.45 => X0 ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax3,axiom,
% 0.30/0.45 ! [X0: $o,X1: $o] :
% 0.30/0.45 ( ( c_iff @ X0 @ X1 )
% 0.30/0.45 => ( X0 = X1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax4,axiom,
% 0.30/0.45 ! [X0: $i,X1: $i] :
% 0.30/0.45 ( ( c_Subq @ X0 @ X1 )
% 0.30/0.45 => ( ( c_Subq @ X1 @ X0 )
% 0.30/0.45 => ( X0 = X1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax5,axiom,
% 0.30/0.45 ( c_not
% 0.30/0.45 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax6,axiom,
% 0.30/0.45 ! [X0: $i,X1: $i] :
% 0.30/0.45 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.30/0.45 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax7,axiom,
% 0.30/0.45 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax8,axiom,
% 0.30/0.45 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.30/0.45 ( c_iff
% 0.30/0.45 @ ( c_In @ X2
% 0.30/0.45 @ ( c_Repl @ X0
% 0.30/0.45 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.30/0.45 @ ? [X3: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X3 @ X0 )
% 0.30/0.45 @ ( X2
% 0.30/0.45 = ( X1 @ X3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax9,axiom,
% 0.30/0.45 ! [X0: $i > $o] :
% 0.30/0.45 ( ! [X1: $i] :
% 0.30/0.45 ( ( X0 @ X1 )
% 0.30/0.45 => ! [X2: $i] :
% 0.30/0.45 ( ( c_In @ X2 @ X1 )
% 0.30/0.45 => ( X0 @ X2 ) ) )
% 0.30/0.45 => ( ( X0 @ c_Empty )
% 0.30/0.45 => ( ! [X1: $i] :
% 0.30/0.45 ( ( X0 @ X1 )
% 0.30/0.45 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.30/0.45 => ( ! [X1: $i] :
% 0.30/0.45 ( ( X0 @ X1 )
% 0.30/0.45 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.30/0.45 => ( ! [X1: $i] :
% 0.30/0.45 ( ( X0 @ X1 )
% 0.30/0.45 => ! [X2: $i > $i] :
% 0.30/0.45 ( ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X1 )
% 0.30/0.45 => ( X0 @ ( X2 @ X3 ) ) )
% 0.30/0.45 => ( X0
% 0.30/0.45 @ ( c_Repl @ X1
% 0.30/0.45 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.30/0.45 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax10,axiom,
% 0.30/0.45 ! [X0: $i > $o] :
% 0.30/0.45 ( ! [X1: $i] :
% 0.30/0.45 ( ! [X2: $i] :
% 0.30/0.45 ( ( c_In @ X2 @ X1 )
% 0.30/0.45 => ( X0 @ X2 ) )
% 0.30/0.45 => ( X0 @ X1 ) )
% 0.30/0.45 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax11,axiom,
% 0.30/0.45 ( c_False
% 0.30/0.45 = ( ! [X0: $o] : X0 ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax12,axiom,
% 0.30/0.45 ( c_True
% 0.30/0.45 = ( ! [X0: $o] :
% 0.30/0.45 ( X0
% 0.30/0.45 => X0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax13,axiom,
% 0.30/0.45 ( c_not
% 0.30/0.45 = ( ^ [X0: $o] :
% 0.30/0.45 ( X0
% 0.30/0.45 => c_False ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax14,axiom,
% 0.30/0.45 ( c_and
% 0.30/0.45 = ( ^ [X0: $o,X1: $o] :
% 0.30/0.45 ! [X2: $o] :
% 0.30/0.45 ( ( X0
% 0.30/0.45 => ( X1
% 0.30/0.45 => X2 ) )
% 0.30/0.45 => X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax15,axiom,
% 0.30/0.45 ( c_or
% 0.30/0.45 = ( ^ [X0: $o,X1: $o] :
% 0.30/0.45 ! [X2: $o] :
% 0.30/0.45 ( ( X0
% 0.30/0.45 => X2 )
% 0.30/0.45 => ( ( X1
% 0.30/0.45 => X2 )
% 0.30/0.45 => X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax16,axiom,
% 0.30/0.45 ( c_iff
% 0.30/0.45 = ( ^ [X0: $o,X1: $o] :
% 0.30/0.45 ( c_and
% 0.30/0.45 @ ( X0
% 0.30/0.45 => X1 )
% 0.30/0.45 @ ( X1
% 0.30/0.45 => X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax17,axiom,
% 0.30/0.45 ( c_Subq
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ! [X2: $i] :
% 0.30/0.45 ( ( c_In @ X2 @ X0 )
% 0.30/0.45 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax18,axiom,
% 0.30/0.45 ( c_TransSet
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ! [X1: $i] :
% 0.30/0.45 ( ( c_In @ X1 @ X0 )
% 0.30/0.45 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax19,axiom,
% 0.30/0.45 ( c_atleast2
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax20,axiom,
% 0.30/0.45 ( c_atleast3
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax21,axiom,
% 0.30/0.45 ( c_atleast4
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax22,axiom,
% 0.30/0.45 ( c_atleast5
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax23,axiom,
% 0.30/0.45 ( c_atleast6
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax24,axiom,
% 0.30/0.45 ( c_exactly2
% 0.30/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax25,axiom,
% 0.30/0.45 ( c_exactly3
% 0.30/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax26,axiom,
% 0.30/0.45 ( c_exactly4
% 0.30/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax27,axiom,
% 0.30/0.45 ( c_exactly5
% 0.30/0.45 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax28,axiom,
% 0.30/0.45 ( c_exu_i
% 0.30/0.45 = ( ^ [X0: $i > $o] :
% 0.30/0.45 ( c_and
% 0.30/0.45 @ ? [X1: $i] : ( X0 @ X1 )
% 0.30/0.45 @ ! [X1: $i,X2: $i] :
% 0.30/0.45 ( ( X0 @ X1 )
% 0.30/0.45 => ( ( X0 @ X2 )
% 0.30/0.45 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax29,axiom,
% 0.30/0.45 ( c_reflexive_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax30,axiom,
% 0.30/0.45 ( c_irreflexive_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax31,axiom,
% 0.30/0.45 ( c_symmetric_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i,X2: $i] :
% 0.30/0.45 ( ( X0 @ X1 @ X2 )
% 0.30/0.45 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax32,axiom,
% 0.30/0.45 ( c_antisymmetric_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i,X2: $i] :
% 0.30/0.45 ( ( X0 @ X1 @ X2 )
% 0.30/0.45 => ( ( X0 @ X2 @ X1 )
% 0.30/0.45 => ( X1 = X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax33,axiom,
% 0.30/0.45 ( c_transitive_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i,X2: $i,X3: $i] :
% 0.30/0.45 ( ( X0 @ X1 @ X2 )
% 0.30/0.45 => ( ( X0 @ X2 @ X3 )
% 0.30/0.45 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax34,axiom,
% 0.30/0.45 ( c_eqreln_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax35,axiom,
% 0.30/0.45 ( c_per_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax36,axiom,
% 0.30/0.45 ( c_linear_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax37,axiom,
% 0.30/0.45 ( c_trichotomous_or_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] :
% 0.30/0.45 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax38,axiom,
% 0.30/0.45 ( c_partialorder_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax39,axiom,
% 0.30/0.45 ( c_totalorder_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax40,axiom,
% 0.30/0.45 ( c_strictpartialorder_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax41,axiom,
% 0.30/0.45 ( c_stricttotalorder_i
% 0.30/0.45 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax42,axiom,
% 0.30/0.45 ( c_If_i
% 0.30/0.45 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.30/0.45 ( c_Eps_i
% 0.30/0.45 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax43,axiom,
% 0.30/0.45 ( c_exactly1of2
% 0.30/0.45 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax44,axiom,
% 0.30/0.45 ( c_exactly1of3
% 0.30/0.45 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax45,axiom,
% 0.30/0.45 ( c_nIn
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax46,axiom,
% 0.30/0.45 ( c_nSubq
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax47,axiom,
% 0.30/0.45 ( c_UPair
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.30/0.45 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax48,axiom,
% 0.30/0.45 ( c_Sing
% 0.30/0.45 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax49,axiom,
% 0.30/0.45 ( c_binunion
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax50,axiom,
% 0.30/0.45 ( c_SetAdjoin
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax51,axiom,
% 0.30/0.45 ( c_famunion
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i] :
% 0.30/0.45 ( c_Union
% 0.30/0.45 @ ( c_Repl @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax52,axiom,
% 0.30/0.45 ( c_Sep
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o] :
% 0.30/0.45 ( c_If_i
% 0.30/0.45 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.30/0.45 @ ( c_Repl @ X0
% 0.30/0.45 @ ^ [X2: $i] :
% 0.30/0.45 ( ^ [X3: $i] :
% 0.30/0.45 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.30/0.45 @ ( c_Eps_i
% 0.30/0.45 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.30/0.45 @ X2 ) )
% 0.30/0.45 @ c_Empty ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax53,axiom,
% 0.30/0.45 ( c_ReplSep
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.30/0.45 ( c_Repl
% 0.30/0.45 @ ( c_Sep @ X0
% 0.30/0.45 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.30/0.45 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax54,axiom,
% 0.30/0.45 ( c_binintersect
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_Sep @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax55,axiom,
% 0.30/0.45 ( c_setminus
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_Sep @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax56,axiom,
% 0.30/0.45 ( c_inj
% 0.30/0.45 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.30/0.45 ( c_and
% 0.30/0.45 @ ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X0 )
% 0.30/0.45 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.30/0.45 @ ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X0 )
% 0.30/0.45 => ! [X4: $i] :
% 0.30/0.45 ( ( c_In @ X4 @ X0 )
% 0.30/0.45 => ( ( ( X2 @ X3 )
% 0.30/0.45 = ( X2 @ X4 ) )
% 0.30/0.45 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax57,axiom,
% 0.30/0.45 ( c_bij
% 0.30/0.45 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.30/0.45 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.30/0.45 @ ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X1 )
% 0.30/0.45 => ? [X4: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X4 @ X0 )
% 0.30/0.45 @ ( ( X2 @ X4 )
% 0.30/0.45 = X3 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax58,axiom,
% 0.30/0.45 ( c_atleastp
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax59,axiom,
% 0.30/0.45 ( c_equip
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax60,axiom,
% 0.30/0.45 ( c_In_rec_poly_G_i
% 0.30/0.45 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.30/0.45 ! [X3: $i > $i > $o] :
% 0.30/0.45 ( ! [X4: $i,X5: $i > $i] :
% 0.30/0.45 ( ! [X6: $i] :
% 0.30/0.45 ( ( c_In @ X6 @ X4 )
% 0.30/0.45 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.30/0.45 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.30/0.45 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax61,axiom,
% 0.30/0.45 ( c_In_rec_poly_i
% 0.30/0.45 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.30/0.45 ( c_Eps_i
% 0.30/0.45 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax62,axiom,
% 0.30/0.45 ( c_ordsucc
% 0.30/0.45 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax63,axiom,
% 0.30/0.45 ( c_nat_p
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ! [X1: $i > $o] :
% 0.30/0.45 ( ( X1 @ c_Empty )
% 0.30/0.45 => ( ! [X2: $i] :
% 0.30/0.45 ( ( X1 @ X2 )
% 0.30/0.45 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.30/0.45 => ( X1 @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax64,axiom,
% 0.30/0.45 ( c_nat_primrec
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.30/0.45 ( c_In_rec_poly_i
% 0.30/0.45 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax65,axiom,
% 0.30/0.45 ( c_add_nat
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_nat_primrec @ X0
% 0.30/0.45 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.30/0.45 @ X1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax66,axiom,
% 0.30/0.45 ( c_mul_nat
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_nat_primrec @ c_Empty
% 0.30/0.45 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.30/0.45 @ X1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax67,axiom,
% 0.30/0.45 ( c_ordinal
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( c_and @ ( c_TransSet @ X0 )
% 0.30/0.45 @ ! [X1: $i] :
% 0.30/0.45 ( ( c_In @ X1 @ X0 )
% 0.30/0.45 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax68,axiom,
% 0.30/0.45 ( c_V_
% 0.30/0.45 = ( c_In_rec_poly_i
% 0.30/0.45 @ ^ [X0: $i,X1: $i > $i] :
% 0.30/0.45 ( c_famunion @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax69,axiom,
% 0.30/0.45 ( c_Inj1
% 0.30/0.45 = ( c_In_rec_poly_i
% 0.30/0.45 @ ^ [X0: $i,X1: $i > $i] :
% 0.30/0.45 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.30/0.45 @ ( c_Repl @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax70,axiom,
% 0.30/0.45 ( c_Inj0
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( c_Repl @ X0
% 0.30/0.45 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax71,axiom,
% 0.30/0.45 ( c_Unj
% 0.30/0.45 = ( c_In_rec_poly_i
% 0.30/0.45 @ ^ [X0: $i,X1: $i > $i] :
% 0.30/0.45 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.30/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax72,axiom,
% 0.30/0.45 ( c_combine_funcs
% 0.30/0.45 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.30/0.45 ( c_If_i
% 0.30/0.45 @ ( X4
% 0.30/0.45 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.30/0.45 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.30/0.45 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax73,axiom,
% 0.30/0.45 ( c_setsum
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_binunion
% 0.30/0.45 @ ( c_Repl @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.30/0.45 @ ( c_Repl @ X1
% 0.30/0.45 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax74,axiom,
% 0.30/0.45 ( c_proj0
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( c_ReplSep @ X0
% 0.30/0.45 @ ^ [X1: $i] :
% 0.30/0.45 ? [X2: $i] :
% 0.30/0.45 ( ( c_Inj0 @ X2 )
% 0.30/0.45 = X1 )
% 0.30/0.45 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax75,axiom,
% 0.30/0.45 ( c_proj1
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( c_ReplSep @ X0
% 0.30/0.45 @ ^ [X1: $i] :
% 0.30/0.45 ? [X2: $i] :
% 0.30/0.45 ( ( c_Inj1 @ X2 )
% 0.30/0.45 = X1 )
% 0.30/0.45 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax76,axiom,
% 0.30/0.45 ( c_binrep
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax77,axiom,
% 0.30/0.45 ( c_lam
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i] :
% 0.30/0.45 ( c_famunion @ X0
% 0.30/0.45 @ ^ [X2: $i] :
% 0.30/0.45 ( c_Repl @ ( X1 @ X2 )
% 0.30/0.45 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax78,axiom,
% 0.30/0.45 ( c_setprod
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_lam @ X0
% 0.30/0.45 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax79,axiom,
% 0.30/0.45 ( c_ap
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_ReplSep @ X0
% 0.30/0.45 @ ^ [X2: $i] :
% 0.30/0.45 ? [X3: $i] :
% 0.30/0.45 ( X2
% 0.30/0.45 = ( c_setsum @ X1 @ X3 ) )
% 0.30/0.45 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax80,axiom,
% 0.30/0.45 ( c_setsum_p
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.30/0.45 = X0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax81,axiom,
% 0.30/0.45 ( c_tuple_p
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ! [X2: $i] :
% 0.30/0.45 ( ( c_In @ X2 @ X1 )
% 0.30/0.45 => ? [X3: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X3 @ X0 )
% 0.30/0.45 @ ? [X4: $i] :
% 0.30/0.45 ( X2
% 0.30/0.45 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax82,axiom,
% 0.30/0.45 ( c_Pi
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i] :
% 0.30/0.45 ( c_Sep
% 0.30/0.45 @ ( c_Power
% 0.30/0.45 @ ( c_lam @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.30/0.45 @ ^ [X2: $i] :
% 0.30/0.45 ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X0 )
% 0.30/0.45 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax83,axiom,
% 0.30/0.45 ( c_setexp
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_Pi @ X1
% 0.30/0.45 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax84,axiom,
% 0.30/0.45 ( c_Sep2
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.30/0.45 ( c_Sep
% 0.30/0.45 @ ( c_lam @ X0
% 0.30/0.45 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.30/0.45 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax85,axiom,
% 0.30/0.45 ( c_set_of_pairs
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ! [X1: $i] :
% 0.30/0.45 ( ( c_In @ X1 @ X0 )
% 0.30/0.45 => ? [X2: $i,X3: $i] :
% 0.30/0.45 ( X1
% 0.30/0.45 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.30/0.45 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax86,axiom,
% 0.30/0.45 ( c_lam2
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.30/0.45 ( c_lam @ X0
% 0.30/0.45 @ ^ [X3: $i] :
% 0.30/0.45 ( c_lam @ ( X1 @ X3 )
% 0.30/0.45 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax87,axiom,
% 0.30/0.45 ( c_PNoEq_
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.30/0.45 ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X0 )
% 0.30/0.45 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax88,axiom,
% 0.30/0.45 ( c_PNoLt_
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.30/0.45 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax89,axiom,
% 0.30/0.45 ( c_PNoLt
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax90,axiom,
% 0.30/0.45 ( c_PNoLe
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax91,axiom,
% 0.30/0.45 ( c_PNo_downc
% 0.30/0.45 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.30/0.45 ? [X3: $i] :
% 0.30/0.45 ( c_and @ ( c_ordinal @ X3 )
% 0.30/0.45 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax92,axiom,
% 0.30/0.45 ( c_PNo_upc
% 0.30/0.45 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.30/0.45 ? [X3: $i] :
% 0.30/0.45 ( c_and @ ( c_ordinal @ X3 )
% 0.30/0.45 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax93,axiom,
% 0.30/0.45 ( c_SNoElts_
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( c_binunion @ X0
% 0.30/0.45 @ ( c_Repl @ X0
% 0.30/0.45 @ ^ [X1: $i] :
% 0.30/0.45 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.30/0.45 @ X1 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax94,axiom,
% 0.30/0.45 ( c_SNo_
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.30/0.45 @ ! [X2: $i] :
% 0.30/0.45 ( ( c_In @ X2 @ X0 )
% 0.30/0.45 => ( c_exactly1of2
% 0.30/0.45 @ ( c_In
% 0.30/0.45 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.30/0.45 @ X2 )
% 0.30/0.45 @ X1 )
% 0.30/0.45 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax95,axiom,
% 0.30/0.45 ( c_PSNo
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $o] :
% 0.30/0.45 ( c_binunion
% 0.30/0.45 @ ( c_Sep @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.30/0.45 @ ( c_ReplSep @ X0
% 0.30/0.45 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.30/0.45 @ ^ [X2: $i] :
% 0.30/0.45 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.30/0.45 @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax96,axiom,
% 0.30/0.45 ( c_SNo
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax97,axiom,
% 0.30/0.45 ( c_SNoLev
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ( c_Eps_i
% 0.30/0.45 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax98,axiom,
% 0.30/0.45 ( c_SNoEq_
% 0.30/0.45 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.30/0.45 ( c_PNoEq_ @ X0
% 0.30/0.45 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.30/0.45 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax99,axiom,
% 0.30/0.45 ( c_SNoLt
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.30/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.30/0.45 @ ( c_SNoLev @ X1 )
% 0.30/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax100,axiom,
% 0.30/0.45 ( c_SNoLe
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.30/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.30/0.45 @ ( c_SNoLev @ X1 )
% 0.30/0.45 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax101,axiom,
% 0.30/0.45 ( c_binop_on
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.30/0.45 ! [X2: $i] :
% 0.30/0.45 ( ( c_In @ X2 @ X0 )
% 0.30/0.45 => ! [X3: $i] :
% 0.30/0.45 ( ( c_In @ X3 @ X0 )
% 0.30/0.45 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax102,axiom,
% 0.30/0.45 ( c_Loop
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.30/0.45 ( c_and
% 0.30/0.45 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.30/0.45 @ ! [X5: $i] :
% 0.30/0.45 ( ( c_In @ X5 @ X0 )
% 0.30/0.45 => ( c_and
% 0.30/0.45 @ ( ( X1 @ X4 @ X5 )
% 0.30/0.45 = X5 )
% 0.30/0.45 @ ( ( X1 @ X5 @ X4 )
% 0.30/0.45 = X5 ) ) ) )
% 0.30/0.45 @ ! [X5: $i] :
% 0.30/0.45 ( ( c_In @ X5 @ X0 )
% 0.30/0.45 => ! [X6: $i] :
% 0.30/0.45 ( ( c_In @ X6 @ X0 )
% 0.30/0.45 => ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.30/0.45 = X6 )
% 0.30/0.45 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.30/0.45 = X6 ) )
% 0.30/0.45 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.30/0.45 = X5 ) )
% 0.30/0.45 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.30/0.45 = X5 ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax103,axiom,
% 0.30/0.45 ( c_Loop_with_defs
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.30/0.45 ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.30/0.45 @ ! [X14: $i] :
% 0.30/0.45 ( ( c_In @ X14 @ X0 )
% 0.30/0.45 => ! [X15: $i] :
% 0.30/0.45 ( ( c_In @ X15 @ X0 )
% 0.30/0.45 => ( ( X5 @ X14 @ X15 )
% 0.30/0.45 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.30/0.45 @ ! [X14: $i] :
% 0.30/0.45 ( ( c_In @ X14 @ X0 )
% 0.30/0.45 => ! [X15: $i] :
% 0.30/0.45 ( ( c_In @ X15 @ X0 )
% 0.30/0.45 => ! [X16: $i] :
% 0.30/0.45 ( ( c_In @ X16 @ X0 )
% 0.30/0.45 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.30/0.45 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.30/0.45 @ ! [X14: $i] :
% 0.30/0.45 ( ( c_In @ X14 @ X0 )
% 0.30/0.45 => ! [X15: $i] :
% 0.30/0.45 ( ( c_In @ X15 @ X0 )
% 0.30/0.45 => ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( c_and
% 0.30/0.45 @ ( ( X7 @ X14 @ X15 )
% 0.30/0.45 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.30/0.45 @ ( ( X10 @ X14 @ X15 )
% 0.30/0.45 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.30/0.45 @ ( ( X11 @ X14 @ X15 )
% 0.30/0.45 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.30/0.45 @ ( ( X12 @ X14 @ X15 )
% 0.30/0.45 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.30/0.45 @ ( ( X13 @ X14 @ X15 )
% 0.30/0.45 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.30/0.45 @ ! [X14: $i] :
% 0.30/0.45 ( ( c_In @ X14 @ X0 )
% 0.30/0.45 => ! [X15: $i] :
% 0.30/0.45 ( ( c_In @ X15 @ X0 )
% 0.30/0.45 => ! [X16: $i] :
% 0.30/0.45 ( ( c_In @ X16 @ X0 )
% 0.30/0.45 => ( c_and
% 0.30/0.45 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.30/0.45 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.30/0.45 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.30/0.45 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax104,axiom,
% 0.30/0.45 ( c_Loop_with_defs_cex1
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.30/0.45 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.30/0.45 @ ? [X14: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X14 @ X0 )
% 0.30/0.45 @ ? [X15: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X15 @ X0 )
% 0.30/0.45 @ ? [X16: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X16 @ X0 )
% 0.30/0.45 @ ? [X17: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X17 @ X0 )
% 0.30/0.45 @ ( c_not
% 0.30/0.45 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.30/0.45 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax105,axiom,
% 0.30/0.45 ( c_Loop_with_defs_cex2
% 0.30/0.45 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 0.30/0.45 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.30/0.45 @ ? [X14: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X14 @ X0 )
% 0.30/0.45 @ ? [X15: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X15 @ X0 )
% 0.30/0.45 @ ? [X16: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X16 @ X0 )
% 0.30/0.45 @ ? [X17: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X17 @ X0 )
% 0.30/0.45 @ ? [X18: $i] :
% 0.30/0.45 ( c_and @ ( c_In @ X18 @ X0 )
% 0.30/0.45 @ ( c_not
% 0.30/0.45 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.30/0.45 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax106,axiom,
% 0.30/0.45 ( c_combinator
% 0.30/0.45 = ( ^ [X0: $i] :
% 0.30/0.45 ! [X1: $i > $o] :
% 0.30/0.45 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.30/0.45 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.30/0.45 => ( ! [X2: $i,X3: $i] :
% 0.30/0.45 ( ( X1 @ X2 )
% 0.30/0.45 => ( ( X1 @ X3 )
% 0.30/0.45 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.30/0.45 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax107,axiom,
% 0.30/0.45 ( c_combinator_equiv
% 0.30/0.45 = ( ^ [X0: $i,X1: $i] :
% 0.30/0.45 ! [X2: $i > $i > $o] :
% 0.30/0.45 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.30/0.45 ( ( c_per_i @ X2 )
% 0.30/0.45 => ( ! [X6: $i] :
% 0.30/0.45 ( ( c_combinator @ X6 )
% 0.30/0.45 => ( X2 @ X6 @ X6 ) )
% 0.30/0.45 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.30/0.45 ( ( c_combinator @ X6 )
% 0.30/0.45 => ( ( c_combinator @ X7 )
% 0.30/0.45 => ( ( c_combinator @ X8 )
% 0.30/0.45 => ( ( c_combinator @ X9 )
% 0.30/0.45 => ( ( X2 @ X6 @ X8 )
% 0.30/0.45 => ( ( X2 @ X7 @ X9 )
% 0.30/0.45 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.30/0.45 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.30/0.45 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.30/0.45 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.30/0.45 @ ( c_Inj0 @ c_Empty )
% 0.30/0.45 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.30/0.45 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(ax108,axiom,
% 0.30/0.45 ( c_equip_mod
% 0.30/0.45 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.30/0.45 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(conj,conjecture,
% 0.30/0.45 ( c_not
% 0.30/0.45 @ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
% 0.30/0.45 ( ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X1 @ X7 @ ( X1 @ ( X1 @ ( X1 @ X5 @ X5 ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X6 @ ( X1 @ X5 @ ( X1 @ X5 @ X7 ) ) ) @ X5 ) ) @ X7 ) @ ( X1 @ ( X4 @ X6 ) @ X7 ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) @ ( X1 @ X6 @ X6 ) ) @ ( X1 @ X6 @ ( X1 @ X7 @ X5 ) ) ) @ X5 ) ) ) @ X7 ) ) ) @ X5 ) ) @ X6 ) @ ( X1 @ X6 @ ( X1 @ X5 @ ( X1 @ ( X1 @ ( X4 @ X5 ) @ ( X1 @ ( X1 @ X6 @ X6 ) @ X6 ) ) @ X5 ) ) ) ) @ ( X4 @ ( X4 @ X6 ) ) ) @ X5 ) )
% 0.30/0.45 = ( X4 @ ( X4 @ X7 ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 2.05/1.39 ---- Embedded in THF ---
% 2.05/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.05/1.39 %%% Generated on Tue Feb 24 14:48:41 EST 2026
% 2.05/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 2.05/1.39 %%% Logic specification used:
% 2.05/1.39 %%% thf(spec, logic, $$dhol).
% 2.05/1.39
% 2.05/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2DTF30392.p
% 2.05/1.39 thf(c_Eps_i_tp, type, c_Eps_i: (($i > $o) > $i)).
% 2.05/1.39 thf(c_False_tp, type, c_False: $o).
% 2.05/1.39 thf(c_True_tp, type, c_True: $o).
% 2.05/1.39 thf(c_not_tp, type, c_not: ($o > $o)).
% 2.05/1.39 thf(c_and_tp, type, c_and: ($o > ($o > $o))).
% 2.05/1.39 thf(c_or_tp, type, c_or: ($o > ($o > $o))).
% 2.05/1.39 thf(c_iff_tp, type, c_iff: ($o > ($o > $o))).
% 2.05/1.39 thf(c_In_tp, type, c_In: ($i > ($i > $o))).
% 2.05/1.39 thf(c_Subq_tp, type, c_Subq: ($i > ($i > $o))).
% 2.05/1.39 thf(c_Empty_tp, type, c_Empty: $i).
% 2.05/1.39 thf(c_Union_tp, type, c_Union: ($i > $i)).
% 2.05/1.39 thf(c_Power_tp, type, c_Power: ($i > $i)).
% 2.05/1.39 thf(c_Repl_tp, type, c_Repl: ($i > (($i > $i) > $i))).
% 2.05/1.39 thf(c_TransSet_tp, type, c_TransSet: ($i > $o)).
% 2.05/1.39 thf(c_atleast2_tp, type, c_atleast2: ($i > $o)).
% 2.05/1.39 thf(c_atleast3_tp, type, c_atleast3: ($i > $o)).
% 2.05/1.39 thf(c_atleast4_tp, type, c_atleast4: ($i > $o)).
% 2.05/1.39 thf(c_atleast5_tp, type, c_atleast5: ($i > $o)).
% 2.05/1.39 thf(c_atleast6_tp, type, c_atleast6: ($i > $o)).
% 2.05/1.39 thf(c_exactly2_tp, type, c_exactly2: ($i > $o)).
% 2.05/1.39 thf(c_exactly3_tp, type, c_exactly3: ($i > $o)).
% 2.05/1.39 thf(c_exactly4_tp, type, c_exactly4: ($i > $o)).
% 2.05/1.39 thf(c_exactly5_tp, type, c_exactly5: ($i > $o)).
% 2.05/1.39 thf(c_exu_i_tp, type, c_exu_i: (($i > $o) > $o)).
% 2.05/1.39 thf(c_reflexive_i_tp, type, c_reflexive_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_irreflexive_i_tp, type, c_irreflexive_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_symmetric_i_tp, type, c_symmetric_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_antisymmetric_i_tp, type, c_antisymmetric_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_transitive_i_tp, type, c_transitive_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_eqreln_i_tp, type, c_eqreln_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_per_i_tp, type, c_per_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_linear_i_tp, type, c_linear_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_trichotomous_or_i_tp, type, c_trichotomous_or_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_partialorder_i_tp, type, c_partialorder_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_totalorder_i_tp, type, c_totalorder_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_strictpartialorder_i_tp, type, c_strictpartialorder_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_stricttotalorder_i_tp, type, c_stricttotalorder_i: (($i > ($i > $o)) > $o)).
% 2.05/1.39 thf(c_If_i_tp, type, c_If_i: ($o > ($i > ($i > $i)))).
% 2.05/1.39 thf(c_exactly1of2_tp, type, c_exactly1of2: ($o > ($o > $o))).
% 2.05/1.39 thf(c_exactly1of3_tp, type, c_exactly1of3: ($o > ($o > ($o > $o)))).
% 2.05/1.39 thf(c_nIn_tp, type, c_nIn: ($i > ($i > $o))).
% 2.05/1.39 thf(c_nSubq_tp, type, c_nSubq: ($i > ($i > $o))).
% 2.05/1.39 thf(c_UPair_tp, type, c_UPair: ($i > ($i > $i))).
% 2.05/1.39 thf(c_Sing_tp, type, c_Sing: ($i > $i)).
% 2.05/1.39 thf(c_binunion_tp, type, c_binunion: ($i > ($i > $i))).
% 2.05/1.39 thf(c_SetAdjoin_tp, type, c_SetAdjoin: ($i > ($i > $i))).
% 2.05/1.39 thf(c_famunion_tp, type, c_famunion: ($i > (($i > $i) > $i))).
% 2.05/1.39 thf(c_Sep_tp, type, c_Sep: ($i > (($i > $o) > $i))).
% 2.05/1.39 thf(c_ReplSep_tp, type, c_ReplSep: ($i > (($i > $o) > (($i > $i) > $i)))).
% 2.05/1.39 thf(c_binintersect_tp, type, c_binintersect: ($i > ($i > $i))).
% 2.05/1.39 thf(c_setminus_tp, type, c_setminus: ($i > ($i > $i))).
% 2.05/1.39 thf(c_inj_tp, type, c_inj: ($i > ($i > (($i > $i) > $o)))).
% 2.05/1.39 thf(c_bij_tp, type, c_bij: ($i > ($i > (($i > $i) > $o)))).
% 2.05/1.39 thf(c_atleastp_tp, type, c_atleastp: ($i > ($i > $o))).
% 2.05/1.39 thf(c_equip_tp, type, c_equip: ($i > ($i > $o))).
% 2.05/1.39 thf(c_In_rec_poly_G_i_tp, type, c_In_rec_poly_G_i: (($i > (($i > $i) > $i)) > ($i > ($i > $o)))).
% 2.05/1.39 thf(c_In_rec_poly_i_tp, type, c_In_rec_poly_i: (($i > (($i > $i) > $i)) > ($i > $i))).
% 2.05/1.39 thf(c_ordsucc_tp, type, c_ordsucc: ($i > $i)).
% 2.05/1.39 thf(c_nat_p_tp, type, c_nat_p: ($i > $o)).
% 2.05/1.39 thf(c_nat_primrec_tp, type, c_nat_primrec: ($i > (($i > ($i > $i)) > ($i > $i)))).
% 2.05/1.39 thf(c_add_nat_tp, type, c_add_nat: ($i > ($i > $i))).
% 2.05/1.39 thf(c_mul_nat_tp, type, c_mul_nat: ($i > ($i > $i))).
% 2.05/1.39 thf(c_ordinal_tp, type, c_ordinal: ($i > $o)).
% 2.05/1.39 thf(c_V__tp, type, c_V_: ($i > $i)).
% 2.05/1.39 thf(c_Inj1_tp, type, c_Inj1: ($i > $i)).
% 2.05/1.39 thf(c_Inj0_tp, type, c_Inj0: ($i > $i)).
% 2.05/1.39 thf(c_Unj_tp, type, c_Unj: ($i > $i)).
% 2.05/1.39 thf(c_combine_funcs_tp, type, c_combine_funcs: ($i > ($i > (($i > $i) > (($i > $i) > ($i > $i)))))).
% 2.05/1.39 thf(c_setsum_tp, type, c_setsum: ($i > ($i > $i))).
% 2.05/1.39 thf(c_proj0_tp, type, c_proj0: ($i > $i)).
% 2.05/1.39 thf(c_proj1_tp, type, c_proj1: ($i > $i)).
% 2.05/1.39 thf(c_binrep_tp, type, c_binrep: ($i > ($i > $i))).
% 2.05/1.39 thf(c_lam_tp, type, c_lam: ($i > (($i > $i) > $i))).
% 2.05/1.39 thf(c_setprod_tp, type, c_setprod: ($i > ($i > $i))).
% 2.05/1.39 thf(c_ap_tp, type, c_ap: ($i > ($i > $i))).
% 2.05/1.39 thf(c_setsum_p_tp, type, c_setsum_p: ($i > $o)).
% 2.05/1.39 thf(c_tuple_p_tp, type, c_tuple_p: ($i > ($i > $o))).
% 2.05/1.39 thf(c_Pi_tp, type, c_Pi: ($i > (($i > $i) > $i))).
% 2.05/1.39 thf(c_setexp_tp, type, c_setexp: ($i > ($i > $i))).
% 2.05/1.39 thf(c_Sep2_tp, type, c_Sep2: ($i > (($i > $i) > (($i > ($i > $o)) > $i)))).
% 2.05/1.39 thf(c_set_of_pairs_tp, type, c_set_of_pairs: ($i > $o)).
% 2.05/1.39 thf(c_lam2_tp, type, c_lam2: ($i > (($i > $i) > (($i > ($i > $i)) > $i)))).
% 2.05/1.39 thf(c_PNoEq__tp, type, c_PNoEq_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 2.05/1.39 thf(c_PNoLt__tp, type, c_PNoLt_: ($i > (($i > $o) > (($i > $o) > $o)))).
% 2.05/1.39 thf(c_PNoLt_tp, type, c_PNoLt: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 2.05/1.39 thf(c_PNoLe_tp, type, c_PNoLe: ($i > (($i > $o) > ($i > (($i > $o) > $o))))).
% 2.05/1.39 thf(c_PNo_downc_tp, type, c_PNo_downc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 2.05/1.39 thf(c_PNo_upc_tp, type, c_PNo_upc: (($i > (($i > $o) > $o)) > ($i > (($i > $o) > $o)))).
% 2.05/1.39 thf(c_SNoElts__tp, type, c_SNoElts_: ($i > $i)).
% 2.05/1.39 thf(c_SNo__tp, type, c_SNo_: ($i > ($i > $o))).
% 2.05/1.39 thf(c_PSNo_tp, type, c_PSNo: ($i > (($i > $o) > $i))).
% 2.05/1.39 thf(c_SNo_tp, type, c_SNo: ($i > $o)).
% 2.05/1.39 thf(c_SNoLev_tp, type, c_SNoLev: ($i > $i)).
% 2.05/1.39 thf(c_SNoEq__tp, type, c_SNoEq_: ($i > ($i > ($i > $o)))).
% 2.05/1.39 thf(c_SNoLt_tp, type, c_SNoLt: ($i > ($i > $o))).
% 2.05/1.39 thf(c_SNoLe_tp, type, c_SNoLe: ($i > ($i > $o))).
% 2.05/1.39 thf(c_binop_on_tp, type, c_binop_on: ($i > (($i > ($i > $i)) > $o))).
% 2.05/1.39 thf(c_Loop_tp, type, c_Loop: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > $o)))))).
% 2.05/1.39 thf(c_Loop_with_defs_tp, type, c_Loop_with_defs: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.05/1.39 thf(c_Loop_with_defs_cex1_tp, type, c_Loop_with_defs_cex1: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.05/1.39 thf(c_Loop_with_defs_cex2_tp, type, c_Loop_with_defs_cex2: ($i > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > ($i > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > ($i > $i))) > (($i > ($i > ($i > $i))) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > (($i > ($i > $i)) > $o))))))))))))))).
% 2.05/1.39 thf(c_combinator_tp, type, c_combinator: ($i > $o)).
% 2.05/1.39 thf(c_combinator_equiv_tp, type, c_combinator_equiv: ($i > ($i > $o))).
% 2.05/1.39 thf(c_equip_mod_tp, type, c_equip_mod: ($i > ($i > ($i > $o)))).
% 2.05/1.39 thf(ax1, axiom, (! [X0:($i > $o),X1:$i]: (((X0 @ X1) => (X0 @ (c_Eps_i @ X0)))))).
% 2.05/1.39 thf(ax2, axiom, (! [X0:$o]: (((c_not @ (c_not @ X0)) => X0)))).
% 2.05/1.39 thf(ax3, axiom, (! [X0:$o,X1:$o]: ((((c_iff @ X0) @ X1) => (X0 = X1))))).
% 2.05/1.39 thf(ax4, axiom, (! [X0:$i,X1:$i]: ((((c_Subq @ X0) @ X1) => (((c_Subq @ X1) @ X0) => (X0 = X1)))))).
% 2.05/1.39 thf(ax5, axiom, (c_not @ (? [X0:$i]: (((c_In @ X0) @ c_Empty))))).
% 2.05/1.39 thf(ax6, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ (? [X2:$i]: (((c_and @ ((c_In @ X1) @ X2)) @ ((c_In @ X2) @ X0)))))))).
% 2.05/1.39 thf(ax7, axiom, (! [X0:$i,X1:$i]: (((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))))).
% 2.05/1.39 thf(ax8, axiom, (! [X0:$i,X1:($i > $i),X2:$i]: (((c_iff @ ((c_In @ X2) @ ((c_Repl @ X0) @ (^ [X3:$i]: ((X1 @ X3)))))) @ (? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ (X2 = (X1 @ X3))))))))).
% 2.05/1.39 thf(ax9, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((X0 @ X1) => (! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2))))))) => ((X0 @ c_Empty) => ((! [X1:$i]: (((X0 @ X1) => (X0 @ (c_Union @ X1))))) => ((! [X1:$i]: (((X0 @ X1) => (X0 @ (c_Power @ X1))))) => ((! [X1:$i]: (((X0 @ X1) => (! [X2:($i > $i)]: (((! [X3:$i]: ((((c_In @ X3) @ X1) => (X0 @ (X2 @ X3))))) => (X0 @ ((c_Repl @ X1) @ (^ [X3:$i]: ((X2 @ X3))))))))))) => (! [X1:$i]: ((X0 @ X1))))))))))).
% 2.05/1.39 thf(ax10, axiom, (! [X0:($i > $o)]: (((! [X1:$i]: (((! [X2:$i]: ((((c_In @ X2) @ X1) => (X0 @ X2)))) => (X0 @ X1)))) => (! [X1:$i]: ((X0 @ X1))))))).
% 2.05/1.39 thf(ax11, axiom, (c_False = (! [X0:$o]: (X0)))).
% 2.05/1.39 thf(ax12, axiom, (c_True = (! [X0:$o]: ((X0 => X0))))).
% 2.05/1.39 thf(ax13, axiom, (c_not = (^ [X0:$o]: ((X0 => c_False))))).
% 2.05/1.39 thf(ax14, axiom, (c_and = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => (X1 => X2)) => X2))))))).
% 2.05/1.39 thf(ax15, axiom, (c_or = (^ [X0:$o,X1:$o]: ((! [X2:$o]: (((X0 => X2) => ((X1 => X2) => X2)))))))).
% 2.05/1.39 thf(ax16, axiom, (c_iff = (^ [X0:$o,X1:$o]: (((c_and @ (X0 => X1)) @ (X1 => X0)))))).
% 2.05/1.39 thf(ax17, axiom, (c_Subq = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax18, axiom, (c_TransSet = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => ((c_Subq @ X1) @ X0)))))))).
% 2.05/1.39 thf(ax19, axiom, (c_atleast2 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_In @ X1) @ X0)) @ (c_not @ ((c_Subq @ X0) @ (c_Power @ X1)))))))))).
% 2.05/1.39 thf(ax20, axiom, (c_atleast3 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast2 @ X1))))))))).
% 2.05/1.39 thf(ax21, axiom, (c_atleast4 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast3 @ X1))))))))).
% 2.05/1.39 thf(ax22, axiom, (c_atleast5 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast4 @ X1))))))))).
% 2.05/1.39 thf(ax23, axiom, (c_atleast6 = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ ((c_Subq @ X1) @ X0)) @ ((c_and @ (c_not @ ((c_Subq @ X0) @ X1))) @ (c_atleast5 @ X1))))))))).
% 2.05/1.39 thf(ax24, axiom, (c_exactly2 = (^ [X0:$i]: (((c_and @ (c_atleast2 @ X0)) @ (c_not @ (c_atleast3 @ X0))))))).
% 2.05/1.39 thf(ax25, axiom, (c_exactly3 = (^ [X0:$i]: (((c_and @ (c_atleast3 @ X0)) @ (c_not @ (c_atleast4 @ X0))))))).
% 2.05/1.39 thf(ax26, axiom, (c_exactly4 = (^ [X0:$i]: (((c_and @ (c_atleast4 @ X0)) @ (c_not @ (c_atleast5 @ X0))))))).
% 2.05/1.39 thf(ax27, axiom, (c_exactly5 = (^ [X0:$i]: (((c_and @ (c_atleast5 @ X0)) @ (c_not @ (c_atleast6 @ X0))))))).
% 2.05/1.39 thf(ax28, axiom, (c_exu_i = (^ [X0:($i > $o)]: (((c_and @ (? [X1:$i]: ((X0 @ X1)))) @ (! [X1:$i,X2:$i]: (((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))))))).
% 2.05/1.39 thf(ax29, axiom, (c_reflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: (((X0 @ X1) @ X1))))))).
% 2.05/1.39 thf(ax30, axiom, (c_irreflexive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i]: ((c_not @ ((X0 @ X1) @ X1)))))))).
% 2.05/1.39 thf(ax31, axiom, (c_symmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => ((X0 @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax32, axiom, (c_antisymmetric_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X1) => (X1 = X2))))))))).
% 2.05/1.39 thf(ax33, axiom, (c_transitive_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i,X3:$i]: ((((X0 @ X1) @ X2) => (((X0 @ X2) @ X3) => ((X0 @ X1) @ X3))))))))).
% 2.05/1.39 thf(ax34, axiom, (c_eqreln_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_symmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 2.05/1.39 thf(ax35, axiom, (c_per_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_symmetric_i @ X0)) @ (c_transitive_i @ X0)))))).
% 2.05/1.39 thf(ax36, axiom, (c_linear_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((X0 @ X1) @ X2)) @ ((X0 @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax37, axiom, (c_trichotomous_or_i = (^ [X0:($i > ($i > $o))]: ((! [X1:$i,X2:$i]: (((c_or @ ((c_or @ ((X0 @ X1) @ X2)) @ (X1 = X2))) @ ((X0 @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax38, axiom, (c_partialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ ((c_and @ (c_reflexive_i @ X0)) @ (c_antisymmetric_i @ X0))) @ (c_transitive_i @ X0)))))).
% 2.05/1.39 thf(ax39, axiom, (c_totalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_partialorder_i @ X0)) @ (c_linear_i @ X0)))))).
% 2.05/1.39 thf(ax40, axiom, (c_strictpartialorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_irreflexive_i @ X0)) @ (c_transitive_i @ X0)))))).
% 2.05/1.39 thf(ax41, axiom, (c_stricttotalorder_i = (^ [X0:($i > ($i > $o))]: (((c_and @ (c_strictpartialorder_i @ X0)) @ (c_trichotomous_or_i @ X0)))))).
% 2.05/1.39 thf(ax42, axiom, (c_If_i = (^ [X0:$o,X1:$i,X2:$i]: ((c_Eps_i @ (^ [X3:$i]: (((c_or @ ((c_and @ X0) @ (X3 = X1))) @ ((c_and @ (c_not @ X0)) @ (X3 = X2)))))))))).
% 2.05/1.39 thf(ax43, axiom, (c_exactly1of2 = (^ [X0:$o,X1:$o]: (((c_or @ ((c_and @ X0) @ (c_not @ X1))) @ ((c_and @ (c_not @ X0)) @ X1)))))).
% 2.05/1.39 thf(ax44, axiom, (c_exactly1of3 = (^ [X0:$o,X1:$o,X2:$o]: (((c_or @ ((c_and @ ((c_exactly1of2 @ X0) @ X1)) @ (c_not @ X2))) @ ((c_and @ ((c_and @ (c_not @ X0)) @ (c_not @ X1))) @ X2)))))).
% 2.05/1.39 thf(ax45, axiom, (c_nIn = (^ [X0:$i,X1:$i]: ((c_not @ ((c_In @ X0) @ X1)))))).
% 2.05/1.39 thf(ax46, axiom, (c_nSubq = (^ [X0:$i,X1:$i]: ((c_not @ ((c_Subq @ X0) @ X1)))))).
% 2.05/1.39 thf(ax47, axiom, (c_UPair = (^ [X0:$i,X1:$i]: (((c_Repl @ (c_Power @ (c_Power @ c_Empty))) @ (^ [X2:$i]: ((((c_If_i @ ((c_In @ c_Empty) @ X2)) @ X0) @ X1)))))))).
% 2.05/1.39 thf(ax48, axiom, (c_Sing = (^ [X0:$i]: (((c_UPair @ X0) @ X0))))).
% 2.05/1.39 thf(ax49, axiom, (c_binunion = (^ [X0:$i,X1:$i]: ((c_Union @ ((c_UPair @ X0) @ X1)))))).
% 2.05/1.39 thf(ax50, axiom, (c_SetAdjoin = (^ [X0:$i,X1:$i]: (((c_binunion @ X0) @ (c_Sing @ X1)))))).
% 2.05/1.39 thf(ax51, axiom, (c_famunion = (^ [X0:$i,X1:($i > $i)]: ((c_Union @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 2.05/1.39 thf(ax52, axiom, (c_Sep = (^ [X0:$i,X1:($i > $o)]: ((((c_If_i @ (? [X2:$i]: (((c_and @ ((c_In @ X2) @ X0)) @ (X1 @ X2))))) @ ((c_Repl @ X0) @ (^ [X2:$i]: (((^ [X3:$i]: ((((c_If_i @ (X1 @ X3)) @ X3) @ (c_Eps_i @ (^ [X4:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ (X1 @ X4)))))))) @ X2))))) @ c_Empty))))).
% 2.05/1.39 thf(ax53, axiom, (c_ReplSep = (^ [X0:$i,X1:($i > $o),X2:($i > $i)]: (((c_Repl @ ((c_Sep @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: ((X2 @ X3)))))))).
% 2.05/1.39 thf(ax54, axiom, (c_binintersect = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax55, axiom, (c_setminus = (^ [X0:$i,X1:$i]: (((c_Sep @ X0) @ (^ [X2:$i]: (((c_nIn @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax56, axiom, (c_inj = (^ [X0:$i,X1:$i,X2:($i > $i)]: (((c_and @ (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ (X2 @ X3)) @ X1))))) @ (! [X3:$i]: ((((c_In @ X3) @ X0) => (! [X4:$i]: ((((c_In @ X4) @ X0) => (((X2 @ X3) = (X2 @ X4)) => (X3 = X4))))))))))))).
% 2.05/1.39 thf(ax57, axiom, (c_bij = (^ [X0:$i,X1:$i,X2:($i > $i)]: (((c_and @ (((c_inj @ X0) @ X1) @ X2)) @ (! [X3:$i]: ((((c_In @ X3) @ X1) => (? [X4:$i]: (((c_and @ ((c_In @ X4) @ X0)) @ ((X2 @ X4) = X3)))))))))))).
% 2.05/1.39 thf(ax58, axiom, (c_atleastp = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_inj @ X0) @ X1) @ X2))))))).
% 2.05/1.39 thf(ax59, axiom, (c_equip = (^ [X0:$i,X1:$i]: ((? [X2:($i > $i)]: ((((c_bij @ X0) @ X1) @ X2))))))).
% 2.05/1.39 thf(ax60, axiom, (c_In_rec_poly_G_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i,X2:$i]: ((! [X3:($i > ($i > $o))]: (((! [X4:$i,X5:($i > $i)]: (((! [X6:$i]: ((((c_In @ X6) @ X4) => ((X3 @ X6) @ (X5 @ X6))))) => ((X3 @ X4) @ ((X0 @ X4) @ X5))))) => ((X3 @ X1) @ X2)))))))).
% 2.05/1.39 thf(ax61, axiom, (c_In_rec_poly_i = (^ [X0:($i > (($i > $i) > $i)),X1:$i]: ((c_Eps_i @ (^ [X2:$i]: ((((c_In_rec_poly_G_i @ X0) @ X1) @ X2)))))))).
% 2.05/1.39 thf(ax62, axiom, (c_ordsucc = (^ [X0:$i]: (((c_binunion @ X0) @ (c_Sing @ X0)))))).
% 2.05/1.39 thf(ax63, axiom, (c_nat_p = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ c_Empty) => ((! [X2:$i]: (((X1 @ X2) => (X1 @ (c_ordsucc @ X2))))) => (X1 @ X0))))))))).
% 2.05/1.39 thf(ax64, axiom, (c_nat_primrec = (^ [X0:$i,X1:($i > ($i > $i))]: ((c_In_rec_poly_i @ (^ [X2:$i,X3:($i > $i)]: ((((c_If_i @ ((c_In @ (c_Union @ X2)) @ X2)) @ ((X1 @ (c_Union @ X2)) @ (X3 @ (c_Union @ X2)))) @ X0)))))))).
% 2.05/1.39 thf(ax65, axiom, (c_add_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ X0) @ (^ [X2:$i,X3:$i]: ((c_ordsucc @ X3)))) @ X1))))).
% 2.05/1.39 thf(ax66, axiom, (c_mul_nat = (^ [X0:$i,X1:$i]: ((((c_nat_primrec @ c_Empty) @ (^ [X2:$i,X3:$i]: (((c_add_nat @ X0) @ X3)))) @ X1))))).
% 2.05/1.39 thf(ax67, axiom, (c_ordinal = (^ [X0:$i]: (((c_and @ (c_TransSet @ X0)) @ (! [X1:$i]: ((((c_In @ X1) @ X0) => (c_TransSet @ X1))))))))).
% 2.05/1.39 thf(ax68, axiom, (c_V_ = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: ((c_Power @ (X1 @ X2)))))))))).
% 2.05/1.39 thf(ax69, axiom, (c_Inj1 = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_binunion @ (c_Sing @ c_Empty)) @ ((c_Repl @ X0) @ (^ [X2:$i]: ((X1 @ X2)))))))))).
% 2.05/1.39 thf(ax70, axiom, (c_Inj0 = (^ [X0:$i]: (((c_Repl @ X0) @ (^ [X1:$i]: ((c_Inj1 @ X1)))))))).
% 2.05/1.39 thf(ax71, axiom, (c_Unj = (c_In_rec_poly_i @ (^ [X0:$i,X1:($i > $i)]: (((c_Repl @ ((c_setminus @ X0) @ (c_Sing @ c_Empty))) @ (^ [X2:$i]: ((X1 @ X2))))))))).
% 2.05/1.39 thf(ax72, axiom, (c_combine_funcs = (^ [X0:$i,X1:$i,X2:($i > $i),X3:($i > $i),X4:$i]: ((((c_If_i @ (X4 = (c_Inj0 @ (c_Unj @ X4)))) @ (X2 @ (c_Unj @ X4))) @ (X3 @ (c_Unj @ X4))))))).
% 2.05/1.39 thf(ax73, axiom, (c_setsum = (^ [X0:$i,X1:$i]: (((c_binunion @ ((c_Repl @ X0) @ (^ [X2:$i]: ((c_Inj0 @ X2))))) @ ((c_Repl @ X1) @ (^ [X2:$i]: ((c_Inj1 @ X2))))))))).
% 2.05/1.39 thf(ax74, axiom, (c_proj0 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj0 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 2.05/1.39 thf(ax75, axiom, (c_proj1 = (^ [X0:$i]: ((((c_ReplSep @ X0) @ (^ [X1:$i]: ((? [X2:$i]: (((c_Inj1 @ X2) = X1)))))) @ (^ [X1:$i]: ((c_Unj @ X1)))))))).
% 2.05/1.39 thf(ax76, axiom, (c_binrep = (^ [X0:$i,X1:$i]: (((c_setsum @ X0) @ (c_Power @ X1)))))).
% 2.05/1.39 thf(ax77, axiom, (c_lam = (^ [X0:$i,X1:($i > $i)]: (((c_famunion @ X0) @ (^ [X2:$i]: (((c_Repl @ (X1 @ X2)) @ (^ [X3:$i]: (((c_setsum @ X2) @ X3))))))))))).
% 2.05/1.39 thf(ax78, axiom, (c_setprod = (^ [X0:$i,X1:$i]: (((c_lam @ X0) @ (^ [X2:$i]: (X1))))))).
% 2.05/1.39 thf(ax79, axiom, (c_ap = (^ [X0:$i,X1:$i]: ((((c_ReplSep @ X0) @ (^ [X2:$i]: ((? [X3:$i]: ((X2 = ((c_setsum @ X1) @ X3))))))) @ (^ [X2:$i]: ((c_proj1 @ X2)))))))).
% 2.05/1.39 thf(ax80, axiom, (c_setsum_p = (^ [X0:$i]: ((((c_setsum @ ((c_ap @ X0) @ c_Empty)) @ ((c_ap @ X0) @ (c_ordsucc @ c_Empty))) = X0))))).
% 2.05/1.39 thf(ax81, axiom, (c_tuple_p = (^ [X0:$i,X1:$i]: ((! [X2:$i]: ((((c_In @ X2) @ X1) => (? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ (? [X4:$i]: ((X2 = ((c_setsum @ X3) @ X4)))))))))))))).
% 2.05/1.39 thf(ax82, axiom, (c_Pi = (^ [X0:$i,X1:($i > $i)]: (((c_Sep @ (c_Power @ ((c_lam @ X0) @ (^ [X2:$i]: ((c_Union @ (X1 @ X2))))))) @ (^ [X2:$i]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((c_ap @ X2) @ X3)) @ (X1 @ X3)))))))))))).
% 2.05/1.39 thf(ax83, axiom, (c_setexp = (^ [X0:$i,X1:$i]: (((c_Pi @ X1) @ (^ [X2:$i]: (X0))))))).
% 2.05/1.39 thf(ax84, axiom, (c_Sep2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $o))]: (((c_Sep @ ((c_lam @ X0) @ (^ [X3:$i]: ((X1 @ X3))))) @ (^ [X3:$i]: (((X2 @ ((c_ap @ X3) @ c_Empty)) @ ((c_ap @ X3) @ (c_ordsucc @ c_Empty)))))))))).
% 2.05/1.39 thf(ax85, axiom, (c_set_of_pairs = (^ [X0:$i]: ((! [X1:$i]: ((((c_In @ X1) @ X0) => (? [X2:$i,X3:$i]: ((X1 = ((c_lam @ (c_ordsucc @ (c_ordsucc @ c_Empty))) @ (^ [X4:$i]: ((((c_If_i @ (X4 = c_Empty)) @ X2) @ X3)))))))))))))).
% 2.05/1.39 thf(ax86, axiom, (c_lam2 = (^ [X0:$i,X1:($i > $i),X2:($i > ($i > $i))]: (((c_lam @ X0) @ (^ [X3:$i]: (((c_lam @ (X1 @ X3)) @ (^ [X4:$i]: (((X2 @ X3) @ X4))))))))))).
% 2.05/1.39 thf(ax87, axiom, (c_PNoEq_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_iff @ (X1 @ X3)) @ (X2 @ X3))))))))).
% 2.05/1.39 thf(ax88, axiom, (c_PNoLt_ = (^ [X0:$i,X1:($i > $o),X2:($i > $o)]: ((? [X3:$i]: (((c_and @ ((c_In @ X3) @ X0)) @ ((c_and @ ((c_and @ (((c_PNoEq_ @ X3) @ X1) @ X2)) @ (c_not @ (X1 @ X3)))) @ (X2 @ X3))))))))).
% 2.05/1.39 thf(ax89, axiom, (c_PNoLt = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((c_or @ (((c_PNoLt_ @ ((c_binintersect @ X0) @ X2)) @ X1) @ X3)) @ ((c_and @ ((c_and @ ((c_In @ X0) @ X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))) @ (X3 @ X0)))) @ ((c_and @ ((c_and @ ((c_In @ X2) @ X0)) @ (((c_PNoEq_ @ X2) @ X1) @ X3))) @ (c_not @ (X1 @ X2)))))))).
% 2.05/1.39 thf(ax90, axiom, (c_PNoLe = (^ [X0:$i,X1:($i > $o),X2:$i,X3:($i > $o)]: (((c_or @ ((((c_PNoLt @ X0) @ X1) @ X2) @ X3)) @ ((c_and @ (X0 = X2)) @ (((c_PNoEq_ @ X0) @ X1) @ X3))))))).
% 2.05/1.39 thf(ax91, axiom, (c_PNo_downc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X1) @ X2) @ X3) @ X4))))))))))).
% 2.05/1.39 thf(ax92, axiom, (c_PNo_upc = (^ [X0:($i > (($i > $o) > $o)),X1:$i,X2:($i > $o)]: ((? [X3:$i]: (((c_and @ (c_ordinal @ X3)) @ (? [X4:($i > $o)]: (((c_and @ ((X0 @ X3) @ X4)) @ ((((c_PNoLe @ X3) @ X4) @ X1) @ X2))))))))))).
% 2.05/1.39 thf(ax93, axiom, (c_SNoElts_ = (^ [X0:$i]: (((c_binunion @ X0) @ ((c_Repl @ X0) @ (^ [X1:$i]: (((^ [X2:$i]: (((c_SetAdjoin @ X2) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X1))))))))).
% 2.05/1.39 thf(ax94, axiom, (c_SNo_ = (^ [X0:$i,X1:$i]: (((c_and @ ((c_Subq @ X1) @ (c_SNoElts_ @ X0))) @ (! [X2:$i]: ((((c_In @ X2) @ X0) => ((c_exactly1of2 @ ((c_In @ ((^ [X3:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2)) @ X1)) @ ((c_In @ X2) @ X1)))))))))).
% 2.05/1.39 thf(ax95, axiom, (c_PSNo = (^ [X0:$i,X1:($i > $o)]: (((c_binunion @ ((c_Sep @ X0) @ (^ [X2:$i]: ((X1 @ X2))))) @ (((c_ReplSep @ X0) @ (^ [X2:$i]: ((c_not @ (X1 @ X2))))) @ (^ [X2:$i]: (((^ [X3:$i]: (((c_SetAdjoin @ X3) @ (c_Sing @ (c_ordsucc @ c_Empty))))) @ X2))))))))).
% 2.05/1.39 thf(ax96, axiom, (c_SNo = (^ [X0:$i]: ((? [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0)))))))).
% 2.05/1.39 thf(ax97, axiom, (c_SNoLev = (^ [X0:$i]: ((c_Eps_i @ (^ [X1:$i]: (((c_and @ (c_ordinal @ X1)) @ ((c_SNo_ @ X1) @ X0))))))))).
% 2.05/1.39 thf(ax98, axiom, (c_SNoEq_ = (^ [X0:$i,X1:$i,X2:$i]: ((((c_PNoEq_ @ X0) @ (^ [X3:$i]: (((c_In @ X3) @ X1)))) @ (^ [X3:$i]: (((c_In @ X3) @ X2)))))))).
% 2.05/1.39 thf(ax99, axiom, (c_SNoLt = (^ [X0:$i,X1:$i]: (((((c_PNoLt @ (c_SNoLev @ X0)) @ (^ [X2:$i]: (((c_In @ X2) @ X0)))) @ (c_SNoLev @ X1)) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax100, axiom, (c_SNoLe = (^ [X0:$i,X1:$i]: (((((c_PNoLe @ (c_SNoLev @ X0)) @ (^ [X2:$i]: (((c_In @ X2) @ X0)))) @ (c_SNoLev @ X1)) @ (^ [X2:$i]: (((c_In @ X2) @ X1)))))))).
% 2.05/1.39 thf(ax101, axiom, (c_binop_on = (^ [X0:$i,X1:($i > ($i > $i))]: ((! [X2:$i]: ((((c_In @ X2) @ X0) => (! [X3:$i]: ((((c_In @ X3) @ X0) => ((c_In @ ((X1 @ X2) @ X3)) @ X0))))))))))).
% 2.05/1.39 thf(ax102, axiom, (c_Loop = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i]: (((c_and @ ((c_and @ ((c_and @ ((c_and @ ((c_binop_on @ X0) @ X1)) @ ((c_binop_on @ X0) @ X2))) @ ((c_binop_on @ X0) @ X3))) @ (! [X5:$i]: ((((c_In @ X5) @ X0) => ((c_and @ (((X1 @ X4) @ X5) = X5)) @ (((X1 @ X5) @ X4) = X5))))))) @ (! [X5:$i]: ((((c_In @ X5) @ X0) => (! [X6:$i]: ((((c_In @ X6) @ X0) => ((c_and @ ((c_and @ ((c_and @ (((X2 @ X5) @ ((X1 @ X5) @ X6)) = X6)) @ (((X1 @ X5) @ ((X2 @ X5) @ X6)) = X6))) @ (((X3 @ ((X1 @ X5) @ X6)) @ X6) = X5))) @ (((X1 @ ((X3 @ X5) @ X6)) @ X6) = X5))))))))))))).
% 2.05/1.39 thf(ax103, axiom, (c_Loop_with_defs = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((c_and @ ((c_and @ ((c_and @ (((((c_Loop @ X0) @ X1) @ X2) @ X3) @ X4)) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (((X5 @ X14) @ X15) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X14) @ X15))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (! [X16:$i]: ((((c_In @ X16) @ X0) => ((((X6 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X14) @ ((X1 @ X15) @ X16))) @ ((X1 @ ((X1 @ X14) @ X15)) @ X16)))))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => ((c_and @ ((c_and @ ((c_and @ ((c_and @ (((X7 @ X14) @ X15) = ((X2 @ X14) @ ((X1 @ X15) @ X14)))) @ (((X10 @ X14) @ X15) = ((X1 @ X14) @ ((X1 @ X15) @ ((X2 @ X14) @ X4)))))) @ (((X11 @ X14) @ X15) = ((X1 @ ((X1 @ ((X3 @ X4) @ X14)) @ X15)) @ X14)))) @ (((X12 @ X14) @ X15) = ((X1 @ ((X2 @ X14) @ X15)) @ ((X2 @ ((X2 @ X14) @ X4)) @ X4))))) @ (((X13 @ X14) @ X15) = ((X1 @ ((X3 @ X4) @ ((X3 @ X4) @ X14))) @ ((X3 @ X15) @ X14)))))))))))) @ (! [X14:$i]: ((((c_In @ X14) @ X0) => (! [X15:$i]: ((((c_In @ X15) @ X0) => (! [X16:$i]: ((((c_In @ X16) @ X0) => ((c_and @ ((((X8 @ X14) @ X15) @ X16) = ((X2 @ ((X1 @ X15) @ X14)) @ ((X1 @ X15) @ ((X1 @ X14) @ X16))))) @ ((((X9 @ X14) @ X15) @ X16) = ((X3 @ ((X1 @ ((X1 @ X16) @ X14)) @ X15)) @ ((X1 @ X14) @ X15)))))))))))))))))).
% 2.05/1.39 thf(ax104, axiom, (c_Loop_with_defs_cex1 = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((((((((((((((c_Loop_with_defs @ X0) @ X1) @ X2) @ X3) @ X4) @ X5) @ X6) @ X7) @ X8) @ X9) @ X10) @ X11) @ X12) @ X13)) @ (? [X14:$i]: (((c_and @ ((c_In @ X14) @ X0)) @ (? [X15:$i]: (((c_and @ ((c_In @ X15) @ X0)) @ (? [X16:$i]: (((c_and @ ((c_In @ X16) @ X0)) @ (? [X17:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (c_not @ (((X5 @ ((X1 @ ((X2 @ (((X8 @ X15) @ X16) @ X14)) @ X4)) @ X14)) @ X17) = X4))))))))))))))))))).
% 2.05/1.39 thf(ax105, axiom, (c_Loop_with_defs_cex2 = (^ [X0:$i,X1:($i > ($i > $i)),X2:($i > ($i > $i)),X3:($i > ($i > $i)),X4:$i,X5:($i > ($i > $i)),X6:($i > ($i > ($i > $i))),X7:($i > ($i > $i)),X8:($i > ($i > ($i > $i))),X9:($i > ($i > ($i > $i))),X10:($i > ($i > $i)),X11:($i > ($i > $i)),X12:($i > ($i > $i)),X13:($i > ($i > $i))]: (((c_and @ ((((((((((((((c_Loop_with_defs @ X0) @ X1) @ X2) @ X3) @ X4) @ X5) @ X6) @ X7) @ X8) @ X9) @ X10) @ X11) @ X12) @ X13)) @ (? [X14:$i]: (((c_and @ ((c_In @ X14) @ X0)) @ (? [X15:$i]: (((c_and @ ((c_In @ X15) @ X0)) @ (? [X16:$i]: (((c_and @ ((c_In @ X16) @ X0)) @ (? [X17:$i]: (((c_and @ ((c_In @ X17) @ X0)) @ (? [X18:$i]: (((c_and @ ((c_In @ X18) @ X0)) @ (c_not @ ((((X6 @ X18) @ ((X1 @ ((X3 @ X4) @ X14)) @ (((X9 @ X15) @ X16) @ X14))) @ X17) = X4)))))))))))))))))))))).
% 2.05/1.39 thf(ax106, axiom, (c_combinator = (^ [X0:$i]: ((! [X1:($i > $o)]: (((X1 @ (c_Inj0 @ c_Empty)) => ((X1 @ (c_Inj0 @ (c_Power @ c_Empty))) => ((! [X2:$i,X3:$i]: (((X1 @ X2) => ((X1 @ X3) => (X1 @ (c_Inj1 @ ((c_setsum @ X2) @ X3))))))) => (X1 @ X0)))))))))).
% 2.05/1.39 thf(ax107, axiom, (c_combinator_equiv = (^ [X0:$i,X1:$i]: ((! [X2:($i > ($i > $o))]: (((((^ [X3:$i,X4:$i,X5:($i > ($i > $i))]: (((c_per_i @ X2) => ((! [X6:$i]: (((c_combinator @ X6) => ((X2 @ X6) @ X6)))) => ((! [X6:$i,X7:$i,X8:$i,X9:$i]: (((c_combinator @ X6) => ((c_combinator @ X7) => ((c_combinator @ X8) => ((c_combinator @ X9) => (((X2 @ X6) @ X8) => (((X2 @ X7) @ X9) => ((X2 @ ((X5 @ X6) @ X7)) @ ((X5 @ X8) @ X9)))))))))) => ((! [X6:$i,X7:$i]: (((X2 @ ((X5 @ ((X5 @ X3) @ X6)) @ X7)) @ X6))) => ((! [X6:$i,X7:$i,X8:$i]: (((X2 @ ((X5 @ ((X5 @ ((X5 @ X4) @ X6)) @ X7)) @ X8)) @ ((X5 @ ((X5 @ X6) @ X8)) @ ((X5 @ X7) @ X8))))) => ((X2 @ X0) @ X1)))))))) @ (c_Inj0 @ c_Empty)) @ (c_Inj0 @ (c_Power @ c_Empty))) @ (^ [X3:$i,X4:$i]: ((c_Inj1 @ ((c_setsum @ X3) @ X4))))))))))).
% 2.05/1.39 thf(ax108, axiom, (c_equip_mod = (^ [X0:$i,X1:$i,X2:$i]: ((? [X3:$i,X4:$i]: (((c_or @ ((c_and @ ((c_equip @ ((c_setsum @ X0) @ X3)) @ X1)) @ ((c_equip @ ((c_setprod @ X4) @ X3)) @ X2))) @ ((c_and @ ((c_equip @ ((c_setsum @ X1) @ X3)) @ X0)) @ ((c_equip @ ((c_setprod @ X4) @ X3)) @ X2))))))))).
% 2.05/1.39 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]: (((X4 @ ((X1 @ ((X1 @ ((X1 @ ((X1 @ ((X1 @ ((X1 @ X6) @ X5)) @ ((X1 @ ((X1 @ ((X1 @ X6) @ X5)) @ ((X1 @ X7) @ ((X1 @ ((X1 @ ((X1 @ X5) @ X5)) @ ((X1 @ ((X1 @ ((X1 @ ((X1 @ X5) @ ((X1 @ ((X1 @ X6) @ ((X1 @ X5) @ ((X1 @ X5) @ X7)))) @ X5))) @ X7)) @ ((X1 @ (X4 @ X6)) @ X7))) @ ((X1 @ ((X1 @ ((X1 @ ((X1 @ X5) @ (X4 @ ((X1 @ X7) @ X5)))) @ ((X1 @ X6) @ X6))) @ ((X1 @ X6) @ ((X1 @ X7) @ X5)))) @ X5)))) @ X7)))) @ X5))) @ X6)) @ ((X1 @ X6) @ ((X1 @ X5) @ ((X1 @ ((X1 @ (X4 @ X5)) @ ((X1 @ ((X1 @ X6) @ X6)) @ X6))) @ X5))))) @ (X4 @ (X4 @ X6)))) @ X5)) = (X4 @ (X4 @ X7))))))).
% 2.05/1.39 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2DTF30392.p
% 2.05/1.39 ------------------------
% 2.34/1.41 ---- Cleaned THF ---
% 2.34/1.41 thf(c_Eps_i_tp,type,
% 2.34/1.41 c_Eps_i: ( $i > $o ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_False_tp,type,
% 2.34/1.41 c_False: $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_True_tp,type,
% 2.34/1.41 c_True: $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_not_tp,type,
% 2.34/1.41 c_not: $o > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_and_tp,type,
% 2.34/1.41 c_and: $o > $o > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_or_tp,type,
% 2.34/1.41 c_or: $o > $o > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_iff_tp,type,
% 2.34/1.41 c_iff: $o > $o > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_In_tp,type,
% 2.34/1.41 c_In: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Subq_tp,type,
% 2.34/1.41 c_Subq: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Empty_tp,type,
% 2.34/1.41 c_Empty: $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Union_tp,type,
% 2.34/1.41 c_Union: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Power_tp,type,
% 2.34/1.41 c_Power: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Repl_tp,type,
% 2.34/1.41 c_Repl: $i > ( $i > $i ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_TransSet_tp,type,
% 2.34/1.41 c_TransSet: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_atleast2_tp,type,
% 2.34/1.41 c_atleast2: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_atleast3_tp,type,
% 2.34/1.41 c_atleast3: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_atleast4_tp,type,
% 2.34/1.41 c_atleast4: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_atleast5_tp,type,
% 2.34/1.41 c_atleast5: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_atleast6_tp,type,
% 2.34/1.41 c_atleast6: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_exactly2_tp,type,
% 2.34/1.41 c_exactly2: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_exactly3_tp,type,
% 2.34/1.41 c_exactly3: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_exactly4_tp,type,
% 2.34/1.41 c_exactly4: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_exactly5_tp,type,
% 2.34/1.41 c_exactly5: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_exu_i_tp,type,
% 2.34/1.41 c_exu_i: ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_reflexive_i_tp,type,
% 2.34/1.41 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_irreflexive_i_tp,type,
% 2.34/1.41 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_symmetric_i_tp,type,
% 2.34/1.41 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_antisymmetric_i_tp,type,
% 2.34/1.41 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_transitive_i_tp,type,
% 2.34/1.41 c_transitive_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_eqreln_i_tp,type,
% 2.34/1.41 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_per_i_tp,type,
% 2.34/1.41 c_per_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_linear_i_tp,type,
% 2.34/1.41 c_linear_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_trichotomous_or_i_tp,type,
% 2.34/1.41 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_partialorder_i_tp,type,
% 2.34/1.41 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_totalorder_i_tp,type,
% 2.34/1.41 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_strictpartialorder_i_tp,type,
% 2.34/1.41 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_stricttotalorder_i_tp,type,
% 2.34/1.41 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_If_i_tp,type,
% 2.34/1.41 c_If_i: $o > $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_exactly1of2_tp,type,
% 2.34/1.41 c_exactly1of2: $o > $o > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_exactly1of3_tp,type,
% 2.34/1.41 c_exactly1of3: $o > $o > $o > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_nIn_tp,type,
% 2.34/1.41 c_nIn: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_nSubq_tp,type,
% 2.34/1.41 c_nSubq: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_UPair_tp,type,
% 2.34/1.41 c_UPair: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Sing_tp,type,
% 2.34/1.41 c_Sing: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_binunion_tp,type,
% 2.34/1.41 c_binunion: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_SetAdjoin_tp,type,
% 2.34/1.41 c_SetAdjoin: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_famunion_tp,type,
% 2.34/1.41 c_famunion: $i > ( $i > $i ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Sep_tp,type,
% 2.34/1.41 c_Sep: $i > ( $i > $o ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_ReplSep_tp,type,
% 2.34/1.41 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_binintersect_tp,type,
% 2.34/1.41 c_binintersect: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_setminus_tp,type,
% 2.34/1.41 c_setminus: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_inj_tp,type,
% 2.34/1.41 c_inj: $i > $i > ( $i > $i ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_bij_tp,type,
% 2.34/1.41 c_bij: $i > $i > ( $i > $i ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_atleastp_tp,type,
% 2.34/1.41 c_atleastp: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_equip_tp,type,
% 2.34/1.41 c_equip: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_In_rec_poly_G_i_tp,type,
% 2.34/1.41 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_In_rec_poly_i_tp,type,
% 2.34/1.41 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_ordsucc_tp,type,
% 2.34/1.41 c_ordsucc: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_nat_p_tp,type,
% 2.34/1.41 c_nat_p: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_nat_primrec_tp,type,
% 2.34/1.41 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_add_nat_tp,type,
% 2.34/1.41 c_add_nat: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_mul_nat_tp,type,
% 2.34/1.41 c_mul_nat: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_ordinal_tp,type,
% 2.34/1.41 c_ordinal: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_V__tp,type,
% 2.34/1.41 c_V_: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Inj1_tp,type,
% 2.34/1.41 c_Inj1: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Inj0_tp,type,
% 2.34/1.41 c_Inj0: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Unj_tp,type,
% 2.34/1.41 c_Unj: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_combine_funcs_tp,type,
% 2.34/1.41 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_setsum_tp,type,
% 2.34/1.41 c_setsum: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_proj0_tp,type,
% 2.34/1.41 c_proj0: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_proj1_tp,type,
% 2.34/1.41 c_proj1: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_binrep_tp,type,
% 2.34/1.41 c_binrep: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_lam_tp,type,
% 2.34/1.41 c_lam: $i > ( $i > $i ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_setprod_tp,type,
% 2.34/1.41 c_setprod: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_ap_tp,type,
% 2.34/1.41 c_ap: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_setsum_p_tp,type,
% 2.34/1.41 c_setsum_p: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_tuple_p_tp,type,
% 2.34/1.41 c_tuple_p: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Pi_tp,type,
% 2.34/1.41 c_Pi: $i > ( $i > $i ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_setexp_tp,type,
% 2.34/1.41 c_setexp: $i > $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_Sep2_tp,type,
% 2.34/1.41 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_set_of_pairs_tp,type,
% 2.34/1.41 c_set_of_pairs: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_lam2_tp,type,
% 2.34/1.41 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_PNoEq__tp,type,
% 2.34/1.41 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_PNoLt__tp,type,
% 2.34/1.41 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_PNoLt_tp,type,
% 2.34/1.41 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_PNoLe_tp,type,
% 2.34/1.41 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_PNo_downc_tp,type,
% 2.34/1.41 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_PNo_upc_tp,type,
% 2.34/1.41 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNoElts__tp,type,
% 2.34/1.41 c_SNoElts_: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNo__tp,type,
% 2.34/1.41 c_SNo_: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_PSNo_tp,type,
% 2.34/1.41 c_PSNo: $i > ( $i > $o ) > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNo_tp,type,
% 2.34/1.41 c_SNo: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNoLev_tp,type,
% 2.34/1.41 c_SNoLev: $i > $i ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNoEq__tp,type,
% 2.34/1.41 c_SNoEq_: $i > $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNoLt_tp,type,
% 2.34/1.41 c_SNoLt: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_SNoLe_tp,type,
% 2.34/1.41 c_SNoLe: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_binop_on_tp,type,
% 2.34/1.41 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Loop_tp,type,
% 2.34/1.41 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Loop_with_defs_tp,type,
% 2.34/1.41 c_Loop_with_defs: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Loop_with_defs_cex1_tp,type,
% 2.34/1.41 c_Loop_with_defs_cex1: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_Loop_with_defs_cex2_tp,type,
% 2.34/1.41 c_Loop_with_defs_cex2: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_combinator_tp,type,
% 2.34/1.41 c_combinator: $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_combinator_equiv_tp,type,
% 2.34/1.41 c_combinator_equiv: $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(c_equip_mod_tp,type,
% 2.34/1.41 c_equip_mod: $i > $i > $i > $o ).
% 2.34/1.41
% 2.34/1.41 thf(ax1,axiom,
% 2.34/1.41 ! [X0: $i > $o,X1: $i] :
% 2.34/1.41 ( ( X0 @ X1 )
% 2.34/1.41 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 2.34/1.41
% 2.34/1.41 thf(ax2,axiom,
% 2.34/1.41 ! [X0: $o] :
% 2.34/1.41 ( ( c_not @ ( c_not @ X0 ) )
% 2.34/1.42 => X0 ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax3,axiom,
% 2.34/1.42 ! [X0: $o,X1: $o] :
% 2.34/1.42 ( ( c_iff @ X0 @ X1 )
% 2.34/1.42 => ( X0 = X1 ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax4,axiom,
% 2.34/1.42 ! [X0: $i,X1: $i] :
% 2.34/1.42 ( ( c_Subq @ X0 @ X1 )
% 2.34/1.42 => ( ( c_Subq @ X1 @ X0 )
% 2.34/1.42 => ( X0 = X1 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax5,axiom,
% 2.34/1.42 ( c_not
% 2.34/1.42 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax6,axiom,
% 2.34/1.42 ! [X0: $i,X1: $i] :
% 2.34/1.42 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 2.34/1.42 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax7,axiom,
% 2.34/1.42 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax8,axiom,
% 2.34/1.42 ! [X0: $i,X1: $i > $i,X2: $i] :
% 2.34/1.42 ( c_iff
% 2.34/1.42 @ ( c_In @ X2
% 2.34/1.42 @ ( c_Repl @ X0
% 2.34/1.42 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 2.34/1.42 @ ? [X3: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X3 @ X0 )
% 2.34/1.42 @ ( X2
% 2.34/1.42 = ( X1 @ X3 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax9,axiom,
% 2.34/1.42 ! [X0: $i > $o] :
% 2.34/1.42 ( ! [X1: $i] :
% 2.34/1.42 ( ( X0 @ X1 )
% 2.34/1.42 => ! [X2: $i] :
% 2.34/1.42 ( ( c_In @ X2 @ X1 )
% 2.34/1.42 => ( X0 @ X2 ) ) )
% 2.34/1.42 => ( ( X0 @ c_Empty )
% 2.34/1.42 => ( ! [X1: $i] :
% 2.34/1.42 ( ( X0 @ X1 )
% 2.34/1.42 => ( X0 @ ( c_Union @ X1 ) ) )
% 2.34/1.42 => ( ! [X1: $i] :
% 2.34/1.42 ( ( X0 @ X1 )
% 2.34/1.42 => ( X0 @ ( c_Power @ X1 ) ) )
% 2.34/1.42 => ( ! [X1: $i] :
% 2.34/1.42 ( ( X0 @ X1 )
% 2.34/1.42 => ! [X2: $i > $i] :
% 2.34/1.42 ( ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X1 )
% 2.34/1.42 => ( X0 @ ( X2 @ X3 ) ) )
% 2.34/1.42 => ( X0
% 2.34/1.42 @ ( c_Repl @ X1
% 2.34/1.42 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 2.34/1.42 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax10,axiom,
% 2.34/1.42 ! [X0: $i > $o] :
% 2.34/1.42 ( ! [X1: $i] :
% 2.34/1.42 ( ! [X2: $i] :
% 2.34/1.42 ( ( c_In @ X2 @ X1 )
% 2.34/1.42 => ( X0 @ X2 ) )
% 2.34/1.42 => ( X0 @ X1 ) )
% 2.34/1.42 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax11,axiom,
% 2.34/1.42 ( c_False
% 2.34/1.42 = ( ! [X0: $o] : X0 ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax12,axiom,
% 2.34/1.42 ( c_True
% 2.34/1.42 = ( ! [X0: $o] :
% 2.34/1.42 ( X0
% 2.34/1.42 => X0 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax13,axiom,
% 2.34/1.42 ( c_not
% 2.34/1.42 = ( ^ [X0: $o] :
% 2.34/1.42 ( X0
% 2.34/1.42 => c_False ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax14,axiom,
% 2.34/1.42 ( c_and
% 2.34/1.42 = ( ^ [X0: $o,X1: $o] :
% 2.34/1.42 ! [X2: $o] :
% 2.34/1.42 ( ( X0
% 2.34/1.42 => ( X1
% 2.34/1.42 => X2 ) )
% 2.34/1.42 => X2 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax15,axiom,
% 2.34/1.42 ( c_or
% 2.34/1.42 = ( ^ [X0: $o,X1: $o] :
% 2.34/1.42 ! [X2: $o] :
% 2.34/1.42 ( ( X0
% 2.34/1.42 => X2 )
% 2.34/1.42 => ( ( X1
% 2.34/1.42 => X2 )
% 2.34/1.42 => X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax16,axiom,
% 2.34/1.42 ( c_iff
% 2.34/1.42 = ( ^ [X0: $o,X1: $o] :
% 2.34/1.42 ( c_and
% 2.34/1.42 @ ( X0
% 2.34/1.42 => X1 )
% 2.34/1.42 @ ( X1
% 2.34/1.42 => X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax17,axiom,
% 2.34/1.42 ( c_Subq
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ! [X2: $i] :
% 2.34/1.42 ( ( c_In @ X2 @ X0 )
% 2.34/1.42 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax18,axiom,
% 2.34/1.42 ( c_TransSet
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ! [X1: $i] :
% 2.34/1.42 ( ( c_In @ X1 @ X0 )
% 2.34/1.42 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax19,axiom,
% 2.34/1.42 ( c_atleast2
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax20,axiom,
% 2.34/1.42 ( c_atleast3
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax21,axiom,
% 2.34/1.42 ( c_atleast4
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax22,axiom,
% 2.34/1.42 ( c_atleast5
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax23,axiom,
% 2.34/1.42 ( c_atleast6
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax24,axiom,
% 2.34/1.42 ( c_exactly2
% 2.34/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax25,axiom,
% 2.34/1.42 ( c_exactly3
% 2.34/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax26,axiom,
% 2.34/1.42 ( c_exactly4
% 2.34/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax27,axiom,
% 2.34/1.42 ( c_exactly5
% 2.34/1.42 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax28,axiom,
% 2.34/1.42 ( c_exu_i
% 2.34/1.42 = ( ^ [X0: $i > $o] :
% 2.34/1.42 ( c_and
% 2.34/1.42 @ ? [X1: $i] : ( X0 @ X1 )
% 2.34/1.42 @ ! [X1: $i,X2: $i] :
% 2.34/1.42 ( ( X0 @ X1 )
% 2.34/1.42 => ( ( X0 @ X2 )
% 2.34/1.42 => ( X1 = X2 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax29,axiom,
% 2.34/1.42 ( c_reflexive_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax30,axiom,
% 2.34/1.42 ( c_irreflexive_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax31,axiom,
% 2.34/1.42 ( c_symmetric_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i,X2: $i] :
% 2.34/1.42 ( ( X0 @ X1 @ X2 )
% 2.34/1.42 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax32,axiom,
% 2.34/1.42 ( c_antisymmetric_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i,X2: $i] :
% 2.34/1.42 ( ( X0 @ X1 @ X2 )
% 2.34/1.42 => ( ( X0 @ X2 @ X1 )
% 2.34/1.42 => ( X1 = X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax33,axiom,
% 2.34/1.42 ( c_transitive_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i,X2: $i,X3: $i] :
% 2.34/1.42 ( ( X0 @ X1 @ X2 )
% 2.34/1.42 => ( ( X0 @ X2 @ X3 )
% 2.34/1.42 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax34,axiom,
% 2.34/1.42 ( c_eqreln_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax35,axiom,
% 2.34/1.42 ( c_per_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax36,axiom,
% 2.34/1.42 ( c_linear_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax37,axiom,
% 2.34/1.42 ( c_trichotomous_or_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] :
% 2.34/1.42 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax38,axiom,
% 2.34/1.42 ( c_partialorder_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax39,axiom,
% 2.34/1.42 ( c_totalorder_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax40,axiom,
% 2.34/1.42 ( c_strictpartialorder_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax41,axiom,
% 2.34/1.42 ( c_stricttotalorder_i
% 2.34/1.42 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax42,axiom,
% 2.34/1.42 ( c_If_i
% 2.34/1.42 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 2.34/1.42 ( c_Eps_i
% 2.34/1.42 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax43,axiom,
% 2.34/1.42 ( c_exactly1of2
% 2.34/1.42 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax44,axiom,
% 2.34/1.42 ( c_exactly1of3
% 2.34/1.42 = ( ^ [X0: $o,X1: $o,X2: $o] : ( c_or @ ( c_and @ ( c_exactly1of2 @ X0 @ X1 ) @ ( c_not @ X2 ) ) @ ( c_and @ ( c_and @ ( c_not @ X0 ) @ ( c_not @ X1 ) ) @ X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax45,axiom,
% 2.34/1.42 ( c_nIn
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax46,axiom,
% 2.34/1.42 ( c_nSubq
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax47,axiom,
% 2.34/1.42 ( c_UPair
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 2.34/1.42 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax48,axiom,
% 2.34/1.42 ( c_Sing
% 2.34/1.42 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax49,axiom,
% 2.34/1.42 ( c_binunion
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax50,axiom,
% 2.34/1.42 ( c_SetAdjoin
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax51,axiom,
% 2.34/1.42 ( c_famunion
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i] :
% 2.34/1.42 ( c_Union
% 2.34/1.42 @ ( c_Repl @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax52,axiom,
% 2.34/1.42 ( c_Sep
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o] :
% 2.34/1.42 ( c_If_i
% 2.34/1.42 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 2.34/1.42 @ ( c_Repl @ X0
% 2.34/1.42 @ ^ [X2: $i] :
% 2.34/1.42 ( ^ [X3: $i] :
% 2.34/1.42 ( c_If_i @ ( X1 @ X3 ) @ X3
% 2.34/1.42 @ ( c_Eps_i
% 2.34/1.42 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 2.34/1.42 @ X2 ) )
% 2.34/1.42 @ c_Empty ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax53,axiom,
% 2.34/1.42 ( c_ReplSep
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 2.34/1.42 ( c_Repl
% 2.34/1.42 @ ( c_Sep @ X0
% 2.34/1.42 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.34/1.42 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax54,axiom,
% 2.34/1.42 ( c_binintersect
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_Sep @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax55,axiom,
% 2.34/1.42 ( c_setminus
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_Sep @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax56,axiom,
% 2.34/1.42 ( c_inj
% 2.34/1.42 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.34/1.42 ( c_and
% 2.34/1.42 @ ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X0 )
% 2.34/1.42 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 2.34/1.42 @ ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X0 )
% 2.34/1.42 => ! [X4: $i] :
% 2.34/1.42 ( ( c_In @ X4 @ X0 )
% 2.34/1.42 => ( ( ( X2 @ X3 )
% 2.34/1.42 = ( X2 @ X4 ) )
% 2.34/1.42 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax57,axiom,
% 2.34/1.42 ( c_bij
% 2.34/1.42 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 2.34/1.42 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 2.34/1.42 @ ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X1 )
% 2.34/1.42 => ? [X4: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X4 @ X0 )
% 2.34/1.42 @ ( ( X2 @ X4 )
% 2.34/1.42 = X3 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax58,axiom,
% 2.34/1.42 ( c_atleastp
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax59,axiom,
% 2.34/1.42 ( c_equip
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax60,axiom,
% 2.34/1.42 ( c_In_rec_poly_G_i
% 2.34/1.42 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 2.34/1.42 ! [X3: $i > $i > $o] :
% 2.34/1.42 ( ! [X4: $i,X5: $i > $i] :
% 2.34/1.42 ( ! [X6: $i] :
% 2.34/1.42 ( ( c_In @ X6 @ X4 )
% 2.34/1.42 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 2.34/1.42 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 2.34/1.42 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax61,axiom,
% 2.34/1.42 ( c_In_rec_poly_i
% 2.34/1.42 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 2.34/1.42 ( c_Eps_i
% 2.34/1.42 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax62,axiom,
% 2.34/1.42 ( c_ordsucc
% 2.34/1.42 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax63,axiom,
% 2.34/1.42 ( c_nat_p
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ! [X1: $i > $o] :
% 2.34/1.42 ( ( X1 @ c_Empty )
% 2.34/1.42 => ( ! [X2: $i] :
% 2.34/1.42 ( ( X1 @ X2 )
% 2.34/1.42 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 2.34/1.42 => ( X1 @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax64,axiom,
% 2.34/1.42 ( c_nat_primrec
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.34/1.42 ( c_In_rec_poly_i
% 2.34/1.42 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax65,axiom,
% 2.34/1.42 ( c_add_nat
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_nat_primrec @ X0
% 2.34/1.42 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 2.34/1.42 @ X1 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax66,axiom,
% 2.34/1.42 ( c_mul_nat
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_nat_primrec @ c_Empty
% 2.34/1.42 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 2.34/1.42 @ X1 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax67,axiom,
% 2.34/1.42 ( c_ordinal
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( c_and @ ( c_TransSet @ X0 )
% 2.34/1.42 @ ! [X1: $i] :
% 2.34/1.42 ( ( c_In @ X1 @ X0 )
% 2.34/1.42 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax68,axiom,
% 2.34/1.42 ( c_V_
% 2.34/1.42 = ( c_In_rec_poly_i
% 2.34/1.42 @ ^ [X0: $i,X1: $i > $i] :
% 2.34/1.42 ( c_famunion @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax69,axiom,
% 2.34/1.42 ( c_Inj1
% 2.34/1.42 = ( c_In_rec_poly_i
% 2.34/1.42 @ ^ [X0: $i,X1: $i > $i] :
% 2.34/1.42 ( c_binunion @ ( c_Sing @ c_Empty )
% 2.34/1.42 @ ( c_Repl @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax70,axiom,
% 2.34/1.42 ( c_Inj0
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( c_Repl @ X0
% 2.34/1.42 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax71,axiom,
% 2.34/1.42 ( c_Unj
% 2.34/1.42 = ( c_In_rec_poly_i
% 2.34/1.42 @ ^ [X0: $i,X1: $i > $i] :
% 2.34/1.42 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 2.34/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax72,axiom,
% 2.34/1.42 ( c_combine_funcs
% 2.34/1.42 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 2.34/1.42 ( c_If_i
% 2.34/1.42 @ ( X4
% 2.34/1.42 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 2.34/1.42 @ ( X2 @ ( c_Unj @ X4 ) )
% 2.34/1.42 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax73,axiom,
% 2.34/1.42 ( c_setsum
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_binunion
% 2.34/1.42 @ ( c_Repl @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 2.34/1.42 @ ( c_Repl @ X1
% 2.34/1.42 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax74,axiom,
% 2.34/1.42 ( c_proj0
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( c_ReplSep @ X0
% 2.34/1.42 @ ^ [X1: $i] :
% 2.34/1.42 ? [X2: $i] :
% 2.34/1.42 ( ( c_Inj0 @ X2 )
% 2.34/1.42 = X1 )
% 2.34/1.42 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax75,axiom,
% 2.34/1.42 ( c_proj1
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( c_ReplSep @ X0
% 2.34/1.42 @ ^ [X1: $i] :
% 2.34/1.42 ? [X2: $i] :
% 2.34/1.42 ( ( c_Inj1 @ X2 )
% 2.34/1.42 = X1 )
% 2.34/1.42 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax76,axiom,
% 2.34/1.42 ( c_binrep
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax77,axiom,
% 2.34/1.42 ( c_lam
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i] :
% 2.34/1.42 ( c_famunion @ X0
% 2.34/1.42 @ ^ [X2: $i] :
% 2.34/1.42 ( c_Repl @ ( X1 @ X2 )
% 2.34/1.42 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax78,axiom,
% 2.34/1.42 ( c_setprod
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_lam @ X0
% 2.34/1.42 @ ^ [X2: $i] : X1 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax79,axiom,
% 2.34/1.42 ( c_ap
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_ReplSep @ X0
% 2.34/1.42 @ ^ [X2: $i] :
% 2.34/1.42 ? [X3: $i] :
% 2.34/1.42 ( X2
% 2.34/1.42 = ( c_setsum @ X1 @ X3 ) )
% 2.34/1.42 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax80,axiom,
% 2.34/1.42 ( c_setsum_p
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 2.34/1.42 = X0 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax81,axiom,
% 2.34/1.42 ( c_tuple_p
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ! [X2: $i] :
% 2.34/1.42 ( ( c_In @ X2 @ X1 )
% 2.34/1.42 => ? [X3: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X3 @ X0 )
% 2.34/1.42 @ ? [X4: $i] :
% 2.34/1.42 ( X2
% 2.34/1.42 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax82,axiom,
% 2.34/1.42 ( c_Pi
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i] :
% 2.34/1.42 ( c_Sep
% 2.34/1.42 @ ( c_Power
% 2.34/1.42 @ ( c_lam @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 2.34/1.42 @ ^ [X2: $i] :
% 2.34/1.42 ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X0 )
% 2.34/1.42 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax83,axiom,
% 2.34/1.42 ( c_setexp
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_Pi @ X1
% 2.34/1.42 @ ^ [X2: $i] : X0 ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax84,axiom,
% 2.34/1.42 ( c_Sep2
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 2.34/1.42 ( c_Sep
% 2.34/1.42 @ ( c_lam @ X0
% 2.34/1.42 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 2.34/1.42 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax85,axiom,
% 2.34/1.42 ( c_set_of_pairs
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ! [X1: $i] :
% 2.34/1.42 ( ( c_In @ X1 @ X0 )
% 2.34/1.42 => ? [X2: $i,X3: $i] :
% 2.34/1.42 ( X1
% 2.34/1.42 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 2.34/1.42 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax86,axiom,
% 2.34/1.42 ( c_lam2
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 2.34/1.42 ( c_lam @ X0
% 2.34/1.42 @ ^ [X3: $i] :
% 2.34/1.42 ( c_lam @ ( X1 @ X3 )
% 2.34/1.42 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax87,axiom,
% 2.34/1.42 ( c_PNoEq_
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.34/1.42 ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X0 )
% 2.34/1.42 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax88,axiom,
% 2.34/1.42 ( c_PNoLt_
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 2.34/1.42 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax89,axiom,
% 2.34/1.42 ( c_PNoLt
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_or @ ( c_PNoLt_ @ ( c_binintersect @ X0 @ X2 ) @ X1 @ X3 ) @ ( c_and @ ( c_and @ ( c_In @ X0 @ X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) @ ( X3 @ X0 ) ) ) @ ( c_and @ ( c_and @ ( c_In @ X2 @ X0 ) @ ( c_PNoEq_ @ X2 @ X1 @ X3 ) ) @ ( c_not @ ( X1 @ X2 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax90,axiom,
% 2.34/1.42 ( c_PNoLe
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o,X2: $i,X3: $i > $o] : ( c_or @ ( c_PNoLt @ X0 @ X1 @ X2 @ X3 ) @ ( c_and @ ( X0 = X2 ) @ ( c_PNoEq_ @ X0 @ X1 @ X3 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax91,axiom,
% 2.34/1.42 ( c_PNo_downc
% 2.34/1.42 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.34/1.42 ? [X3: $i] :
% 2.34/1.42 ( c_and @ ( c_ordinal @ X3 )
% 2.34/1.42 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax92,axiom,
% 2.34/1.42 ( c_PNo_upc
% 2.34/1.42 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 2.34/1.42 ? [X3: $i] :
% 2.34/1.42 ( c_and @ ( c_ordinal @ X3 )
% 2.34/1.42 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax93,axiom,
% 2.34/1.42 ( c_SNoElts_
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( c_binunion @ X0
% 2.34/1.42 @ ( c_Repl @ X0
% 2.34/1.42 @ ^ [X1: $i] :
% 2.34/1.42 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.34/1.42 @ X1 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax94,axiom,
% 2.34/1.42 ( c_SNo_
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 2.34/1.42 @ ! [X2: $i] :
% 2.34/1.42 ( ( c_In @ X2 @ X0 )
% 2.34/1.42 => ( c_exactly1of2
% 2.34/1.42 @ ( c_In
% 2.34/1.42 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.34/1.42 @ X2 )
% 2.34/1.42 @ X1 )
% 2.34/1.42 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax95,axiom,
% 2.34/1.42 ( c_PSNo
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $o] :
% 2.34/1.42 ( c_binunion
% 2.34/1.42 @ ( c_Sep @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 2.34/1.42 @ ( c_ReplSep @ X0
% 2.34/1.42 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 2.34/1.42 @ ^ [X2: $i] :
% 2.34/1.42 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 2.34/1.42 @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax96,axiom,
% 2.34/1.42 ( c_SNo
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax97,axiom,
% 2.34/1.42 ( c_SNoLev
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ( c_Eps_i
% 2.34/1.42 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax98,axiom,
% 2.34/1.42 ( c_SNoEq_
% 2.34/1.42 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.34/1.42 ( c_PNoEq_ @ X0
% 2.34/1.42 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 2.34/1.42 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax99,axiom,
% 2.34/1.42 ( c_SNoLt
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 2.34/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.34/1.42 @ ( c_SNoLev @ X1 )
% 2.34/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax100,axiom,
% 2.34/1.42 ( c_SNoLe
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 2.34/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 2.34/1.42 @ ( c_SNoLev @ X1 )
% 2.34/1.42 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax101,axiom,
% 2.34/1.42 ( c_binop_on
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 2.34/1.42 ! [X2: $i] :
% 2.34/1.42 ( ( c_In @ X2 @ X0 )
% 2.34/1.42 => ! [X3: $i] :
% 2.34/1.42 ( ( c_In @ X3 @ X0 )
% 2.34/1.42 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax102,axiom,
% 2.34/1.42 ( c_Loop
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 2.34/1.42 ( c_and
% 2.34/1.42 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 2.34/1.42 @ ! [X5: $i] :
% 2.34/1.42 ( ( c_In @ X5 @ X0 )
% 2.34/1.42 => ( c_and
% 2.34/1.42 @ ( ( X1 @ X4 @ X5 )
% 2.34/1.42 = X5 )
% 2.34/1.42 @ ( ( X1 @ X5 @ X4 )
% 2.34/1.42 = X5 ) ) ) )
% 2.34/1.42 @ ! [X5: $i] :
% 2.34/1.42 ( ( c_In @ X5 @ X0 )
% 2.34/1.42 => ! [X6: $i] :
% 2.34/1.42 ( ( c_In @ X6 @ X0 )
% 2.34/1.42 => ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 2.34/1.42 = X6 )
% 2.34/1.42 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 2.34/1.42 = X6 ) )
% 2.34/1.42 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 2.34/1.42 = X5 ) )
% 2.34/1.42 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 2.34/1.42 = X5 ) ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax103,axiom,
% 2.34/1.42 ( c_Loop_with_defs
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.34/1.42 ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 2.34/1.42 @ ! [X14: $i] :
% 2.34/1.42 ( ( c_In @ X14 @ X0 )
% 2.34/1.42 => ! [X15: $i] :
% 2.34/1.42 ( ( c_In @ X15 @ X0 )
% 2.34/1.42 => ( ( X5 @ X14 @ X15 )
% 2.34/1.42 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 2.34/1.42 @ ! [X14: $i] :
% 2.34/1.42 ( ( c_In @ X14 @ X0 )
% 2.34/1.42 => ! [X15: $i] :
% 2.34/1.42 ( ( c_In @ X15 @ X0 )
% 2.34/1.42 => ! [X16: $i] :
% 2.34/1.42 ( ( c_In @ X16 @ X0 )
% 2.34/1.42 => ( ( X6 @ X14 @ X15 @ X16 )
% 2.34/1.42 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 2.34/1.42 @ ! [X14: $i] :
% 2.34/1.42 ( ( c_In @ X14 @ X0 )
% 2.34/1.42 => ! [X15: $i] :
% 2.34/1.42 ( ( c_In @ X15 @ X0 )
% 2.34/1.42 => ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( c_and
% 2.34/1.42 @ ( ( X7 @ X14 @ X15 )
% 2.34/1.42 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 2.34/1.42 @ ( ( X10 @ X14 @ X15 )
% 2.34/1.42 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 2.34/1.42 @ ( ( X11 @ X14 @ X15 )
% 2.34/1.42 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 2.34/1.42 @ ( ( X12 @ X14 @ X15 )
% 2.34/1.42 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 2.34/1.42 @ ( ( X13 @ X14 @ X15 )
% 2.34/1.42 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 2.34/1.42 @ ! [X14: $i] :
% 2.34/1.42 ( ( c_In @ X14 @ X0 )
% 2.34/1.42 => ! [X15: $i] :
% 2.34/1.42 ( ( c_In @ X15 @ X0 )
% 2.34/1.42 => ! [X16: $i] :
% 2.34/1.42 ( ( c_In @ X16 @ X0 )
% 2.34/1.42 => ( c_and
% 2.34/1.42 @ ( ( X8 @ X14 @ X15 @ X16 )
% 2.34/1.42 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 2.34/1.42 @ ( ( X9 @ X14 @ X15 @ X16 )
% 2.34/1.42 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax104,axiom,
% 2.34/1.42 ( c_Loop_with_defs_cex1
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.34/1.42 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.34/1.42 @ ? [X14: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X14 @ X0 )
% 2.34/1.42 @ ? [X15: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X15 @ X0 )
% 2.34/1.42 @ ? [X16: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X16 @ X0 )
% 2.34/1.42 @ ? [X17: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X17 @ X0 )
% 2.34/1.42 @ ( c_not
% 2.34/1.42 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 2.34/1.42 = X4 ) ) ) ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax105,axiom,
% 2.34/1.42 ( c_Loop_with_defs_cex2
% 2.34/1.42 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i,X5: $i > $i > $i,X6: $i > $i > $i > $i,X7: $i > $i > $i,X8: $i > $i > $i > $i,X9: $i > $i > $i > $i,X10: $i > $i > $i,X11: $i > $i > $i,X12: $i > $i > $i,X13: $i > $i > $i] :
% 2.34/1.42 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 2.34/1.42 @ ? [X14: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X14 @ X0 )
% 2.34/1.42 @ ? [X15: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X15 @ X0 )
% 2.34/1.42 @ ? [X16: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X16 @ X0 )
% 2.34/1.42 @ ? [X17: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X17 @ X0 )
% 2.34/1.42 @ ? [X18: $i] :
% 2.34/1.42 ( c_and @ ( c_In @ X18 @ X0 )
% 2.34/1.42 @ ( c_not
% 2.34/1.42 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 2.34/1.42 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax106,axiom,
% 2.34/1.42 ( c_combinator
% 2.34/1.42 = ( ^ [X0: $i] :
% 2.34/1.42 ! [X1: $i > $o] :
% 2.34/1.42 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 2.34/1.42 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 2.34/1.42 => ( ! [X2: $i,X3: $i] :
% 2.34/1.42 ( ( X1 @ X2 )
% 2.34/1.42 => ( ( X1 @ X3 )
% 2.34/1.42 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 2.34/1.42 => ( X1 @ X0 ) ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax107,axiom,
% 2.34/1.42 ( c_combinator_equiv
% 2.34/1.42 = ( ^ [X0: $i,X1: $i] :
% 2.34/1.42 ! [X2: $i > $i > $o] :
% 2.34/1.42 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 2.34/1.42 ( ( c_per_i @ X2 )
% 2.34/1.42 => ( ! [X6: $i] :
% 2.34/1.42 ( ( c_combinator @ X6 )
% 2.34/1.42 => ( X2 @ X6 @ X6 ) )
% 2.34/1.42 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 2.34/1.42 ( ( c_combinator @ X6 )
% 2.34/1.42 => ( ( c_combinator @ X7 )
% 2.34/1.42 => ( ( c_combinator @ X8 )
% 2.34/1.42 => ( ( c_combinator @ X9 )
% 2.34/1.42 => ( ( X2 @ X6 @ X8 )
% 2.34/1.42 => ( ( X2 @ X7 @ X9 )
% 2.34/1.42 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 2.34/1.42 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 2.34/1.42 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 2.34/1.42 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 2.34/1.42 @ ( c_Inj0 @ c_Empty )
% 2.34/1.42 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 2.34/1.42 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(ax108,axiom,
% 2.34/1.42 ( c_equip_mod
% 2.34/1.42 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 2.34/1.42 ? [X3: $i,X4: $i] : ( c_or @ ( c_and @ ( c_equip @ ( c_setsum @ X0 @ X3 ) @ X1 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) @ ( c_and @ ( c_equip @ ( c_setsum @ X1 @ X3 ) @ X0 ) @ ( c_equip @ ( c_setprod @ X4 @ X3 ) @ X2 ) ) ) ) ) ).
% 2.34/1.42
% 2.34/1.42 thf(conj,conjecture,
% 2.34/1.42 ( c_not
% 2.34/1.42 @ ! [X0: $i > $i > $o,X1: $i > $i > $i,X2: $i > $o,X3: $i > $o,X4: $i > $i,X5: $i,X6: $i,X7: $i] :
% 2.34/1.42 ( ( X4 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X1 @ ( X1 @ ( X1 @ X6 @ X5 ) @ ( X1 @ X7 @ ( X1 @ ( X1 @ ( X1 @ X5 @ X5 ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X1 @ ( X1 @ X6 @ ( X1 @ X5 @ ( X1 @ X5 @ X7 ) ) ) @ X5 ) ) @ X7 ) @ ( X1 @ ( X4 @ X6 ) @ X7 ) ) @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X5 @ ( X4 @ ( X1 @ X7 @ X5 ) ) ) @ ( X1 @ X6 @ X6 ) ) @ ( X1 @ X6 @ ( X1 @ X7 @ X5 ) ) ) @ X5 ) ) ) @ X7 ) ) ) @ X5 ) ) @ X6 ) @ ( X1 @ X6 @ ( X1 @ X5 @ ( X1 @ ( X1 @ ( X4 @ X5 ) @ ( X1 @ ( X1 @ X6 @ X6 ) @ X6 ) ) @ X5 ) ) ) ) @ ( X4 @ ( X4 @ X6 ) ) ) @ X5 ) )
% 2.34/1.42 = ( X4 @ ( X4 @ X7 ) ) ) ) ).
% 2.34/1.42 ------------------------
% 2.34/1.43 % (30509)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_30392 for (2999ds/4Mi)
% 2.34/1.43 % (30510)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_30392 for (2999ds/27Mi)
% 2.34/1.43 % (30508)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/183Mi)
% 2.34/1.43 % (30514)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/18Mi)
% 2.34/1.43 % (30509)Instruction limit reached!
% 2.34/1.43 % (30509)------------------------------
% 2.34/1.43 % (30509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.43 % (30509)Termination reason: Unknown
% 2.34/1.43 % (30509)Termination phase: shuffling
% 2.34/1.43
% 2.34/1.43 % (30509)Memory used [KB]: 1279
% 2.34/1.43 % (30509)Time elapsed: 0.003 s
% 2.34/1.43 % (30509)Instructions burned: 6 (million)
% 2.34/1.43 % (30509)------------------------------
% 2.34/1.43 % (30509)------------------------------
% 2.34/1.44 % (30514)Instruction limit reached!
% 2.34/1.44 % (30514)------------------------------
% 2.34/1.44 % (30514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.44 % (30514)Termination reason: Unknown
% 2.34/1.44 % (30514)Termination phase: shuffling
% 2.34/1.44
% 2.34/1.44 % (30514)Memory used [KB]: 1535
% 2.34/1.44 % (30514)Time elapsed: 0.006 s
% 2.34/1.44 % (30514)Instructions burned: 18 (million)
% 2.34/1.44 % (30514)------------------------------
% 2.34/1.44 % (30514)------------------------------
% 2.34/1.44 % (30511)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/2Mi)
% 2.34/1.44 % (30513)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_30392 for (2999ds/275Mi)
% 2.34/1.44 % (30512)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_30392 for (2999ds/2Mi)
% 2.34/1.44 % (30510)Instruction limit reached!
% 2.34/1.44 % (30510)------------------------------
% 2.34/1.44 % (30510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.44 % (30510)Termination reason: Unknown
% 2.34/1.44 % (30510)Termination phase: Preprocessing 2
% 2.34/1.44
% 2.34/1.44 % (30510)Memory used [KB]: 1535
% 2.34/1.44 % (30510)Time elapsed: 0.009 s
% 2.34/1.44 % (30510)Instructions burned: 28 (million)
% 2.34/1.44 % (30510)------------------------------
% 2.34/1.44 % (30510)------------------------------
% 2.34/1.44 % (30511)Instruction limit reached!
% 2.34/1.44 % (30511)------------------------------
% 2.34/1.44 % (30511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.44 % (30512)Instruction limit reached!
% 2.34/1.44 % (30512)------------------------------
% 2.34/1.44 % (30512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.44 % (30512)Termination reason: Unknown
% 2.34/1.44 % (30512)Termination phase: shuffling
% 2.34/1.44
% 2.34/1.44 % (30512)Memory used [KB]: 1151
% 2.34/1.44 % (30512)Time elapsed: 0.003 s
% 2.34/1.44 % (30512)Instructions burned: 2 (million)
% 2.34/1.44 % (30512)------------------------------
% 2.34/1.44 % (30512)------------------------------
% 2.34/1.44 % (30511)Termination reason: Unknown
% 2.34/1.44 % (30511)Termination phase: shuffling
% 2.34/1.44
% 2.34/1.44 % (30511)Memory used [KB]: 1151
% 2.34/1.44 % (30511)Time elapsed: 0.003 s
% 2.34/1.44 % (30511)Instructions burned: 2 (million)
% 2.34/1.44 % (30511)------------------------------
% 2.34/1.44 % (30511)------------------------------
% 2.34/1.44 % (30515)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/3Mi)
% 2.34/1.44 % (30515)Instruction limit reached!
% 2.34/1.44 % (30515)------------------------------
% 2.34/1.44 % (30515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.44 % (30515)Termination reason: Unknown
% 2.34/1.44 % (30515)Termination phase: shuffling
% 2.34/1.44
% 2.34/1.44 % (30515)Memory used [KB]: 1279
% 2.34/1.44 % (30515)Time elapsed: 0.002 s
% 2.34/1.44 % (30515)Instructions burned: 4 (million)
% 2.34/1.44 % (30515)------------------------------
% 2.34/1.44 % (30515)------------------------------
% 2.34/1.45 % (30516)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_30392 for (2999ds/37Mi)
% 2.34/1.45 % (30517)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_30392 for (2999ds/15Mi)
% 2.34/1.45 % (30520)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/7Mi)
% 2.34/1.46 % (30517)Instruction limit reached!
% 2.34/1.46 % (30517)------------------------------
% 2.34/1.46 % (30517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.46 % (30517)Termination reason: Unknown
% 2.34/1.46 % (30517)Termination phase: shuffling
% 2.34/1.46
% 2.34/1.46 % (30517)Memory used [KB]: 1407
% 2.34/1.46 % (30517)Time elapsed: 0.006 s
% 2.34/1.46 % (30517)Instructions burned: 15 (million)
% 2.34/1.46 % (30517)------------------------------
% 2.34/1.46 % (30517)------------------------------
% 2.34/1.46 % (30520)Instruction limit reached!
% 2.34/1.46 % (30520)------------------------------
% 2.34/1.46 % (30520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.46 % (30520)Termination reason: Unknown
% 2.34/1.46 % (30520)Termination phase: shuffling
% 2.34/1.46
% 2.34/1.46 % (30520)Memory used [KB]: 1279
% 2.34/1.46 % (30520)Time elapsed: 0.003 s
% 2.34/1.46 % (30520)Instructions burned: 7 (million)
% 2.34/1.46 % (30520)------------------------------
% 2.34/1.46 % (30520)------------------------------
% 2.34/1.46 % (30513)Refutation not found, incomplete strategy
% 2.34/1.46 % (30513)------------------------------
% 2.34/1.46 % (30513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.46 % (30513)Termination reason: Refutation not found, incomplete strategy
% 2.34/1.46
% 2.34/1.46
% 2.34/1.46 % (30513)Memory used [KB]: 6012
% 2.34/1.46 % (30513)Time elapsed: 0.019 s
% 2.34/1.46 % (30513)Instructions burned: 33 (million)
% 2.34/1.46 % (30513)------------------------------
% 2.34/1.46 % (30513)------------------------------
% 2.34/1.46 % (30516)Instruction limit reached!
% 2.34/1.46 % (30516)------------------------------
% 2.34/1.46 % (30516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.46 % (30516)Termination reason: Unknown
% 2.34/1.46 % (30518)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_30392 for (2999ds/3Mi)
% 2.34/1.46 % (30516)Termination phase: Property scanning
% 2.34/1.46
% 2.34/1.46 % (30516)Memory used [KB]: 1535
% 2.34/1.46 % (30516)Time elapsed: 0.012 s
% 2.34/1.46 % (30516)Instructions burned: 38 (million)
% 2.34/1.46 % (30516)------------------------------
% 2.34/1.46 % (30516)------------------------------
% 2.34/1.46 % (30519)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_30392 for (2999ds/1041Mi)
% 2.34/1.46 % (30518)Instruction limit reached!
% 2.34/1.46 % (30518)------------------------------
% 2.34/1.46 % (30518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.46 % (30518)Termination reason: Unknown
% 2.34/1.46 % (30518)Termination phase: shuffling
% 2.34/1.46
% 2.34/1.46 % (30518)Memory used [KB]: 1279
% 2.34/1.46 % (30518)Time elapsed: 0.004 s
% 2.34/1.46 % (30518)Instructions burned: 4 (million)
% 2.34/1.46 % (30518)------------------------------
% 2.34/1.46 % (30518)------------------------------
% 2.34/1.46 % (30522)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_30392 for (2999ds/3Mi)
% 2.34/1.47 % (30521)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/16Mi)
% 2.34/1.47 % (30522)Instruction limit reached!
% 2.34/1.47 % (30522)------------------------------
% 2.34/1.47 % (30522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.47 % (30522)Termination reason: Unknown
% 2.34/1.47 % (30522)Termination phase: shuffling
% 2.34/1.47
% 2.34/1.47 % (30522)Memory used [KB]: 1279
% 2.34/1.47 % (30522)Time elapsed: 0.002 s
% 2.34/1.47 % (30522)Instructions burned: 4 (million)
% 2.34/1.47 % (30522)------------------------------
% 2.34/1.47 % (30522)------------------------------
% 2.34/1.47 % (30524)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/7Mi)
% 2.34/1.47 % (30521)Instruction limit reached!
% 2.34/1.47 % (30521)------------------------------
% 2.34/1.47 % (30521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.47 % (30521)Termination reason: Unknown
% 2.34/1.47 % (30521)Termination phase: shuffling
% 2.34/1.47
% 2.34/1.47 % (30521)Memory used [KB]: 1535
% 2.34/1.47 % (30521)Time elapsed: 0.006 s
% 2.34/1.47 % (30521)Instructions burned: 17 (million)
% 2.34/1.47 % (30521)------------------------------
% 2.34/1.47 % (30521)------------------------------
% 2.34/1.47 % (30524)Instruction limit reached!
% 2.34/1.47 % (30524)------------------------------
% 2.34/1.47 % (30524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.47 % (30524)Termination reason: Unknown
% 2.34/1.47 % (30524)Termination phase: shuffling
% 2.34/1.47
% 2.34/1.47 % (30524)Memory used [KB]: 1279
% 2.34/1.47 % (30524)Time elapsed: 0.004 s
% 2.34/1.47 % (30524)Instructions burned: 8 (million)
% 2.34/1.47 % (30524)------------------------------
% 2.34/1.47 % (30524)------------------------------
% 2.34/1.48 % (30526)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/4Mi)
% 2.34/1.48 % (30523)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_30392 for (2999ds/3Mi)
% 2.34/1.48 % (30526)Instruction limit reached!
% 2.34/1.48 % (30526)------------------------------
% 2.34/1.48 % (30526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (30526)Termination reason: Unknown
% 2.34/1.48 % (30526)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (30526)Memory used [KB]: 1279
% 2.34/1.48 % (30526)Time elapsed: 0.002 s
% 2.34/1.48 % (30526)Instructions burned: 4 (million)
% 2.34/1.48 % (30526)------------------------------
% 2.34/1.48 % (30526)------------------------------
% 2.34/1.48 % (30523)Instruction limit reached!
% 2.34/1.48 % (30523)------------------------------
% 2.34/1.48 % (30523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (30523)Termination reason: Unknown
% 2.34/1.48 % (30523)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (30523)Memory used [KB]: 1279
% 2.34/1.48 % (30523)Time elapsed: 0.004 s
% 2.34/1.48 % (30523)Instructions burned: 4 (million)
% 2.34/1.48 % (30523)------------------------------
% 2.34/1.48 % (30523)------------------------------
% 2.34/1.48 % (30525)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/3Mi)
% 2.34/1.48 % (30525)Instruction limit reached!
% 2.34/1.48 % (30525)------------------------------
% 2.34/1.48 % (30525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (30525)Termination reason: Unknown
% 2.34/1.48 % (30525)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (30525)Memory used [KB]: 1279
% 2.34/1.48 % (30525)Time elapsed: 0.004 s
% 2.34/1.48 % (30525)Instructions burned: 4 (million)
% 2.34/1.48 % (30525)------------------------------
% 2.34/1.48 % (30525)------------------------------
% 2.34/1.48 % (30527)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/18Mi)
% 2.34/1.48 % (30528)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/710Mi)
% 2.34/1.49 % (30529)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/6Mi)
% 2.34/1.49 % (30527)Instruction limit reached!
% 2.34/1.49 % (30527)------------------------------
% 2.34/1.49 % (30527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (30527)Termination reason: Unknown
% 2.34/1.49 % (30527)Termination phase: Property scanning
% 2.34/1.49
% 2.34/1.49 % (30527)Memory used [KB]: 1535
% 2.34/1.49 % (30527)Time elapsed: 0.007 s
% 2.34/1.49 % (30527)Instructions burned: 18 (million)
% 2.34/1.49 % (30527)------------------------------
% 2.34/1.49 % (30527)------------------------------
% 2.34/1.49 % (30529)Instruction limit reached!
% 2.34/1.49 % (30529)------------------------------
% 2.34/1.49 % (30529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (30529)Termination reason: Unknown
% 2.34/1.49 % (30529)Termination phase: shuffling
% 2.34/1.49
% 2.34/1.49 % (30529)Memory used [KB]: 1279
% 2.34/1.49 % (30529)Time elapsed: 0.003 s
% 2.34/1.49 % (30529)Instructions burned: 8 (million)
% 2.34/1.49 % (30529)------------------------------
% 2.34/1.49 % (30529)------------------------------
% 2.34/1.49 % (30508)Instruction limit reached!
% 2.34/1.49 % (30508)------------------------------
% 2.34/1.49 % (30508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (30508)Termination reason: Unknown
% 2.34/1.49 % (30508)Termination phase: Saturation
% 2.34/1.49
% 2.34/1.49 % (30508)Memory used [KB]: 6908
% 2.34/1.49 % (30508)Time elapsed: 0.056 s
% 2.34/1.49 % (30508)Instructions burned: 183 (million)
% 2.34/1.49 % (30508)------------------------------
% 2.34/1.49 % (30508)------------------------------
% 2.34/1.50 % (30530)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_30392 for (2999ds/902Mi)
% 2.34/1.50 % (30531)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_30392 for (2999ds/21Mi)
% 2.37/1.50 % (30532)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/5Mi)
% 2.37/1.50 % (30533)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_30392 for (2999ds/6Mi)
% 2.37/1.50 % (30534)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/377Mi)
% 2.37/1.50 % (30532)Instruction limit reached!
% 2.37/1.50 % (30532)------------------------------
% 2.37/1.50 % (30532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.50 % (30532)Termination reason: Unknown
% 2.37/1.50 % (30532)Termination phase: shuffling
% 2.37/1.50
% 2.37/1.50 % (30532)Memory used [KB]: 1279
% 2.37/1.50 % (30532)Time elapsed: 0.004 s
% 2.37/1.50 % (30532)Instructions burned: 7 (million)
% 2.37/1.50 % (30532)------------------------------
% 2.37/1.50 % (30532)------------------------------
% 2.37/1.50 % (30533)Instruction limit reached!
% 2.37/1.50 % (30533)------------------------------
% 2.37/1.50 % (30533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.50 % (30533)Termination reason: Unknown
% 2.37/1.50 % (30533)Termination phase: shuffling
% 2.37/1.50
% 2.37/1.50 % (30533)Memory used [KB]: 1279
% 2.37/1.50 % (30533)Time elapsed: 0.003 s
% 2.37/1.50 % (30533)Instructions burned: 8 (million)
% 2.37/1.50 % (30533)------------------------------
% 2.37/1.50 % (30533)------------------------------
% 2.37/1.50 % (30531)Instruction limit reached!
% 2.37/1.50 % (30531)------------------------------
% 2.37/1.50 % (30531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.50 % (30531)Termination reason: Unknown
% 2.37/1.50 % (30531)Termination phase: Property scanning
% 2.37/1.50
% 2.37/1.50 % (30531)Memory used [KB]: 1535
% 2.37/1.50 % (30531)Time elapsed: 0.008 s
% 2.37/1.50 % (30531)Instructions burned: 23 (million)
% 2.37/1.50 % (30531)------------------------------
% 2.37/1.50 % (30531)------------------------------
% 2.37/1.51 % (30536)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_30392 for (2999ds/19Mi)
% 2.37/1.51 % (30535)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_30392 for (2999ds/779Mi)
% 2.37/1.51 % (30537)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30392 for (2999ds/879Mi)
% 2.37/1.51 % (30536)Instruction limit reached!
% 2.37/1.51 % (30536)------------------------------
% 2.37/1.51 % (30536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.51 % (30536)Termination reason: Unknown
% 2.37/1.51 % (30536)Termination phase: Property scanning
% 2.37/1.51
% 2.37/1.51 % (30536)Memory used [KB]: 1535
% 2.37/1.51 % (30536)Time elapsed: 0.006 s
% 2.37/1.51 % (30536)Instructions burned: 20 (million)
% 2.37/1.51 % (30536)------------------------------
% 2.37/1.51 % (30536)------------------------------
% 2.37/1.52 % (30538)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/17Mi)
% 2.37/1.53 % (30530)Refutation not found, incomplete strategy
% 2.37/1.53 % (30530)------------------------------
% 2.37/1.53 % (30530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.53 % (30530)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.53
% 2.37/1.53
% 2.37/1.53 % (30530)Memory used [KB]: 6140
% 2.37/1.53 % (30530)Time elapsed: 0.033 s
% 2.37/1.53 % (30530)Instructions burned: 62 (million)
% 2.37/1.53 % (30530)------------------------------
% 2.37/1.53 % (30530)------------------------------
% 2.37/1.53 % (30538)Instruction limit reached!
% 2.37/1.53 % (30538)------------------------------
% 2.37/1.53 % (30538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.53 % (30538)Termination reason: Unknown
% 2.37/1.53 % (30538)Termination phase: Property scanning
% 2.37/1.53
% 2.37/1.53 % (30538)Memory used [KB]: 1535
% 2.37/1.53 % (30538)Time elapsed: 0.006 s
% 2.37/1.53 % (30538)Instructions burned: 19 (million)
% 2.37/1.53 % (30538)------------------------------
% 2.37/1.53 % (30538)------------------------------
% 2.37/1.54 % (30540)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/30Mi)
% 2.37/1.54 % (30539)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/3Mi)
% 2.37/1.54 % (30539)Instruction limit reached!
% 2.37/1.54 % (30539)------------------------------
% 2.37/1.54 % (30539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.54 % (30539)Termination reason: Unknown
% 2.37/1.54 % (30539)Termination phase: shuffling
% 2.37/1.54
% 2.37/1.54 % (30539)Memory used [KB]: 1151
% 2.37/1.54 % (30539)Time elapsed: 0.002 s
% 2.37/1.54 % (30539)Instructions burned: 3 (million)
% 2.37/1.54 % (30539)------------------------------
% 2.37/1.54 % (30539)------------------------------
% 2.37/1.54 % (30540)Instruction limit reached!
% 2.37/1.54 % (30540)------------------------------
% 2.37/1.54 % (30540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.55 % (30540)Termination reason: Unknown
% 2.37/1.55 % (30540)Termination phase: Property scanning
% 2.37/1.55
% 2.37/1.55 % (30540)Memory used [KB]: 1535
% 2.37/1.55 % (30540)Time elapsed: 0.009 s
% 2.37/1.55 % (30540)Instructions burned: 31 (million)
% 2.37/1.55 % (30540)------------------------------
% 2.37/1.55 % (30540)------------------------------
% 2.37/1.55 % (30541)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/127Mi)
% 2.37/1.55 % (30542)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/100Mi)
% 2.37/1.58 % (30542)Instruction limit reached!
% 2.37/1.58 % (30542)------------------------------
% 2.37/1.58 % (30542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.58 % (30542)Termination reason: Unknown
% 2.37/1.58 % (30542)Termination phase: Saturation
% 2.37/1.58
% 2.37/1.58 % (30542)Memory used [KB]: 6396
% 2.37/1.58 % (30542)Time elapsed: 0.027 s
% 2.37/1.58 % (30542)Instructions burned: 101 (million)
% 2.37/1.58 % (30542)------------------------------
% 2.37/1.58 % (30542)------------------------------
% 2.37/1.59 % (30541)Instruction limit reached!
% 2.37/1.59 % (30541)------------------------------
% 2.37/1.59 % (30541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.59 % (30541)Termination reason: Unknown
% 2.37/1.59 % (30541)Termination phase: Saturation
% 2.37/1.59
% 2.37/1.59 % (30541)Memory used [KB]: 6652
% 2.37/1.59 % (30541)Time elapsed: 0.037 s
% 2.37/1.59 % (30541)Instructions burned: 127 (million)
% 2.37/1.59 % (30541)------------------------------
% 2.37/1.59 % (30541)------------------------------
% 2.37/1.59 % (30543)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/3Mi)
% 2.37/1.59 % (30543)Instruction limit reached!
% 2.37/1.59 % (30543)------------------------------
% 2.37/1.59 % (30543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.59 % (30543)Termination reason: Unknown
% 2.37/1.59 % (30543)Termination phase: shuffling
% 2.37/1.59
% 2.37/1.59 % (30543)Memory used [KB]: 1279
% 2.37/1.59 % (30543)Time elapsed: 0.002 s
% 2.37/1.59 % (30543)Instructions burned: 4 (million)
% 2.37/1.59 % (30543)------------------------------
% 2.37/1.59 % (30543)------------------------------
% 2.37/1.60 % (30544)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/20Mi)
% 2.37/1.60 % (30545)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/86Mi)
% 2.37/1.61 % (30544)Instruction limit reached!
% 2.37/1.61 % (30544)------------------------------
% 2.37/1.61 % (30544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.61 % (30544)Termination reason: Unknown
% 2.37/1.61 % (30544)Termination phase: Property scanning
% 2.37/1.61
% 2.37/1.61 % (30544)Memory used [KB]: 1535
% 2.37/1.61 % (30544)Time elapsed: 0.008 s
% 2.37/1.61 % (30544)Instructions burned: 22 (million)
% 2.37/1.61 % (30544)------------------------------
% 2.37/1.61 % (30544)------------------------------
% 2.37/1.61 % (30534)Refutation not found, non-redundant clauses discarded% (30534)------------------------------
% 2.37/1.61 % (30534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.61 % (30534)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.37/1.61
% 2.37/1.61 % (30534)Memory used [KB]: 7036
% 2.37/1.61 % (30534)Time elapsed: 0.132 s
% 2.37/1.61 % (30534)Instructions burned: 371 (million)
% 2.37/1.61 % (30534)------------------------------
% 2.37/1.61 % (30534)------------------------------
% 2.37/1.62 % (30546)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/107Mi)
% 2.37/1.62 % (30547)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_30392 for (2998ds/39Mi)
% 2.37/1.62 % (30545)Instruction limit reached!
% 2.37/1.62 % (30545)------------------------------
% 2.37/1.62 % (30545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.62 % (30545)Termination reason: Unknown
% 2.37/1.62 % (30545)Termination phase: Saturation
% 2.37/1.62
% 2.37/1.62 % (30545)Memory used [KB]: 6524
% 2.37/1.62 % (30545)Time elapsed: 0.023 s
% 2.37/1.62 % (30545)Instructions burned: 87 (million)
% 2.37/1.62 % (30545)------------------------------
% 2.37/1.62 % (30545)------------------------------
% 2.37/1.63 % (30547)Instruction limit reached!
% 2.37/1.63 % (30547)------------------------------
% 2.37/1.63 % (30547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.63 % (30547)Termination reason: Unknown
% 2.37/1.63 % (30547)Termination phase: Function definition elimination
% 2.37/1.63
% 2.37/1.63 % (30547)Memory used [KB]: 1535
% 2.37/1.63 % (30547)Time elapsed: 0.011 s
% 2.37/1.63 % (30547)Instructions burned: 40 (million)
% 2.37/1.63 % (30547)------------------------------
% 2.37/1.63 % (30547)------------------------------
% 2.37/1.63 % (30548)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/448Mi)
% 2.37/1.64 % (30549)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/46Mi)
% 2.37/1.65 % (30549)Instruction limit reached!
% 2.37/1.65 % (30549)------------------------------
% 2.37/1.65 % (30549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.65 % (30549)Termination reason: Unknown
% 2.37/1.65 % (30549)Termination phase: shuffling
% 2.37/1.65
% 2.37/1.65 % (30549)Memory used [KB]: 1535
% 2.37/1.65 % (30549)Time elapsed: 0.013 s
% 2.37/1.65 % (30549)Instructions burned: 47 (million)
% 2.37/1.65 % (30549)------------------------------
% 2.37/1.65 % (30549)------------------------------
% 2.37/1.65 % (30546)Instruction limit reached!
% 2.37/1.65 % (30546)------------------------------
% 2.37/1.65 % (30546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.65 % (30546)Termination reason: Unknown
% 2.37/1.65 % (30546)Termination phase: Saturation
% 2.37/1.65
% 2.37/1.65 % (30546)Memory used [KB]: 6524
% 2.37/1.65 % (30546)Time elapsed: 0.036 s
% 2.37/1.65 % (30546)Instructions burned: 108 (million)
% 2.37/1.65 % (30546)------------------------------
% 2.37/1.65 % (30546)------------------------------
% 2.37/1.66 % (30550)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/98Mi)
% 2.37/1.66 % (30551)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/507Mi)
% 2.37/1.68 % (30550)Instruction limit reached!
% 2.37/1.68 % (30550)------------------------------
% 2.37/1.68 % (30550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.68 % (30550)Termination reason: Unknown
% 2.37/1.68 % (30550)Termination phase: Saturation
% 2.37/1.68
% 2.37/1.68 % (30550)Memory used [KB]: 1918
% 2.37/1.68 % (30550)Time elapsed: 0.026 s
% 2.37/1.68 % (30550)Instructions burned: 99 (million)
% 2.37/1.68 % (30550)------------------------------
% 2.37/1.68 % (30550)------------------------------
% 2.37/1.69 % (30528)Instruction limit reached!
% 2.37/1.69 % (30528)------------------------------
% 2.37/1.69 % (30528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.69 % (30528)Termination reason: Unknown
% 2.37/1.69 % (30528)Termination phase: Saturation
% 2.37/1.69
% 2.37/1.69 % (30528)Memory used [KB]: 8315
% 2.37/1.69 % (30528)Time elapsed: 0.207 s
% 2.37/1.69 % (30528)Instructions burned: 712 (million)
% 2.37/1.69 % (30528)------------------------------
% 2.37/1.69 % (30528)------------------------------
% 2.37/1.69 % (30552)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/149Mi)
% 2.37/1.70 % (30553)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/39Mi)
% 2.37/1.71 % (30553)Instruction limit reached!
% 2.37/1.71 % (30553)------------------------------
% 2.37/1.71 % (30553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.71 % (30553)Termination reason: Unknown
% 2.37/1.71 % (30553)Termination phase: Function definition elimination
% 2.37/1.71
% 2.37/1.71 % (30553)Memory used [KB]: 1535
% 2.37/1.71 % (30553)Time elapsed: 0.011 s
% 2.37/1.71 % (30553)Instructions burned: 39 (million)
% 2.37/1.71 % (30553)------------------------------
% 2.37/1.71 % (30553)------------------------------
% 2.37/1.72 % (30554)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/6Mi)
% 2.37/1.72 % (30554)Instruction limit reached!
% 2.37/1.72 % (30554)------------------------------
% 2.37/1.72 % (30554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.72 % (30554)Termination reason: Unknown
% 2.37/1.72 % (30554)Termination phase: shuffling
% 2.37/1.72
% 2.37/1.72 % (30554)Memory used [KB]: 1279
% 2.37/1.72 % (30554)Time elapsed: 0.003 s
% 2.37/1.72 % (30554)Instructions burned: 8 (million)
% 2.37/1.72 % (30554)------------------------------
% 2.37/1.72 % (30554)------------------------------
% 2.37/1.73 % (30555)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_30392 for (2997ds/1087Mi)
% 2.37/1.73 % (30552)Instruction limit reached!
% 2.37/1.73 % (30552)------------------------------
% 2.37/1.73 % (30552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.73 % (30552)Termination reason: Unknown
% 2.37/1.73 % (30552)Termination phase: Saturation
% 2.37/1.73
% 2.37/1.73 % (30552)Memory used [KB]: 6652
% 2.37/1.73 % (30552)Time elapsed: 0.042 s
% 2.37/1.73 % (30552)Instructions burned: 149 (million)
% 2.37/1.73 % (30552)------------------------------
% 2.37/1.73 % (30552)------------------------------
% 2.37/1.73 % (30535)Instruction limit reached!
% 2.37/1.73 % (30535)------------------------------
% 2.37/1.73 % (30535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.73 % (30535)Termination reason: Unknown
% 2.37/1.73 % (30535)Termination phase: Saturation
% 2.37/1.73
% 2.37/1.73 % (30535)Memory used [KB]: 7291
% 2.37/1.73 % (30535)Time elapsed: 0.249 s
% 2.37/1.73 % (30535)Instructions burned: 779 (million)
% 2.37/1.73 % (30535)------------------------------
% 2.37/1.73 % (30535)------------------------------
% 2.37/1.74 % (30556)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/47Mi)
% 2.37/1.74 % (30557)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/44Mi)
% 2.37/1.75 % (30556)Instruction limit reached!
% 2.37/1.75 % (30556)------------------------------
% 2.37/1.75 % (30556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.75 % (30556)Termination reason: Unknown
% 2.37/1.75 % (30556)Termination phase: Function definition elimination
% 2.37/1.75
% 2.37/1.75 % (30556)Memory used [KB]: 1663
% 2.37/1.75 % (30556)Time elapsed: 0.013 s
% 2.37/1.75 % (30556)Instructions burned: 49 (million)
% 2.37/1.75 % (30556)------------------------------
% 2.37/1.75 % (30556)------------------------------
% 2.37/1.76 % (30557)Instruction limit reached!
% 2.37/1.76 % (30557)------------------------------
% 2.37/1.76 % (30557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.76 % (30557)Termination reason: Unknown
% 2.37/1.76 % (30557)Termination phase: Saturation
% 2.37/1.76
% 2.37/1.76 % (30557)Memory used [KB]: 1663
% 2.37/1.76 % (30557)Time elapsed: 0.013 s
% 2.37/1.76 % (30557)Instructions burned: 44 (million)
% 2.37/1.76 % (30557)------------------------------
% 2.37/1.76 % (30557)------------------------------
% 2.37/1.76 % (30548)Instruction limit reached!
% 2.37/1.76 % (30548)------------------------------
% 2.37/1.76 % (30548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.76 % (30548)Termination reason: Unknown
% 2.37/1.76 % (30548)Termination phase: Saturation
% 2.37/1.76
% 2.37/1.76 % (30548)Memory used [KB]: 7164
% 2.37/1.76 % (30548)Time elapsed: 0.128 s
% 2.37/1.76 % (30548)Instructions burned: 450 (million)
% 2.37/1.76 % (30548)------------------------------
% 2.37/1.76 % (30548)------------------------------
% 2.37/1.76 % (30537)Instruction limit reached!
% 2.37/1.76 % (30537)------------------------------
% 2.37/1.76 % (30537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.76 % (30537)Termination reason: Unknown
% 2.37/1.76 % (30537)Termination phase: Saturation
% 2.37/1.76
% 2.37/1.76 % (30537)Memory used [KB]: 9210
% 2.37/1.76 % (30537)Time elapsed: 0.253 s
% 2.37/1.76 % (30537)Instructions burned: 879 (million)
% 2.37/1.76 % (30537)------------------------------
% 2.37/1.76 % (30537)------------------------------
% 2.37/1.76 % (30558)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/432Mi)
% 2.37/1.77 % (30559)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/62Mi)
% 2.37/1.77 % (30560)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/31Mi)
% 2.37/1.77 % (30561)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/96Mi)
% 2.37/1.77 % (30519)Instruction limit reached!
% 2.37/1.77 % (30519)------------------------------
% 2.37/1.77 % (30519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.77 % (30519)Termination reason: Unknown
% 2.37/1.77 % (30519)Termination phase: Saturation
% 2.37/1.77
% 2.37/1.77 % (30519)Memory used [KB]: 11129
% 2.37/1.77 % (30519)Time elapsed: 0.318 s
% 2.37/1.77 % (30519)Instructions burned: 1043 (million)
% 2.37/1.77 % (30519)------------------------------
% 2.37/1.77 % (30519)------------------------------
% 2.37/1.78 % (30560)Instruction limit reached!
% 2.37/1.78 % (30560)------------------------------
% 2.37/1.78 % (30560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.78 % (30560)Termination reason: Unknown
% 2.37/1.78 % (30560)Termination phase: Property scanning
% 2.37/1.78
% 2.37/1.78 % (30560)Memory used [KB]: 1535
% 2.37/1.78 % (30560)Time elapsed: 0.009 s
% 2.37/1.78 % (30560)Instructions burned: 31 (million)
% 2.37/1.78 % (30560)------------------------------
% 2.37/1.78 % (30560)------------------------------
% 2.37/1.78 % (30559)Instruction limit reached!
% 2.37/1.78 % (30559)------------------------------
% 2.37/1.78 % (30559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.78 % (30559)Termination reason: Unknown
% 2.37/1.78 % (30559)Termination phase: Function definition elimination
% 2.37/1.78
% 2.37/1.78 % (30559)Memory used [KB]: 1791
% 2.37/1.78 % (30559)Time elapsed: 0.016 s
% 2.37/1.78 % (30559)Instructions burned: 64 (million)
% 2.37/1.78 % (30559)------------------------------
% 2.37/1.78 % (30559)------------------------------
% 2.37/1.79 % (30562)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/453Mi)
% 2.37/1.79 % (30563)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/71Mi)
% 2.37/1.79 % (30564)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/83Mi)
% 2.37/1.80 % (30561)Instruction limit reached!
% 2.37/1.80 % (30561)------------------------------
% 2.37/1.80 % (30561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.80 % (30561)Termination reason: Unknown
% 2.37/1.80 % (30561)Termination phase: Saturation
% 2.37/1.80
% 2.37/1.80 % (30561)Memory used [KB]: 6524
% 2.37/1.80 % (30561)Time elapsed: 0.029 s
% 2.37/1.80 % (30561)Instructions burned: 98 (million)
% 2.37/1.80 % (30561)------------------------------
% 2.37/1.80 % (30561)------------------------------
% 2.37/1.80 % (30563)Instruction limit reached!
% 2.37/1.80 % (30563)------------------------------
% 2.37/1.80 % (30563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.80 % (30563)Termination reason: Unknown
% 2.37/1.80 % (30563)Termination phase: Saturation
% 2.37/1.80
% 2.37/1.80 % (30563)Memory used [KB]: 6268
% 2.37/1.80 % (30563)Time elapsed: 0.018 s
% 2.37/1.80 % (30563)Instructions burned: 72 (million)
% 2.37/1.80 % (30563)------------------------------
% 2.37/1.80 % (30563)------------------------------
% 2.37/1.81 % (30566)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/41Mi)
% 2.37/1.81 % (30565)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/11Mi)
% 2.37/1.81 % (30564)Instruction limit reached!
% 2.37/1.81 % (30564)------------------------------
% 2.37/1.81 % (30564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.81 % (30564)Termination reason: Unknown
% 2.37/1.81 % (30564)Termination phase: Saturation
% 2.37/1.81
% 2.37/1.81 % (30564)Memory used [KB]: 6396
% 2.37/1.81 % (30564)Time elapsed: 0.025 s
% 2.37/1.81 % (30564)Instructions burned: 84 (million)
% 2.37/1.81 % (30564)------------------------------
% 2.37/1.81 % (30564)------------------------------
% 2.37/1.82 % (30565)Instruction limit reached!
% 2.37/1.82 % (30565)------------------------------
% 2.37/1.82 % (30565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.82 % (30565)Termination reason: Unknown
% 2.37/1.82 % (30565)Termination phase: shuffling
% 2.37/1.82
% 2.37/1.82 % (30565)Memory used [KB]: 1407
% 2.37/1.82 % (30565)Time elapsed: 0.005 s
% 2.37/1.82 % (30565)Instructions burned: 11 (million)
% 2.37/1.82 % (30565)------------------------------
% 2.37/1.82 % (30565)------------------------------
% 2.37/1.82 % (30551)Instruction limit reached!
% 2.37/1.82 % (30551)------------------------------
% 2.37/1.82 % (30551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.82 % (30551)Termination reason: Unknown
% 2.37/1.82 % (30551)Termination phase: Saturation
% 2.37/1.82
% 2.37/1.82 % (30551)Memory used [KB]: 7036
% 2.37/1.82 % (30551)Time elapsed: 0.161 s
% 2.37/1.82 % (30551)Instructions burned: 509 (million)
% 2.37/1.82 % (30551)------------------------------
% 2.37/1.82 % (30551)------------------------------
% 2.37/1.82 % (30566)Instruction limit reached!
% 2.37/1.82 % (30566)------------------------------
% 2.37/1.82 % (30566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.82 % (30566)Termination reason: Unknown
% 2.37/1.82 % (30566)Termination phase: Function definition elimination
% 2.37/1.82
% 2.37/1.82 % (30566)Memory used [KB]: 1535
% 2.37/1.82 % (30566)Time elapsed: 0.011 s
% 2.37/1.82 % (30566)Instructions burned: 41 (million)
% 2.37/1.82 % (30566)------------------------------
% 2.37/1.82 % (30566)------------------------------
% 2.37/1.82 % (30567)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/6Mi)
% 2.37/1.82 % (30567)Instruction limit reached!
% 2.37/1.82 % (30567)------------------------------
% 2.37/1.82 % (30567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.82 % (30567)Termination reason: Unknown
% 2.37/1.82 % (30567)Termination phase: shuffling
% 2.37/1.82
% 2.37/1.82 % (30567)Memory used [KB]: 1279
% 2.37/1.82 % (30567)Time elapsed: 0.003 s
% 2.37/1.82 % (30567)Instructions burned: 8 (million)
% 2.37/1.82 % (30567)------------------------------
% 2.37/1.82 % (30567)------------------------------
% 2.37/1.83 % (30568)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/150Mi)
% 2.37/1.83 % (30569)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/343Mi)
% 2.37/1.83 % (30570)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/109Mi)
% 2.37/1.83 % (30571)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_30392 for (2996ds/253Mi)
% 2.37/1.85 % (30571)Refutation not found, incomplete strategy
% 2.37/1.85 % (30571)------------------------------
% 2.37/1.85 % (30571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.85 % (30571)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.85
% 2.37/1.85
% 2.37/1.85 % (30571)Memory used [KB]: 6268
% 2.37/1.85 % (30571)Time elapsed: 0.018 s
% 2.37/1.85 % (30571)Instructions burned: 61 (million)
% 2.37/1.85 % (30571)------------------------------
% 2.37/1.85 % (30571)------------------------------
% 2.37/1.86 % (30570)Instruction limit reached!
% 2.37/1.86 % (30570)------------------------------
% 2.37/1.86 % (30570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.86 % (30570)Termination reason: Unknown
% 2.37/1.86 % (30570)Termination phase: Saturation
% 2.37/1.86
% 2.37/1.86 % (30570)Memory used [KB]: 6524
% 2.37/1.86 % (30570)Time elapsed: 0.030 s
% 2.37/1.86 % (30570)Instructions burned: 109 (million)
% 2.37/1.86 % (30570)------------------------------
% 2.37/1.86 % (30570)------------------------------
% 2.37/1.86 % (30572)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/140Mi)
% 2.37/1.87 % (30568)Instruction limit reached!
% 2.37/1.87 % (30568)------------------------------
% 2.37/1.87 % (30568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.87 % (30568)Termination reason: Unknown
% 2.37/1.87 % (30568)Termination phase: Saturation
% 2.37/1.87
% 2.37/1.87 % (30568)Memory used [KB]: 6652
% 2.37/1.87 % (30568)Time elapsed: 0.043 s
% 2.37/1.87 % (30568)Instructions burned: 151 (million)
% 2.37/1.87 % (30568)------------------------------
% 2.37/1.87 % (30568)------------------------------
% 2.37/1.87 % (30573)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/614Mi)
% 2.37/1.88 % (30574)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/202Mi)
% 2.37/1.88 % (30558)Instruction limit reached!
% 2.37/1.88 % (30558)------------------------------
% 2.37/1.88 % (30558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.88 % (30558)Termination reason: Unknown
% 2.37/1.88 % (30558)Termination phase: Saturation
% 2.37/1.88
% 2.37/1.88 % (30558)Memory used [KB]: 4093
% 2.37/1.88 % (30558)Time elapsed: 0.118 s
% 2.37/1.88 % (30558)Instructions burned: 434 (million)
% 2.37/1.88 % (30558)------------------------------
% 2.37/1.88 % (30558)------------------------------
% 2.37/1.88 % (30572)Refutation not found, incomplete strategy
% 2.37/1.88 % (30572)------------------------------
% 2.37/1.88 % (30572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.88 % (30572)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.88
% 2.37/1.88
% 2.37/1.88 % (30572)Memory used [KB]: 6396
% 2.37/1.88 % (30572)Time elapsed: 0.024 s
% 2.37/1.88 % (30572)Instructions burned: 78 (million)
% 2.37/1.88 % (30572)------------------------------
% 2.37/1.88 % (30572)------------------------------
% 2.37/1.89 % (30574)Refutation not found, incomplete strategy
% 2.37/1.89 % (30574)------------------------------
% 2.37/1.89 % (30574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.89 % (30574)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.89
% 2.37/1.89
% 2.37/1.89 % (30574)Memory used [KB]: 6012
% 2.37/1.89 % (30574)Time elapsed: 0.010 s
% 2.37/1.89 % (30574)Instructions burned: 34 (million)
% 2.37/1.89 % (30574)------------------------------
% 2.37/1.89 % (30574)------------------------------
% 2.37/1.89 % (30575)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/339Mi)
% 2.37/1.89 % (30576)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/283Mi)
% 2.37/1.90 % (30577)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/134Mi)
% 2.37/1.90 % (30569)Refutation not found, incomplete strategy
% 2.37/1.90 % (30569)------------------------------
% 2.37/1.90 % (30569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.90 % (30569)Termination reason: Refutation not found, incomplete strategy
% 2.37/1.90
% 2.37/1.90
% 2.37/1.90 % (30569)Memory used [KB]: 6524
% 2.37/1.90 % (30569)Time elapsed: 0.073 s
% 2.37/1.90 % (30569)Instructions burned: 221 (million)
% 2.37/1.90 % (30569)------------------------------
% 2.37/1.90 % (30569)------------------------------
% 2.37/1.91 % (30562)Instruction limit reached!
% 2.37/1.91 % (30562)------------------------------
% 2.37/1.91 % (30562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.91 % (30562)Termination reason: Unknown
% 2.37/1.91 % (30562)Termination phase: Saturation
% 2.37/1.91
% 2.37/1.91 % (30562)Memory used [KB]: 9338
% 2.37/1.91 % (30562)Time elapsed: 0.125 s
% 2.37/1.91 % (30562)Instructions burned: 455 (million)
% 2.37/1.91 % (30562)------------------------------
% 2.37/1.91 % (30562)------------------------------
% 2.37/1.91 % (30578)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/298Mi)
% 2.37/1.92 % (30579)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30392 for (2995ds/192Mi)
% 2.37/1.93 % (30577)Instruction limit reached!
% 2.37/1.93 % (30577)------------------------------
% 2.37/1.93 % (30577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.93 % (30577)Termination reason: Unknown
% 2.37/1.93 % (30577)Termination phase: Saturation
% 2.37/1.93
% 2.37/1.93 % (30577)Memory used [KB]: 6652
% 2.37/1.93 % (30577)Time elapsed: 0.060 s
% 2.37/1.93 % (30577)Instructions burned: 136 (million)
% 2.37/1.93 % (30577)------------------------------
% 2.37/1.93 % (30577)------------------------------
% 2.37/1.94 % (30583)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/258Mi)
% 2.37/1.97 % (30579)Instruction limit reached!
% 2.37/1.97 % (30579)------------------------------
% 2.37/1.97 % (30579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.97 % (30579)Termination reason: Unknown
% 2.37/1.97 % (30579)Termination phase: Saturation
% 2.37/1.97
% 2.37/1.97 % (30579)Memory used [KB]: 6908
% 2.37/1.97 % (30579)Time elapsed: 0.053 s
% 2.37/1.97 % (30579)Instructions burned: 194 (million)
% 2.37/1.97 % (30579)------------------------------
% 2.37/1.97 % (30579)------------------------------
% 2.37/1.98 % (30576)Instruction limit reached!
% 2.37/1.98 % (30576)------------------------------
% 2.37/1.98 % (30576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/1.98 % (30576)Termination reason: Unknown
% 2.37/1.98 % (30576)Termination phase: Saturation
% 2.37/1.98
% 2.37/1.98 % (30576)Memory used [KB]: 7164
% 2.37/1.98 % (30576)Time elapsed: 0.106 s
% 2.37/1.98 % (30576)Instructions burned: 283 (million)
% 2.37/1.98 % (30576)------------------------------
% 2.37/1.98 % (30576)------------------------------
% 2.37/1.98 % (30598)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/90Mi)
% 2.37/1.99 % (30599)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/231Mi)
% 2.37/2.00 % (30578)Instruction limit reached!
% 2.37/2.00 % (30578)------------------------------
% 2.37/2.00 % (30578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/2.00 % (30578)Termination reason: Unknown
% 2.37/2.00 % (30578)Termination phase: Saturation
% 2.37/2.00
% 2.37/2.00 % (30578)Memory used [KB]: 7164
% 2.37/2.00 % (30578)Time elapsed: 0.089 s
% 2.37/2.00 % (30578)Instructions burned: 299 (million)
% 2.37/2.00 % (30578)------------------------------
% 2.37/2.00 % (30578)------------------------------
% 2.37/2.00 % (30575)Instruction limit reached!
% 2.37/2.00 % (30575)------------------------------
% 2.37/2.00 % (30575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/2.00 % (30575)Termination reason: Unknown
% 2.37/2.00 % (30575)Termination phase: Saturation
% 2.37/2.00
% 2.37/2.00 % (30575)Memory used [KB]: 7547
% 2.37/2.00 % (30575)Time elapsed: 0.111 s
% 2.37/2.00 % (30575)Instructions burned: 342 (million)
% 2.37/2.00 % (30575)------------------------------
% 2.37/2.00 % (30575)------------------------------
% 2.37/2.00 % (30598)Instruction limit reached!
% 2.37/2.00 % (30598)------------------------------
% 2.37/2.00 % (30598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.37/2.00 % (30598)Termination reason: Unknown
% 2.37/2.00 % (30598)Termination phase: Saturation
% 2.37/2.00
% 2.37/2.00 % (30598)Memory used [KB]: 6396
% 2.37/2.00 % (30598)Time elapsed: 0.024 s
% 2.37/2.00 % (30598)Instructions burned: 90 (million)
% 2.37/2.00 % (30598)------------------------------
% 2.37/2.00 % (30598)------------------------------
% 2.37/2.01 % (30600)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/458Mi)
% 2.37/2.01 % (30601)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/31Mi)
% 6.41/2.01 % (30602)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/297Mi)
% 6.41/2.01 % (30583)Instruction limit reached!
% 6.41/2.01 % (30583)------------------------------
% 6.41/2.01 % (30583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.01 % (30583)Termination reason: Unknown
% 6.41/2.01 % (30583)Termination phase: Saturation
% 6.41/2.01
% 6.41/2.01 % (30583)Memory used [KB]: 6908
% 6.41/2.01 % (30583)Time elapsed: 0.072 s
% 6.41/2.01 % (30583)Instructions burned: 259 (million)
% 6.41/2.01 % (30583)------------------------------
% 6.41/2.01 % (30583)------------------------------
% 6.41/2.02 % (30601)Instruction limit reached!
% 6.41/2.02 % (30601)------------------------------
% 6.41/2.02 % (30601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.02 % (30601)Termination reason: Unknown
% 6.41/2.02 % (30601)Termination phase: Property scanning
% 6.41/2.02
% 6.41/2.02 % (30601)Memory used [KB]: 1535
% 6.41/2.02 % (30601)Time elapsed: 0.010 s
% 6.41/2.02 % (30601)Instructions burned: 34 (million)
% 6.41/2.02 % (30601)------------------------------
% 6.41/2.02 % (30601)------------------------------
% 6.41/2.02 % (30603)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/987Mi)
% 6.41/2.03 % (30604)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_30392 for (2994ds/182Mi)
% 6.41/2.06 % (30555)Instruction limit reached!
% 6.41/2.06 % (30555)------------------------------
% 6.41/2.06 % (30555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.06 % (30555)Termination reason: Unknown
% 6.41/2.06 % (30555)Termination phase: Saturation
% 6.41/2.06
% 6.41/2.06 % (30555)Memory used [KB]: 8315
% 6.41/2.06 % (30555)Time elapsed: 0.334 s
% 6.41/2.06 % (30555)Instructions burned: 1089 (million)
% 6.41/2.06 % (30555)------------------------------
% 6.41/2.06 % (30555)------------------------------
% 6.41/2.07 % (30599)Instruction limit reached!
% 6.41/2.07 % (30599)------------------------------
% 6.41/2.07 % (30599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.07 % (30599)Termination reason: Unknown
% 6.41/2.07 % (30599)Termination phase: Saturation
% 6.41/2.07
% 6.41/2.07 % (30599)Memory used [KB]: 6908
% 6.41/2.07 % (30599)Time elapsed: 0.074 s
% 6.41/2.07 % (30599)Instructions burned: 233 (million)
% 6.41/2.07 % (30599)------------------------------
% 6.41/2.07 % (30599)------------------------------
% 6.41/2.07 % (30605)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/182Mi)
% 6.41/2.08 % (30606)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/154Mi)
% 6.41/2.08 % (30573)Instruction limit reached!
% 6.41/2.08 % (30573)------------------------------
% 6.41/2.08 % (30573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.08 % (30573)Termination reason: Unknown
% 6.41/2.08 % (30573)Termination phase: Saturation
% 6.41/2.08
% 6.41/2.08 % (30573)Memory used [KB]: 7419
% 6.41/2.08 % (30573)Time elapsed: 0.225 s
% 6.41/2.08 % (30573)Instructions burned: 614 (million)
% 6.41/2.08 % (30573)------------------------------
% 6.41/2.08 % (30573)------------------------------
% 6.41/2.08 % (30604)Instruction limit reached!
% 6.41/2.08 % (30604)------------------------------
% 6.41/2.08 % (30604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.08 % (30604)Termination reason: Unknown
% 6.41/2.08 % (30604)Termination phase: Saturation
% 6.41/2.08
% 6.41/2.08 % (30604)Memory used [KB]: 6652
% 6.41/2.08 % (30604)Time elapsed: 0.054 s
% 6.41/2.08 % (30604)Instructions burned: 184 (million)
% 6.41/2.08 % (30604)------------------------------
% 6.41/2.08 % (30604)------------------------------
% 6.41/2.09 % (30607)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/79Mi)
% 6.41/2.09 % (30608)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/216Mi)
% 6.41/2.10 % (30602)Instruction limit reached!
% 6.41/2.10 % (30602)------------------------------
% 6.41/2.10 % (30602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.10 % (30602)Termination reason: Unknown
% 6.41/2.10 % (30602)Termination phase: Saturation
% 6.41/2.10
% 6.41/2.10 % (30602)Memory used [KB]: 6780
% 6.41/2.10 % (30602)Time elapsed: 0.088 s
% 6.41/2.10 % (30602)Instructions burned: 298 (million)
% 6.41/2.10 % (30602)------------------------------
% 6.41/2.10 % (30602)------------------------------
% 6.41/2.11 % (30609)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/114Mi)
% 6.41/2.11 % (30607)Instruction limit reached!
% 6.41/2.11 % (30607)------------------------------
% 6.41/2.11 % (30607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.11 % (30607)Termination reason: Unknown
% 6.41/2.11 % (30607)Termination phase: Saturation
% 6.41/2.11
% 6.41/2.11 % (30607)Memory used [KB]: 6396
% 6.41/2.11 % (30607)Time elapsed: 0.021 s
% 6.41/2.11 % (30607)Instructions burned: 80 (million)
% 6.41/2.11 % (30607)------------------------------
% 6.41/2.11 % (30607)------------------------------
% 6.81/2.12 % (30606)Instruction limit reached!
% 6.81/2.12 % (30606)------------------------------
% 6.81/2.12 % (30606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.12 % (30606)Termination reason: Unknown
% 6.81/2.12 % (30606)Termination phase: Saturation
% 6.81/2.12
% 6.81/2.12 % (30606)Memory used [KB]: 6780
% 6.81/2.12 % (30606)Time elapsed: 0.042 s
% 6.81/2.12 % (30606)Instructions burned: 157 (million)
% 6.81/2.12 % (30606)------------------------------
% 6.81/2.12 % (30606)------------------------------
% 6.81/2.12 % (30610)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/922Mi)
% 6.81/2.12 % (30605)Instruction limit reached!
% 6.81/2.12 % (30605)------------------------------
% 6.81/2.12 % (30605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.12 % (30605)Termination reason: Unknown
% 6.81/2.12 % (30605)Termination phase: Saturation
% 6.81/2.12
% 6.81/2.12 % (30605)Memory used [KB]: 6652
% 6.81/2.12 % (30605)Time elapsed: 0.055 s
% 6.81/2.12 % (30605)Instructions burned: 183 (million)
% 6.81/2.12 % (30605)------------------------------
% 6.81/2.12 % (30605)------------------------------
% 6.81/2.13 % (30611)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/182Mi)
% 6.81/2.13 % (30600)Instruction limit reached!
% 6.81/2.13 % (30600)------------------------------
% 6.81/2.13 % (30600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.13 % (30600)Termination reason: Unknown
% 6.81/2.13 % (30600)Termination phase: Saturation
% 6.81/2.13
% 6.81/2.13 % (30600)Memory used [KB]: 8571
% 6.81/2.13 % (30600)Time elapsed: 0.124 s
% 6.81/2.13 % (30600)Instructions burned: 461 (million)
% 6.81/2.13 % (30600)------------------------------
% 6.81/2.13 % (30600)------------------------------
% 6.81/2.13 % (30612)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_30392 for (2993ds/164Mi)
% 6.81/2.13 % (30610)Refutation not found, incomplete strategy
% 6.81/2.13 % (30610)------------------------------
% 6.81/2.13 % (30610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.13 % (30610)Termination reason: Refutation not found, incomplete strategy
% 6.81/2.13
% 6.81/2.13
% 6.81/2.13 % (30610)Memory used [KB]: 6268
% 6.81/2.13 % (30610)Time elapsed: 0.013 s
% 6.81/2.13 % (30610)Instructions burned: 42 (million)
% 6.81/2.13 % (30610)------------------------------
% 6.81/2.13 % (30610)------------------------------
% 6.81/2.14 % (30609)Instruction limit reached!
% 6.81/2.14 % (30609)------------------------------
% 6.81/2.14 % (30609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.14 % (30609)Termination reason: Unknown
% 6.81/2.14 % (30609)Termination phase: Saturation
% 6.81/2.14
% 6.81/2.14 % (30609)Memory used [KB]: 6524
% 6.81/2.14 % (30609)Time elapsed: 0.032 s
% 6.81/2.14 % (30609)Instructions burned: 115 (million)
% 6.81/2.14 % (30609)------------------------------
% 6.81/2.14 % (30609)------------------------------
% 6.81/2.14 % (30613)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/50Mi)
% 6.81/2.14 % (30614)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/368Mi)
% 6.81/2.15 % (30615)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/1021Mi)
% 6.81/2.15 % (30608)Instruction limit reached!
% 6.81/2.15 % (30608)------------------------------
% 6.81/2.15 % (30608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.15 % (30608)Termination reason: Unknown
% 6.81/2.15 % (30608)Termination phase: Saturation
% 6.81/2.15
% 6.81/2.15 % (30608)Memory used [KB]: 6908
% 6.81/2.15 % (30608)Time elapsed: 0.061 s
% 6.81/2.15 % (30608)Instructions burned: 217 (million)
% 6.81/2.15 % (30608)------------------------------
% 6.81/2.15 % (30608)------------------------------
% 6.81/2.15 % (30613)Instruction limit reached!
% 6.81/2.15 % (30613)------------------------------
% 6.81/2.15 % (30613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.15 % (30613)Termination reason: Unknown
% 6.81/2.15 % (30613)Termination phase: Function definition elimination
% 6.81/2.15
% 6.81/2.15 % (30613)Memory used [KB]: 1663
% 6.81/2.15 % (30613)Time elapsed: 0.013 s
% 6.81/2.15 % (30613)Instructions burned: 50 (million)
% 6.81/2.15 % (30613)------------------------------
% 6.81/2.15 % (30613)------------------------------
% 6.81/2.16 % (30616)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/267Mi)
% 6.81/2.16 % (30617)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/204Mi)
% 6.81/2.18 % (30611)Instruction limit reached!
% 6.81/2.18 % (30611)------------------------------
% 6.81/2.18 % (30611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.18 % (30611)Termination reason: Unknown
% 6.81/2.18 % (30611)Termination phase: Saturation
% 6.81/2.18
% 6.81/2.18 % (30611)Memory used [KB]: 6524
% 6.81/2.18 % (30611)Time elapsed: 0.051 s
% 6.81/2.18 % (30611)Instructions burned: 183 (million)
% 6.81/2.18 % (30611)------------------------------
% 6.81/2.18 % (30611)------------------------------
% 6.81/2.18 % (30612)Instruction limit reached!
% 6.81/2.18 % (30612)------------------------------
% 6.81/2.18 % (30612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.18 % (30612)Termination reason: Unknown
% 6.81/2.18 % (30612)Termination phase: Saturation
% 6.81/2.18
% 6.81/2.18 % (30612)Memory used [KB]: 1918
% 6.81/2.18 % (30612)Time elapsed: 0.048 s
% 6.81/2.18 % (30612)Instructions burned: 164 (million)
% 6.81/2.18 % (30612)------------------------------
% 6.81/2.18 % (30612)------------------------------
% 6.81/2.19 % (30618)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/26Mi)
% 6.81/2.19 % (30619)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/53Mi)
% 6.81/2.19 % (30618)Instruction limit reached!
% 6.81/2.19 % (30618)------------------------------
% 6.81/2.19 % (30618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.19 % (30618)Termination reason: Unknown
% 6.81/2.19 % (30618)Termination phase: Preprocessing 1
% 6.81/2.19
% 6.81/2.19 % (30618)Memory used [KB]: 1535
% 6.81/2.19 % (30618)Time elapsed: 0.008 s
% 6.81/2.19 % (30618)Instructions burned: 28 (million)
% 6.81/2.19 % (30618)------------------------------
% 6.81/2.19 % (30618)------------------------------
% 7.35/2.20 % (30620)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/4436Mi)
% 7.35/2.20 % (30619)Instruction limit reached!
% 7.35/2.20 % (30619)------------------------------
% 7.35/2.20 % (30619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.20 % (30619)Termination reason: Unknown
% 7.35/2.20 % (30619)Termination phase: Function definition elimination
% 7.35/2.20
% 7.35/2.20 % (30619)Memory used [KB]: 1663
% 7.35/2.20 % (30619)Time elapsed: 0.014 s
% 7.35/2.20 % (30619)Instructions burned: 54 (million)
% 7.35/2.20 % (30619)------------------------------
% 7.35/2.20 % (30619)------------------------------
% 7.35/2.21 % (30621)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/1539Mi)
% 7.35/2.22 % (30617)Instruction limit reached!
% 7.35/2.22 % (30617)------------------------------
% 7.35/2.22 % (30617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.22 % (30617)Termination reason: Unknown
% 7.35/2.22 % (30617)Termination phase: Saturation
% 7.35/2.22
% 7.35/2.22 % (30617)Memory used [KB]: 6652
% 7.35/2.22 % (30617)Time elapsed: 0.059 s
% 7.35/2.22 % (30617)Instructions burned: 206 (million)
% 7.35/2.22 % (30617)------------------------------
% 7.35/2.22 % (30617)------------------------------
% 7.35/2.23 % (30622)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_30392 for (2992ds/408Mi)
% 7.35/2.24 % (30616)Instruction limit reached!
% 7.35/2.24 % (30616)------------------------------
% 7.35/2.24 % (30616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.24 % (30616)Termination reason: Unknown
% 7.35/2.24 % (30616)Termination phase: Saturation
% 7.35/2.24
% 7.35/2.24 % (30616)Memory used [KB]: 6908
% 7.35/2.24 % (30616)Time elapsed: 0.078 s
% 7.35/2.24 % (30616)Instructions burned: 268 (million)
% 7.35/2.24 % (30616)------------------------------
% 7.35/2.24 % (30616)------------------------------
% 7.35/2.25 % (30623)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_30392 for (2991ds/5205Mi)
% 7.35/2.25 % (30614)Instruction limit reached!
% 7.35/2.25 % (30614)------------------------------
% 7.35/2.25 % (30614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.25 % (30614)Termination reason: Unknown
% 7.35/2.25 % (30614)Termination phase: Saturation
% 7.35/2.25
% 7.35/2.25 % (30614)Memory used [KB]: 7419
% 7.35/2.25 % (30614)Time elapsed: 0.109 s
% 7.35/2.25 % (30614)Instructions burned: 369 (million)
% 7.35/2.25 % (30614)------------------------------
% 7.35/2.25 % (30614)------------------------------
% 7.35/2.26 % (30624)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_30392 for (2991ds/1913Mi)
% 7.35/2.29 % (30603)Instruction limit reached!
% 7.35/2.29 % (30603)------------------------------
% 7.35/2.29 % (30603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.35/2.29 % (30603)Termination reason: Unknown
% 7.35/2.29 % (30603)Termination phase: Saturation
% 7.35/2.29
% 7.35/2.29 % (30603)Memory used [KB]: 8187
% 7.35/2.29 % (30603)Time elapsed: 0.271 s
% 7.35/2.29 % (30603)Instructions burned: 987 (million)
% 7.35/2.29 % (30603)------------------------------
% 7.35/2.29 % (30603)------------------------------
% 7.92/2.30 % (30625)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_30392 for (2991ds/4350Mi)
% 7.92/2.34 % (30622)Instruction limit reached!
% 7.92/2.34 % (30622)------------------------------
% 7.92/2.34 % (30622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.34 % (30622)Termination reason: Unknown
% 7.92/2.34 % (30622)Termination phase: Saturation
% 7.92/2.34
% 7.92/2.34 % (30622)Memory used [KB]: 7547
% 7.92/2.34 % (30622)Time elapsed: 0.133 s
% 7.92/2.34 % (30622)Instructions burned: 410 (million)
% 7.92/2.34 % (30622)------------------------------
% 7.92/2.34 % (30622)------------------------------
% 7.92/2.35 % (30626)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_30392 for (2990ds/68Mi)
% 7.92/2.37 % (30626)Instruction limit reached!
% 7.92/2.37 % (30626)------------------------------
% 7.92/2.37 % (30626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.37 % (30626)Termination reason: Unknown
% 7.92/2.37 % (30626)Termination phase: Function definition elimination
% 7.92/2.37
% 7.92/2.37 % (30626)Memory used [KB]: 1791
% 7.92/2.37 % (30626)Time elapsed: 0.018 s
% 7.92/2.37 % (30626)Instructions burned: 69 (million)
% 7.92/2.37 % (30626)------------------------------
% 7.92/2.37 % (30626)------------------------------
% 7.92/2.38 % (30627)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_30392 for (2990ds/358Mi)
% 8.06/2.44 % (30615)Instruction limit reached!
% 8.06/2.44 % (30615)------------------------------
% 8.06/2.44 % (30615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.44 % (30615)Termination reason: Unknown
% 8.06/2.44 % (30615)Termination phase: Saturation
% 8.06/2.44
% 8.06/2.44 % (30615)Memory used [KB]: 8443
% 8.06/2.44 % (30615)Time elapsed: 0.287 s
% 8.06/2.44 % (30615)Instructions burned: 1023 (million)
% 8.06/2.44 % (30615)------------------------------
% 8.06/2.44 % (30615)------------------------------
% 8.06/2.45 % (30628)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_30392 for (2989ds/31Mi)
% 8.06/2.45 % (30628)Instruction limit reached!
% 8.06/2.45 % (30628)------------------------------
% 8.06/2.45 % (30628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.45 % (30628)Termination reason: Unknown
% 8.06/2.45 % (30628)Termination phase: Property scanning
% 8.06/2.45
% 8.06/2.45 % (30628)Memory used [KB]: 1535
% 8.06/2.45 % (30628)Time elapsed: 0.010 s
% 8.06/2.45 % (30628)Instructions burned: 34 (million)
% 8.06/2.45 % (30628)------------------------------
% 8.06/2.45 % (30628)------------------------------
% 8.06/2.46 % (30629)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30392 for (2989ds/279Mi)
% 8.06/2.48 % (30621)First to succeed.
% 8.06/2.48 % (30629)Refutation not found, incomplete strategy
% 8.06/2.48 % (30629)------------------------------
% 8.06/2.48 % (30629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.48 % (30629)Termination reason: Refutation not found, incomplete strategy
% 8.06/2.48
% 8.06/2.48
% 8.06/2.48 % (30629)Memory used [KB]: 6268
% 8.06/2.48 % (30629)Time elapsed: 0.041 s
% 8.06/2.48 % (30629)Instructions burned: 62 (million)
% 8.06/2.48 % (30629)------------------------------
% 8.06/2.48 % (30629)------------------------------
% 8.06/2.48 % (30621)Refutation found. Thanks to Tanya!
% 8.06/2.48 % SZS status Theorem for DTF2THF_30392
% 8.06/2.48 % SZS output start Proof for DTF2THF_30392
% 8.06/2.48 thf(func_def_0, type, c_Eps_i: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_3, type, c_not: $o > $o).
% 8.06/2.48 thf(func_def_4, type, c_and: $o > $o > $o).
% 8.06/2.48 thf(func_def_5, type, c_or: $o > $o > $o).
% 8.06/2.48 thf(func_def_6, type, c_iff: $o > $o > $o).
% 8.06/2.48 thf(func_def_7, type, c_In: $i > $i > $o).
% 8.06/2.48 thf(func_def_8, type, c_Subq: $i > $i > $o).
% 8.06/2.48 thf(func_def_10, type, c_Union: $i > $i).
% 8.06/2.48 thf(func_def_11, type, c_Power: $i > $i).
% 8.06/2.48 thf(func_def_12, type, c_Repl: $i > ($i > $i) > $i).
% 8.06/2.48 thf(func_def_13, type, c_TransSet: $i > $o).
% 8.06/2.48 thf(func_def_14, type, c_atleast2: $i > $o).
% 8.06/2.48 thf(func_def_15, type, c_atleast3: $i > $o).
% 8.06/2.48 thf(func_def_16, type, c_atleast4: $i > $o).
% 8.06/2.48 thf(func_def_17, type, c_atleast5: $i > $o).
% 8.06/2.48 thf(func_def_18, type, c_atleast6: $i > $o).
% 8.06/2.48 thf(func_def_19, type, c_exactly2: $i > $o).
% 8.06/2.48 thf(func_def_20, type, c_exactly3: $i > $o).
% 8.06/2.48 thf(func_def_21, type, c_exactly4: $i > $o).
% 8.06/2.48 thf(func_def_22, type, c_exactly5: $i > $o).
% 8.06/2.48 thf(func_def_23, type, c_exu_i: ($i > $o) > $o).
% 8.06/2.48 thf(func_def_24, type, c_reflexive_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_25, type, c_irreflexive_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_26, type, c_symmetric_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_27, type, c_antisymmetric_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_28, type, c_transitive_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_29, type, c_eqreln_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_30, type, c_per_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_31, type, c_linear_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_32, type, c_trichotomous_or_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_33, type, c_partialorder_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_34, type, c_totalorder_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_35, type, c_strictpartialorder_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_36, type, c_stricttotalorder_i: ($i > $i > $o) > $o).
% 8.06/2.48 thf(func_def_37, type, c_If_i: $o > $i > $i > $i).
% 8.06/2.48 thf(func_def_38, type, c_exactly1of2: $o > $o > $o).
% 8.06/2.48 thf(func_def_39, type, c_exactly1of3: $o > $o > $o > $o).
% 8.06/2.48 thf(func_def_40, type, c_nIn: $i > $i > $o).
% 8.06/2.48 thf(func_def_41, type, c_nSubq: $i > $i > $o).
% 8.06/2.48 thf(func_def_42, type, c_UPair: $i > $i > $i).
% 8.06/2.48 thf(func_def_43, type, c_Sing: $i > $i).
% 8.06/2.48 thf(func_def_44, type, c_binunion: $i > $i > $i).
% 8.06/2.48 thf(func_def_45, type, c_SetAdjoin: $i > $i > $i).
% 8.06/2.48 thf(func_def_46, type, c_famunion: $i > ($i > $i) > $i).
% 8.06/2.48 thf(func_def_47, type, c_Sep: $i > ($i > $o) > $i).
% 8.06/2.48 thf(func_def_48, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i).
% 8.06/2.48 thf(func_def_49, type, c_binintersect: $i > $i > $i).
% 8.06/2.48 thf(func_def_50, type, c_setminus: $i > $i > $i).
% 8.06/2.48 thf(func_def_51, type, c_inj: $i > $i > ($i > $i) > $o).
% 8.06/2.48 thf(func_def_52, type, c_bij: $i > $i > ($i > $i) > $o).
% 8.06/2.48 thf(func_def_53, type, c_atleastp: $i > $i > $o).
% 8.06/2.48 thf(func_def_54, type, c_equip: $i > $i > $o).
% 8.06/2.48 thf(func_def_55, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o).
% 8.06/2.48 thf(func_def_56, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i).
% 8.06/2.48 thf(func_def_57, type, c_ordsucc: $i > $i).
% 8.06/2.48 thf(func_def_58, type, c_nat_p: $i > $o).
% 8.06/2.48 thf(func_def_59, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i).
% 8.06/2.48 thf(func_def_60, type, c_add_nat: $i > $i > $i).
% 8.06/2.48 thf(func_def_61, type, c_mul_nat: $i > $i > $i).
% 8.06/2.48 thf(func_def_62, type, c_ordinal: $i > $o).
% 8.06/2.48 thf(func_def_63, type, c_V_: $i > $i).
% 8.06/2.48 thf(func_def_64, type, c_Inj1: $i > $i).
% 8.06/2.48 thf(func_def_65, type, c_Inj0: $i > $i).
% 8.06/2.48 thf(func_def_66, type, c_Unj: $i > $i).
% 8.06/2.48 thf(func_def_67, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i).
% 8.06/2.48 thf(func_def_68, type, c_setsum: $i > $i > $i).
% 8.06/2.48 thf(func_def_69, type, c_proj0: $i > $i).
% 8.06/2.48 thf(func_def_70, type, c_proj1: $i > $i).
% 8.06/2.48 thf(func_def_71, type, c_binrep: $i > $i > $i).
% 8.06/2.48 thf(func_def_72, type, c_lam: $i > ($i > $i) > $i).
% 8.06/2.48 thf(func_def_73, type, c_setprod: $i > $i > $i).
% 8.06/2.48 thf(func_def_74, type, c_ap: $i > $i > $i).
% 8.06/2.48 thf(func_def_75, type, c_setsum_p: $i > $o).
% 8.06/2.48 thf(func_def_76, type, c_tuple_p: $i > $i > $o).
% 8.06/2.48 thf(func_def_77, type, c_Pi: $i > ($i > $i) > $i).
% 8.06/2.48 thf(func_def_78, type, c_setexp: $i > $i > $i).
% 8.06/2.48 thf(func_def_79, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i).
% 8.06/2.48 thf(func_def_80, type, c_set_of_pairs: $i > $o).
% 8.06/2.48 thf(func_def_81, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i).
% 8.06/2.48 thf(func_def_82, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o).
% 8.06/2.48 thf(func_def_83, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o).
% 8.06/2.48 thf(func_def_84, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o).
% 8.06/2.48 thf(func_def_85, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o).
% 8.06/2.48 thf(func_def_86, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 8.06/2.48 thf(func_def_87, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o).
% 8.06/2.48 thf(func_def_88, type, c_SNoElts_: $i > $i).
% 8.06/2.48 thf(func_def_89, type, c_SNo_: $i > $i > $o).
% 8.06/2.48 thf(func_def_90, type, c_PSNo: $i > ($i > $o) > $i).
% 8.06/2.48 thf(func_def_91, type, c_SNo: $i > $o).
% 8.06/2.48 thf(func_def_92, type, c_SNoLev: $i > $i).
% 8.06/2.48 thf(func_def_93, type, c_SNoEq_: $i > $i > $i > $o).
% 8.06/2.48 thf(func_def_94, type, c_SNoLt: $i > $i > $o).
% 8.06/2.48 thf(func_def_95, type, c_SNoLe: $i > $i > $o).
% 8.06/2.48 thf(func_def_96, type, c_binop_on: $i > ($i > $i > $i) > $o).
% 8.06/2.48 thf(func_def_97, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o).
% 8.06/2.48 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).
% 8.06/2.48 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).
% 8.06/2.48 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).
% 8.06/2.48 thf(func_def_101, type, c_combinator: $i > $o).
% 8.06/2.48 thf(func_def_102, type, c_combinator_equiv: $i > $i > $o).
% 8.06/2.48 thf(func_def_103, type, c_equip_mod: $i > $i > $i > $o).
% 8.06/2.48 thf(func_def_131, type, sP0: ($i > $o) > $o).
% 8.06/2.48 thf(func_def_132, type, sP1: ($i > $o) > $o).
% 8.06/2.48 thf(func_def_133, type, sK2: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_134, type, sK3: ($i > $o) > $i > $i).
% 8.06/2.48 thf(func_def_135, type, sK4: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_136, type, sK5: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_137, type, sK6: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_138, type, sK7: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_139, type, sK8: ($i > $o) > $i).
% 8.06/2.48 thf(func_def_142, type, sK11: $i > $i > $i).
% 8.06/2.48 thf(func_def_143, type, sK12: $i > $i > $i > $o).
% 8.06/2.48 thf(func_def_144, type, sK13: $o > $o > $o).
% 8.06/2.48 thf(func_def_145, type, sK14: $o > $o > $o).
% 8.06/2.48 thf(func_def_146, type, sK15: ($i > $i) > $i > $i > $i).
% 8.06/2.48 thf(func_def_147, type, sK16: ($i > $i) > $i > $i > $i > $o).
% 8.06/2.48 thf(func_def_149, type, sK18: $i > $i > $i).
% 8.06/2.48 thf(func_def_150, type, sK19: $i > $i > $i).
% 8.06/2.48 thf(func_def_151, type, sK20: $i > $i > $i).
% 8.06/2.48 thf(func_def_152, type, sK21: $i > $i > $i).
% 8.06/2.48 thf(func_def_154, type, ph22: !>[X0: $tType]:(X0)).
% 8.06/2.48 thf(f2507,plain,(
% 8.06/2.48 $false),
% 8.06/2.48 inference(avatar_sat_refutation,[status(thm)],[f684,f691,f729,f2506])).
% 8.06/2.48 thf(f2506,plain,(
% 8.06/2.48 spl9_2 | ~spl9_3),
% 8.06/2.48 inference(avatar_split_clause,[status(thm)],[f2504,f689,f686])).
% 8.06/2.48 thf(f686,definition,(
% 8.06/2.48 spl9_2 <=> ! [X1 : $o] : ($true = X1)),
% 8.06/2.48 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 8.06/2.48 thf(f689,definition,(
% 8.06/2.48 spl9_3 <=> ! [X2 : $i] : ((c_In @ X2 @ c_Empty) = $false)),
% 8.06/2.48 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 8.06/2.48 thf(f2504,plain,(
% 8.06/2.48 ( ! [X2 : $o] : (($true = X2)) ) | ~spl9_3),
% 8.06/2.48 inference(trivial_inequality_removal,[status(thm)],[f2503])).
% 8.06/2.48 thf(f2503,plain,(
% 8.06/2.48 ( ! [X2 : $o] : (($true = $false) | ($true = X2)) ) | ~spl9_3),
% 8.06/2.48 inference(forward_demodulation,[status(thm)],[f2502,f1225])).
% 8.06/2.48 thf(f1225,plain,(
% 8.06/2.48 ( ! [X0 : $i,X1 : $i] : (((c_In @ X1 @ X0) = $false)) ) | ~spl9_3),
% 8.06/2.48 inference(superposition,[status(thm)],[f690,f1094])).
% 8.06/2.48 thf(f1094,plain,(
% 8.06/2.48 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f1090])).
% 8.06/2.48 thf(f1090,plain,(
% 8.06/2.48 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: (Y0)) @ ((^[Y0 : $i]: (Y0)) @ X1)) = X0)) )),
% 8.06/2.48 inference(superposition,[status(thm)],[f697,f876])).
% 8.06/2.48 thf(f876,plain,(
% 8.06/2.48 ( ! [X3 : $i,X0 : $i,X1 : $i > $i] : (((X1 @ (X1 @ X3)) = (X1 @ X0))) )),
% 8.06/2.48 inference(superposition,[status(thm)],[f640,f697])).
% 8.06/2.48 thf(f640,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i > $i > $i] : (((X2 @ (X5 @ (X5 @ (X5 @ (X5 @ (X5 @ (X5 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X3 @ X4) @ (X5 @ X1 @ (X5 @ (X5 @ (X5 @ X4 @ X4) @ (X5 @ (X5 @ (X5 @ (X5 @ X4 @ (X5 @ (X5 @ X3 @ (X5 @ X4 @ (X5 @ X4 @ X1))) @ X4)) @ X1) @ (X5 @ (X2 @ X3) @ X1)) @ (X5 @ (X5 @ (X5 @ (X5 @ X4 @ (X2 @ (X5 @ X1 @ X4))) @ (X5 @ X3 @ X3)) @ (X5 @ X3 @ (X5 @ X1 @ X4))) @ X4))) @ X1))) @ X4)) @ X3) @ (X5 @ X3 @ (X5 @ X4 @ (X5 @ (X5 @ (X2 @ X4) @ (X5 @ (X5 @ X3 @ X3) @ X3)) @ X4)))) @ (X2 @ (X2 @ X3))) @ X4)) = (X2 @ (X2 @ X1)))) )),
% 8.06/2.48 inference(equality_proxy_clausification,[status(thm)],[f639])).
% 8.06/2.48 thf(f639,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i > $i > $i] : (($true = ((X2 @ (X5 @ (X5 @ (X5 @ (X5 @ (X5 @ (X5 @ X3 @ X4) @ (X5 @ (X5 @ (X5 @ X3 @ X4) @ (X5 @ X1 @ (X5 @ (X5 @ (X5 @ X4 @ X4) @ (X5 @ (X5 @ (X5 @ (X5 @ X4 @ (X5 @ (X5 @ X3 @ (X5 @ X4 @ (X5 @ X4 @ X1))) @ X4)) @ X1) @ (X5 @ (X2 @ X3) @ X1)) @ (X5 @ (X5 @ (X5 @ (X5 @ X4 @ (X2 @ (X5 @ X1 @ X4))) @ (X5 @ X3 @ X3)) @ (X5 @ X3 @ (X5 @ X1 @ X4))) @ X4))) @ X1))) @ X4)) @ X3) @ (X5 @ X3 @ (X5 @ X4 @ (X5 @ (X5 @ (X2 @ X4) @ (X5 @ (X5 @ X3 @ X3) @ X3)) @ X4)))) @ (X2 @ (X2 @ X3))) @ X4)) = (X2 @ (X2 @ X1))))) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f638])).
% 8.06/2.48 thf(f638,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i > $i > $i] : ((((^[Y0 : $i > $i > $i]: ((X2 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ X4) @ (Y0 @ (Y0 @ (Y0 @ X3 @ X4) @ (Y0 @ X1 @ (Y0 @ (Y0 @ (Y0 @ X4 @ X4) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X4 @ (Y0 @ (Y0 @ X3 @ (Y0 @ X4 @ (Y0 @ X4 @ X1))) @ X4)) @ X1) @ (Y0 @ (X2 @ X3) @ X1)) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X4 @ (X2 @ (Y0 @ X1 @ X4))) @ (Y0 @ X3 @ X3)) @ (Y0 @ X3 @ (Y0 @ X1 @ X4))) @ X4))) @ X1))) @ X4)) @ X3) @ (Y0 @ X3 @ (Y0 @ X4 @ (Y0 @ (Y0 @ (X2 @ X4) @ (Y0 @ (Y0 @ X3 @ X3) @ X3)) @ X4)))) @ (X2 @ (X2 @ X3))) @ X4)) = (X2 @ (X2 @ X1)))) @ X5) = $true)) )),
% 8.06/2.48 inference(pi_clausification,[status(thm)],[f637])).
% 8.06/2.48 thf(f637,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (!! @ ($i > $i > $i) @ (^[Y0 : $i > $i > $i]: ((X2 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ X4) @ (Y0 @ (Y0 @ (Y0 @ X3 @ X4) @ (Y0 @ X1 @ (Y0 @ (Y0 @ (Y0 @ X4 @ X4) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X4 @ (Y0 @ (Y0 @ X3 @ (Y0 @ X4 @ (Y0 @ X4 @ X1))) @ X4)) @ X1) @ (Y0 @ (X2 @ X3) @ X1)) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X4 @ (X2 @ (Y0 @ X1 @ X4))) @ (Y0 @ X3 @ X3)) @ (Y0 @ X3 @ (Y0 @ X1 @ X4))) @ X4))) @ X1))) @ X4)) @ X3) @ (Y0 @ X3 @ (Y0 @ X4 @ (Y0 @ (Y0 @ (X2 @ X4) @ (Y0 @ (Y0 @ X3 @ X3) @ X3)) @ X4)))) @ (X2 @ (X2 @ X3))) @ X4)) = (X2 @ (X2 @ X1))))))) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f636])).
% 8.06/2.48 thf(f636,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: ((X2 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ Y0) @ (Y1 @ (Y1 @ (Y1 @ X3 @ Y0) @ (Y1 @ X1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ Y0) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ X3 @ (Y1 @ Y0 @ (Y1 @ Y0 @ X1))) @ Y0)) @ X1) @ (Y1 @ (X2 @ X3) @ X1)) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (X2 @ (Y1 @ X1 @ Y0))) @ (Y1 @ X3 @ X3)) @ (Y1 @ X3 @ (Y1 @ X1 @ Y0))) @ Y0))) @ X1))) @ Y0)) @ X3) @ (Y1 @ X3 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ (X2 @ Y0) @ (Y1 @ (Y1 @ X3 @ X3) @ X3)) @ Y0)))) @ (X2 @ (X2 @ X3))) @ Y0)) = (X2 @ (X2 @ X1)))))) @ X4))) )),
% 8.06/2.48 inference(pi_clausification,[status(thm)],[f635])).
% 8.06/2.48 thf(f635,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: ((X2 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ Y0) @ (Y1 @ (Y1 @ (Y1 @ X3 @ Y0) @ (Y1 @ X1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ Y0) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ X3 @ (Y1 @ Y0 @ (Y1 @ Y0 @ X1))) @ Y0)) @ X1) @ (Y1 @ (X2 @ X3) @ X1)) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (X2 @ (Y1 @ X1 @ Y0))) @ (Y1 @ X3 @ X3)) @ (Y1 @ X3 @ (Y1 @ X1 @ Y0))) @ Y0))) @ X1))) @ Y0)) @ X3) @ (Y1 @ X3 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ (X2 @ Y0) @ (Y1 @ (Y1 @ X3 @ X3) @ X3)) @ Y0)))) @ (X2 @ (X2 @ X3))) @ Y0)) = (X2 @ (X2 @ X1))))))))) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f634])).
% 8.06/2.48 thf(f634,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: ((X2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y0 @ Y1) @ (Y2 @ (Y2 @ (Y2 @ Y0 @ Y1) @ (Y2 @ X1 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ Y1) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ Y0 @ (Y2 @ Y1 @ (Y2 @ Y1 @ X1))) @ Y1)) @ X1) @ (Y2 @ (X2 @ Y0) @ X1)) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (X2 @ (Y2 @ X1 @ Y1))) @ (Y2 @ Y0 @ Y0)) @ (Y2 @ Y0 @ (Y2 @ X1 @ Y1))) @ Y1))) @ X1))) @ Y1)) @ Y0) @ (Y2 @ Y0 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ (X2 @ Y1) @ (Y2 @ (Y2 @ Y0 @ Y0) @ Y0)) @ Y1)))) @ (X2 @ (X2 @ Y0))) @ Y1)) = (X2 @ (X2 @ X1)))))))) @ X3) = $true)) )),
% 8.06/2.48 inference(pi_clausification,[status(thm)],[f633])).
% 8.06/2.48 thf(f633,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: ((X2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y0 @ Y1) @ (Y2 @ (Y2 @ (Y2 @ Y0 @ Y1) @ (Y2 @ X1 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ Y1) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ Y0 @ (Y2 @ Y1 @ (Y2 @ Y1 @ X1))) @ Y1)) @ X1) @ (Y2 @ (X2 @ Y0) @ X1)) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (X2 @ (Y2 @ X1 @ Y1))) @ (Y2 @ Y0 @ Y0)) @ (Y2 @ Y0 @ (Y2 @ X1 @ Y1))) @ Y1))) @ X1))) @ Y1)) @ Y0) @ (Y2 @ Y0 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ (X2 @ Y1) @ (Y2 @ (Y2 @ Y0 @ Y0) @ Y0)) @ Y1)))) @ (X2 @ (X2 @ Y0))) @ Y1)) = (X2 @ (X2 @ X1))))))))))) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f632])).
% 8.06/2.48 thf(f632,plain,(
% 8.06/2.48 ( ! [X2 : $i > $i,X1 : $i] : (($true = ((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: ((Y0 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y1 @ Y2) @ (Y3 @ (Y3 @ (Y3 @ Y1 @ Y2) @ (Y3 @ X1 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ Y2) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ Y1 @ (Y3 @ Y2 @ (Y3 @ Y2 @ X1))) @ Y2)) @ X1) @ (Y3 @ (Y0 @ Y1) @ X1)) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y0 @ (Y3 @ X1 @ Y2))) @ (Y3 @ Y1 @ Y1)) @ (Y3 @ Y1 @ (Y3 @ X1 @ Y2))) @ Y2))) @ X1))) @ Y2)) @ Y1) @ (Y3 @ Y1 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ (Y0 @ Y2) @ (Y3 @ (Y3 @ Y1 @ Y1) @ Y1)) @ Y2)))) @ (Y0 @ (Y0 @ Y1))) @ Y2)) = (Y0 @ (Y0 @ X1)))))))))) @ X2))) )),
% 8.06/2.48 inference(pi_clausification,[status(thm)],[f631])).
% 8.06/2.48 thf(f631,plain,(
% 8.06/2.48 ( ! [X1 : $i] : (($true = (!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: ((Y0 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y1 @ Y2) @ (Y3 @ (Y3 @ (Y3 @ Y1 @ Y2) @ (Y3 @ X1 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ Y2) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ Y1 @ (Y3 @ Y2 @ (Y3 @ Y2 @ X1))) @ Y2)) @ X1) @ (Y3 @ (Y0 @ Y1) @ X1)) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y0 @ (Y3 @ X1 @ Y2))) @ (Y3 @ Y1 @ Y1)) @ (Y3 @ Y1 @ (Y3 @ X1 @ Y2))) @ Y2))) @ X1))) @ Y2)) @ Y1) @ (Y3 @ Y1 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ (Y0 @ Y2) @ (Y3 @ (Y3 @ Y1 @ Y1) @ Y1)) @ Y2)))) @ (Y0 @ (Y0 @ Y1))) @ Y2)) = (Y0 @ (Y0 @ X1))))))))))))) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f630])).
% 8.06/2.48 thf(f630,plain,(
% 8.06/2.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0)))))))))))) @ X1))) )),
% 8.06/2.48 inference(pi_clausification,[status(thm)],[f629])).
% 8.06/2.48 thf(f629,plain,(
% 8.06/2.48 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0))))))))))))))),
% 8.06/2.48 inference(binary_proxy_clausification,[status(thm)],[f627])).
% 8.06/2.48 thf(f627,plain,(
% 8.06/2.48 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0))))))))))))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f523])).
% 8.06/2.48 thf(f523,plain,(
% 8.06/2.48 ($true != ((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0)))))))))))))))),
% 8.06/2.48 inference(definition_unfolding,[status(thm)],[f323,f436])).
% 8.06/2.48 thf(f436,plain,(
% 8.06/2.48 (c_not = (^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))))),
% 8.06/2.48 inference(definition_unfolding,[status(thm)],[f334,f366])).
% 8.06/2.48 thf(f366,plain,(
% 8.06/2.48 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f159])).
% 8.06/2.48 thf(f159,plain,(
% 8.06/2.48 (c_False = (!! @ $o @ (^[Y0 : $o]: (Y0))))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f158])).
% 8.06/2.48 thf(f158,plain,(
% 8.06/2.48 (! [X0 : $o] : X0 = c_False)),
% 8.06/2.48 inference(rectify,[status(thm)],[f11])).
% 8.06/2.48 thf(f11,axiom,(
% 8.06/2.48 (! [X0 : $o] : X0 = c_False)),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax11)).
% 8.06/2.48 thf(f334,plain,(
% 8.06/2.48 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f145])).
% 8.06/2.48 thf(f145,plain,(
% 8.06/2.48 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f144])).
% 8.06/2.48 thf(f144,plain,(
% 8.06/2.48 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 8.06/2.48 inference(rectify,[status(thm)],[f13])).
% 8.06/2.48 thf(f13,axiom,(
% 8.06/2.48 ((^[X0 : $o] : (X0 => c_False)) = c_not)),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax13)).
% 8.06/2.48 thf(f323,plain,(
% 8.06/2.48 ($true != (c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0)))))))))))))))),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f288])).
% 8.06/2.48 thf(f288,plain,(
% 8.06/2.48 ($true != (c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0)))))))))))))))),
% 8.06/2.48 inference(flattening,[status(thm)],[f213])).
% 8.06/2.48 thf(f213,plain,(
% 8.06/2.48 ~($true = (c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: ((Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ Y2 @ Y3) @ (Y4 @ Y0 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ Y3) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y0))) @ Y3)) @ Y0) @ (Y4 @ (Y1 @ Y2) @ Y0)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y1 @ (Y4 @ Y0 @ Y3))) @ (Y4 @ Y2 @ Y2)) @ (Y4 @ Y2 @ (Y4 @ Y0 @ Y3))) @ Y3))) @ Y0))) @ Y3)) @ Y2) @ (Y4 @ Y2 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y1 @ Y3) @ (Y4 @ (Y4 @ Y2 @ Y2) @ Y2)) @ Y3)))) @ (Y1 @ (Y1 @ Y2))) @ Y3)) = (Y1 @ (Y1 @ Y0)))))))))))))))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f212])).
% 8.06/2.48 thf(f212,plain,(
% 8.06/2.48 ~(c_not @ ! [X0 : $i > $i > $i,X1 : $i,X2 : $i,X4 : $i > $i,X5 : $i] : ((X4 @ (X0 @ (X0 @ (X0 @ (X0 @ (X0 @ (X0 @ X2 @ X1) @ (X0 @ (X0 @ (X0 @ X2 @ X1) @ (X0 @ X5 @ (X0 @ (X0 @ (X0 @ X1 @ X1) @ (X0 @ (X0 @ (X0 @ (X0 @ X1 @ (X0 @ (X0 @ X2 @ (X0 @ X1 @ (X0 @ X1 @ X5))) @ X1)) @ X5) @ (X0 @ (X4 @ X2) @ X5)) @ (X0 @ (X0 @ (X0 @ (X0 @ X1 @ (X4 @ (X0 @ X5 @ X1))) @ (X0 @ X2 @ X2)) @ (X0 @ X2 @ (X0 @ X5 @ X1))) @ X1))) @ X5))) @ X1)) @ X2) @ (X0 @ X2 @ (X0 @ X1 @ (X0 @ (X0 @ (X4 @ X1) @ (X0 @ (X0 @ X2 @ X2) @ X2)) @ X1)))) @ (X4 @ (X4 @ X2))) @ X1)) = (X4 @ (X4 @ X5))))),
% 8.06/2.48 inference(rectify,[status(thm)],[f110])).
% 8.06/2.48 thf(f110,negated_conjecture,(
% 8.06/2.48 ~(c_not @ ! [X1 : $i > $i > $i,X5 : $i,X6 : $i,X3 : $i > $o,X4 : $i > $i,X7 : $i,X2 : $i > $o,X0 : $i > $i > $o] : ((X4 @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ X6 @ X5) @ (X1 @ (X1 @ (X1 @ X6 @ X5) @ (X1 @ X7 @ (X1 @ (X1 @ (X1 @ X5 @ X5) @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ (X1 @ (X1 @ X6 @ (X1 @ X5 @ (X1 @ X5 @ X7))) @ X5)) @ X7) @ (X1 @ (X4 @ X6) @ X7)) @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ (X4 @ (X1 @ X7 @ X5))) @ (X1 @ X6 @ X6)) @ (X1 @ X6 @ (X1 @ X7 @ X5))) @ X5))) @ X7))) @ X5)) @ X6) @ (X1 @ X6 @ (X1 @ X5 @ (X1 @ (X1 @ (X4 @ X5) @ (X1 @ (X1 @ X6 @ X6) @ X6)) @ X5)))) @ (X4 @ (X4 @ X6))) @ X5)) = (X4 @ (X4 @ X7))))),
% 8.06/2.48 inference(negated_conjecture,[status(cth)],[f109])).
% 8.06/2.48 thf(f109,conjecture,(
% 8.06/2.48 (c_not @ ! [X1 : $i > $i > $i,X5 : $i,X6 : $i,X3 : $i > $o,X4 : $i > $i,X7 : $i,X2 : $i > $o,X0 : $i > $i > $o] : ((X4 @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ X6 @ X5) @ (X1 @ (X1 @ (X1 @ X6 @ X5) @ (X1 @ X7 @ (X1 @ (X1 @ (X1 @ X5 @ X5) @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ (X1 @ (X1 @ X6 @ (X1 @ X5 @ (X1 @ X5 @ X7))) @ X5)) @ X7) @ (X1 @ (X4 @ X6) @ X7)) @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ (X4 @ (X1 @ X7 @ X5))) @ (X1 @ X6 @ X6)) @ (X1 @ X6 @ (X1 @ X7 @ X5))) @ X5))) @ X7))) @ X5)) @ X6) @ (X1 @ X6 @ (X1 @ X5 @ (X1 @ (X1 @ (X4 @ X5) @ (X1 @ (X1 @ X6 @ X6) @ X6)) @ X5)))) @ (X4 @ (X4 @ X6))) @ X5)) = (X4 @ (X4 @ X7))))),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',conj)).
% 8.06/2.48 thf(f697,plain,(
% 8.06/2.48 ( ! [X0 : $i] : (((sK8 @ (^[Y0 : $i]: (~ (X0 = Y0)))) = X0)) )),
% 8.06/2.48 inference(leibniz_equality_elimination,[status(thm)],[f422])).
% 8.06/2.48 thf(f422,plain,(
% 8.06/2.48 ( ! [X0 : $i > $o,X1 : $i] : (((X0 @ (sK8 @ X0)) != $true) | ((X0 @ X1) = $true)) )),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f316])).
% 8.06/2.48 thf(f316,plain,(
% 8.06/2.48 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | (((X0 @ (sK8 @ X0)) != $true) & ! [X3 : $i] : (($true != (c_In @ X3 @ (sK8 @ X0))) | ((X0 @ X3) = $true))))),
% 8.06/2.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f314,f315])).
% 8.06/2.48 thf(f315,plain,(
% 8.06/2.48 ! [X0 : $i > $o] : (? [X2 : $i] : (((X0 @ X2) != $true) & ! [X3 : $i] : (((c_In @ X3 @ X2) != $true) | ((X0 @ X3) = $true))) => (((X0 @ (sK8 @ X0)) != $true) & ! [X3 : $i] : (($true != (c_In @ X3 @ (sK8 @ X0))) | ((X0 @ X3) = $true))))),
% 8.06/2.48 introduced(definition,[],[choice_axiom])).
% 8.06/2.48 thf(f314,plain,(
% 8.06/2.48 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) = $true) | ? [X2 : $i] : (((X0 @ X2) != $true) & ! [X3 : $i] : (((c_In @ X3 @ X2) != $true) | ((X0 @ X3) = $true))))),
% 8.06/2.48 inference(rectify,[status(thm)],[f291])).
% 8.06/2.48 thf(f291,plain,(
% 8.06/2.48 ! [X0 : $i > $o] : (! [X3 : $i] : ((X0 @ X3) = $true) | ? [X1 : $i] : (((X0 @ X1) != $true) & ! [X2 : $i] : (((c_In @ X2 @ X1) != $true) | ((X0 @ X2) = $true))))),
% 8.06/2.48 inference(ennf_transformation,[status(thm)],[f279])).
% 8.06/2.48 thf(f279,plain,(
% 8.06/2.48 ! [X0 : $i > $o] : (! [X1 : $i] : (! [X2 : $i] : (((c_In @ X2 @ X1) = $true) => ((X0 @ X2) = $true)) => ((X0 @ X1) = $true)) => ! [X3 : $i] : ((X0 @ X3) = $true))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f278])).
% 8.06/2.48 thf(f278,plain,(
% 8.06/2.48 ! [X0 : $i > $o] : (! [X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X3 : $i] : (X0 @ X3))),
% 8.06/2.48 inference(rectify,[status(thm)],[f10])).
% 8.06/2.48 thf(f10,axiom,(
% 8.06/2.48 ! [X0 : $i > $o] : (! [X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X1) => (X0 @ X2)) => (X0 @ X1)) => ! [X1 : $i] : (X0 @ X1))),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax10)).
% 8.06/2.48 thf(f690,plain,(
% 8.06/2.48 ( ! [X2 : $i] : (((c_In @ X2 @ c_Empty) = $false)) ) | ~spl9_3),
% 8.06/2.48 inference(avatar_component_clause,[status(thm)],[f689])).
% 8.06/2.48 thf(f2502,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X1 @ (c_Power @ X0)) = $true) | ($true = X2)) ) | ~spl9_3),
% 8.06/2.48 inference(trivial_inequality_removal,[status(thm)],[f2501])).
% 8.06/2.48 thf(f2501,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X1 @ (c_Power @ X0)) = $true) | ($true = $false) | ($true = X2)) ) | ~spl9_3),
% 8.06/2.48 inference(forward_demodulation,[status(thm)],[f679,f1225])).
% 8.06/2.48 thf(f679,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (c_In @ (sK21 @ X1 @ X0) @ X1)) | ((c_In @ X1 @ (c_Power @ X0)) = $true) | ($true = X2)) )),
% 8.06/2.48 inference(binary_proxy_clausification,[status(thm)],[f677])).
% 8.06/2.48 thf(f677,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((c_In @ X1 @ (c_Power @ X0)) = $true) | (((c_In @ (sK21 @ X1 @ X0) @ X1) => (c_In @ (sK21 @ X1 @ X0) @ X0)) = $false)) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f676])).
% 8.06/2.48 thf(f676,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ((c_In @ X1 @ (c_Power @ X0)) = $true) | (((^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0))) @ (sK21 @ X1 @ X0)) = $false)) )),
% 8.06/2.48 inference(sigma_clausification,[status(thm)],[f675])).
% 8.06/2.48 thf(f675,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((c_In @ X1 @ (c_Power @ X0)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) = $false) | ($true = X2)) )),
% 8.06/2.48 inference(binary_proxy_clausification,[status(thm)],[f674])).
% 8.06/2.48 thf(f674,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))))) )),
% 8.06/2.48 inference(binary_proxy_clausification,[status(thm)],[f667])).
% 8.06/2.48 thf(f667,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => X2) = $false) | ($true = X2)) )),
% 8.06/2.48 inference(binary_proxy_clausification,[status(thm)],[f666])).
% 8.06/2.48 thf(f666,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => X2)) = $false) | ($true = X2)) )),
% 8.06/2.48 inference(binary_proxy_clausification,[status(thm)],[f665])).
% 8.06/2.48 thf(f665,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => X2)) => X2))) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f664])).
% 8.06/2.48 thf(f664,plain,(
% 8.06/2.48 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((^[Y0 : $o]: ((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => Y0)) => Y0)) @ X2))) )),
% 8.06/2.48 inference(pi_clausification,[status(thm)],[f663])).
% 8.06/2.48 thf(f663,plain,(
% 8.06/2.48 ( ! [X0 : $i,X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: ((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => Y0)) => Y0))) = $true)) )),
% 8.06/2.48 inference(beta_eta_normalization,[status(thm)],[f528])).
% 8.06/2.48 thf(f528,plain,(
% 8.06/2.48 ( ! [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 @ X1 @ (c_Power @ X0)) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))) @ X1 @ X0)))) )),
% 8.06/2.48 inference(definition_unfolding,[status(thm)],[f414,f437,f412])).
% 8.06/2.48 thf(f412,plain,(
% 8.06/2.48 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f276])).
% 8.06/2.48 thf(f276,plain,(
% 8.06/2.48 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f275])).
% 8.06/2.48 thf(f275,plain,(
% 8.06/2.48 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 8.06/2.48 inference(rectify,[status(thm)],[f17])).
% 8.06/2.48 thf(f17,axiom,(
% 8.06/2.48 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax17)).
% 8.06/2.48 thf(f437,plain,(
% 8.06/2.48 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 8.06/2.48 inference(definition_unfolding,[status(thm)],[f382,f365])).
% 8.06/2.48 thf(f365,plain,(
% 8.06/2.48 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f143])).
% 8.06/2.48 thf(f143,plain,(
% 8.06/2.48 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f142])).
% 8.06/2.48 thf(f142,plain,(
% 8.06/2.48 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 8.06/2.48 inference(rectify,[status(thm)],[f14])).
% 8.06/2.48 thf(f14,axiom,(
% 8.06/2.48 ((^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))) = c_and)),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax14)).
% 8.06/2.48 thf(f382,plain,(
% 8.06/2.48 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f127])).
% 8.06/2.48 thf(f127,plain,(
% 8.06/2.48 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f126])).
% 8.06/2.48 thf(f126,plain,(
% 8.06/2.48 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)),
% 8.06/2.48 inference(rectify,[status(thm)],[f16])).
% 8.06/2.48 thf(f16,axiom,(
% 8.06/2.48 ((^[X0 : $o, X1 : $o] : (c_and @ X0 => X1 @ X1 => X0)) = c_iff)),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax16)).
% 8.06/2.48 thf(f414,plain,(
% 8.06/2.48 ( ! [X0 : $i,X1 : $i] : (((c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0)) = $true)) )),
% 8.06/2.48 inference(cnf_transformation,[status(thm)],[f203])).
% 8.06/2.48 thf(f203,plain,(
% 8.06/2.48 ! [X0 : $i,X1 : $i] : ((c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0)) = $true)),
% 8.06/2.48 inference(fool_elimination,[status(thm)],[f202])).
% 8.06/2.48 thf(f202,plain,(
% 8.06/2.48 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 8.06/2.48 inference(rectify,[status(thm)],[f7])).
% 8.06/2.48 thf(f7,axiom,(
% 8.06/2.48 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 8.06/2.48 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax7)).
% 8.06/2.48 thf(f729,plain,(
% 8.06/2.48 ~spl9_1 | ~spl9_2),
% 8.06/2.48 inference(avatar_contradiction_clause,[status(thm)],[f728])).
% 8.06/2.49 thf(f728,plain,(
% 8.06/2.49 $false | (~spl9_1 | ~spl9_2)),
% 8.06/2.49 inference(trivial_inequality_removal,[status(thm)],[f722])).
% 8.06/2.49 thf(f722,plain,(
% 8.06/2.49 ($true = $false) | (~spl9_1 | ~spl9_2)),
% 8.06/2.49 inference(superposition,[status(thm)],[f683,f687])).
% 8.06/2.49 thf(f687,plain,(
% 8.06/2.49 ( ! [X1 : $o] : (($true = X1)) ) | ~spl9_2),
% 8.06/2.49 inference(avatar_component_clause,[status(thm)],[f686])).
% 8.06/2.49 thf(f683,plain,(
% 8.06/2.49 (sK17 = $false) | ~spl9_1),
% 8.06/2.49 inference(avatar_component_clause,[status(thm)],[f681])).
% 8.06/2.49 thf(f681,definition,(
% 8.06/2.49 spl9_1 <=> (sK17 = $false)),
% 8.06/2.49 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 8.06/2.49 thf(f691,plain,(
% 8.06/2.49 spl9_2 | spl9_3),
% 8.06/2.49 inference(avatar_split_clause,[status(thm)],[f648,f689,f686])).
% 8.06/2.49 thf(f648,plain,(
% 8.06/2.49 ( ! [X2 : $i,X1 : $o] : (((c_In @ X2 @ c_Empty) = $false) | ($true = X1)) )),
% 8.06/2.49 inference(beta_eta_normalization,[status(thm)],[f647])).
% 8.06/2.49 thf(f647,plain,(
% 8.06/2.49 ( ! [X2 : $i,X1 : $o] : ((((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X2) = $false) | ($true = X1)) )),
% 8.06/2.49 inference(pi_clausification,[status(thm)],[f646])).
% 8.06/2.49 thf(f646,plain,(
% 8.06/2.49 ( ! [X1 : $o] : (($true = X1) | ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false)) )),
% 8.06/2.49 inference(beta_eta_normalization,[status(thm)],[f645])).
% 8.06/2.49 thf(f645,plain,(
% 8.06/2.49 ( ! [X1 : $o] : (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false) | ($true = ((^[Y0 : $o]: (Y0)) @ X1))) )),
% 8.06/2.49 inference(pi_clausification,[status(thm)],[f644])).
% 8.06/2.49 thf(f644,plain,(
% 8.06/2.49 ($true = (!! @ $o @ (^[Y0 : $o]: (Y0)))) | ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) = $false)),
% 8.06/2.49 inference(binary_proxy_clausification,[status(thm)],[f643])).
% 8.06/2.49 thf(f643,plain,(
% 8.06/2.49 ($true = ((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))),
% 8.06/2.49 inference(beta_eta_normalization,[status(thm)],[f527])).
% 8.06/2.49 thf(f527,plain,(
% 8.06/2.49 ($true = ((^[Y0 : $o]: (Y0 => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 8.06/2.49 inference(definition_unfolding,[status(thm)],[f402,f436])).
% 8.06/2.49 thf(f402,plain,(
% 8.06/2.49 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 8.06/2.49 inference(cnf_transformation,[status(thm)],[f232])).
% 8.06/2.49 thf(f232,plain,(
% 8.06/2.49 ($true = (c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))))),
% 8.06/2.49 inference(fool_elimination,[status(thm)],[f231])).
% 8.06/2.49 thf(f231,plain,(
% 8.06/2.49 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 8.06/2.49 inference(rectify,[status(thm)],[f5])).
% 8.06/2.49 thf(f5,axiom,(
% 8.06/2.49 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 8.06/2.49 file('/export/starexec/sandbox/tmp/tmp.rOd6Etgb1G/DTF2THF_30392.p',ax5)).
% 8.06/2.49 thf(f684,plain,(
% 8.06/2.49 spl9_1),
% 8.06/2.49 inference(avatar_split_clause,[status(thm)],[f642,f681])).
% 8.06/2.49 thf(f642,plain,(
% 8.06/2.49 (sK17 = $false)),
% 8.06/2.49 inference(beta_eta_normalization,[status(thm)],[f641])).
% 8.06/2.49 thf(f641,plain,(
% 8.06/2.49 (((^[Y0 : $o]: (Y0)) @ sK17) = $false)),
% 8.06/2.49 inference(sigma_clausification,[status(thm)],[f628])).
% 8.06/2.49 thf(f628,plain,(
% 8.06/2.49 ((!! @ $o @ (^[Y0 : $o]: (Y0))) = $false)),
% 8.06/2.49 inference(binary_proxy_clausification,[status(thm)],[f627])).
% 8.06/2.49 % SZS output end Proof for DTF2THF_30392
% 8.06/2.49 % (30621)------------------------------
% 8.06/2.49 % (30621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.49 % (30621)Termination reason: Refutation
% 8.06/2.49
% 8.06/2.49 % (30621)Memory used [KB]: 11001
% 8.06/2.49 % (30621)Time elapsed: 0.272 s
% 8.06/2.49 % (30621)Instructions burned: 949 (million)
% 8.06/2.49 % (30621)------------------------------
% 8.06/2.49 % (30621)------------------------------
% 8.06/2.49 % (30507)Success in time 1.072 s
%------------------------------------------------------------------------------