TSTP Solution File: SEV531^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV531^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:22:45 EDT 2023
% Result : Timeout 299.75s 300.21s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV531^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n014.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 24 03:48:19 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.52 %----Proving TH0
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 % File : SEV531^1 : TPTP v8.1.2. Released v7.5.0.
% 0.22/0.53 % Domain : Set Theory
% 0.22/0.53 % Problem : ProofGold problem HOSetConstr_231_pos_th0
% 0.22/0.53 % Version : Especial.
% 0.22/0.53 % English :
% 0.22/0.53
% 0.22/0.53 % Refs : [Urb20] Urban (2020) Email to Geoff Sutcliffe
% 0.22/0.53 % Source : [Urb20]
% 0.22/0.53 % Names : HOSetConstr_231_pos_th0.p [Urb20]
% 0.22/0.53
% 0.22/0.53 % Status : Unknown
% 0.22/0.53 % Rating : 1.00 v7.5.0
% 0.22/0.53 % Syntax : Number of formulae : 213 ( 99 unt; 104 typ; 0 def)
% 0.22/0.53 % Number of atoms : 485 ( 135 equ; 0 cnn)
% 0.22/0.53 % Maximal formula atoms : 6 ( 4 avg)
% 0.22/0.53 % Number of connectives : 1363 ( 0 ~; 0 |; 0 &;1256 @)
% 0.22/0.53 % ( 0 <=>; 107 =>; 0 <=; 0 <~>)
% 0.22/0.53 % Maximal formula depth : 31 ( 2 avg)
% 0.22/0.53 % Number of types : 2 ( 0 usr)
% 0.22/0.53 % Number of type conns : 736 ( 736 >; 0 *; 0 +; 0 <<)
% 0.22/0.53 % Number of symbols : 105 ( 104 usr; 3 con; 0-14 aty)
% 0.22/0.53 % Number of variables : 522 ( 356 ^; 129 !; 37 ?; 522 :)
% 0.22/0.53 % SPC : TH0_UNK_EQU_NAR
% 0.22/0.53
% 0.22/0.53 % Comments : See https://proofgold.org
% 0.22/0.53 %------------------------------------------------------------------------------
% 0.22/0.53 thf(c_Eps_i_tp,type,
% 0.22/0.53 c_Eps_i: ( $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_False_tp,type,
% 0.22/0.53 c_False: $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_True_tp,type,
% 0.22/0.53 c_True: $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_not_tp,type,
% 0.22/0.53 c_not: $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_and_tp,type,
% 0.22/0.53 c_and: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_or_tp,type,
% 0.22/0.53 c_or: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_iff_tp,type,
% 0.22/0.53 c_iff: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_In_tp,type,
% 0.22/0.53 c_In: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_Subq_tp,type,
% 0.22/0.53 c_Subq: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_Empty_tp,type,
% 0.22/0.53 c_Empty: $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Union_tp,type,
% 0.22/0.53 c_Union: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Power_tp,type,
% 0.22/0.53 c_Power: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Repl_tp,type,
% 0.22/0.53 c_Repl: $i > ( $i > $i ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_TransSet_tp,type,
% 0.22/0.53 c_TransSet: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_atleast2_tp,type,
% 0.22/0.53 c_atleast2: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_atleast3_tp,type,
% 0.22/0.53 c_atleast3: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_atleast4_tp,type,
% 0.22/0.53 c_atleast4: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_atleast5_tp,type,
% 0.22/0.53 c_atleast5: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_atleast6_tp,type,
% 0.22/0.53 c_atleast6: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_exactly2_tp,type,
% 0.22/0.53 c_exactly2: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_exactly3_tp,type,
% 0.22/0.53 c_exactly3: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_exactly4_tp,type,
% 0.22/0.53 c_exactly4: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_exactly5_tp,type,
% 0.22/0.53 c_exactly5: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_exu_i_tp,type,
% 0.22/0.53 c_exu_i: ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_reflexive_i_tp,type,
% 0.22/0.53 c_reflexive_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_irreflexive_i_tp,type,
% 0.22/0.53 c_irreflexive_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_symmetric_i_tp,type,
% 0.22/0.53 c_symmetric_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_antisymmetric_i_tp,type,
% 0.22/0.53 c_antisymmetric_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_transitive_i_tp,type,
% 0.22/0.53 c_transitive_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_eqreln_i_tp,type,
% 0.22/0.53 c_eqreln_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_per_i_tp,type,
% 0.22/0.53 c_per_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_linear_i_tp,type,
% 0.22/0.53 c_linear_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_trichotomous_or_i_tp,type,
% 0.22/0.53 c_trichotomous_or_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_partialorder_i_tp,type,
% 0.22/0.53 c_partialorder_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_totalorder_i_tp,type,
% 0.22/0.53 c_totalorder_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_strictpartialorder_i_tp,type,
% 0.22/0.53 c_strictpartialorder_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_stricttotalorder_i_tp,type,
% 0.22/0.53 c_stricttotalorder_i: ( $i > $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_If_i_tp,type,
% 0.22/0.53 c_If_i: $o > $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_exactly1of2_tp,type,
% 0.22/0.53 c_exactly1of2: $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_exactly1of3_tp,type,
% 0.22/0.53 c_exactly1of3: $o > $o > $o > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_nIn_tp,type,
% 0.22/0.53 c_nIn: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_nSubq_tp,type,
% 0.22/0.53 c_nSubq: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_UPair_tp,type,
% 0.22/0.53 c_UPair: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Sing_tp,type,
% 0.22/0.53 c_Sing: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_binunion_tp,type,
% 0.22/0.53 c_binunion: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_SetAdjoin_tp,type,
% 0.22/0.53 c_SetAdjoin: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_famunion_tp,type,
% 0.22/0.53 c_famunion: $i > ( $i > $i ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Sep_tp,type,
% 0.22/0.53 c_Sep: $i > ( $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_ReplSep_tp,type,
% 0.22/0.53 c_ReplSep: $i > ( $i > $o ) > ( $i > $i ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_binintersect_tp,type,
% 0.22/0.53 c_binintersect: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_setminus_tp,type,
% 0.22/0.53 c_setminus: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_inj_tp,type,
% 0.22/0.53 c_inj: $i > $i > ( $i > $i ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_bij_tp,type,
% 0.22/0.53 c_bij: $i > $i > ( $i > $i ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_atleastp_tp,type,
% 0.22/0.53 c_atleastp: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_equip_tp,type,
% 0.22/0.53 c_equip: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_In_rec_poly_G_i_tp,type,
% 0.22/0.53 c_In_rec_poly_G_i: ( $i > ( $i > $i ) > $i ) > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_In_rec_poly_i_tp,type,
% 0.22/0.53 c_In_rec_poly_i: ( $i > ( $i > $i ) > $i ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_ordsucc_tp,type,
% 0.22/0.53 c_ordsucc: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_nat_p_tp,type,
% 0.22/0.53 c_nat_p: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_nat_primrec_tp,type,
% 0.22/0.53 c_nat_primrec: $i > ( $i > $i > $i ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_add_nat_tp,type,
% 0.22/0.53 c_add_nat: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_mul_nat_tp,type,
% 0.22/0.53 c_mul_nat: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_ordinal_tp,type,
% 0.22/0.53 c_ordinal: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_V__tp,type,
% 0.22/0.53 c_V_: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Inj1_tp,type,
% 0.22/0.53 c_Inj1: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Inj0_tp,type,
% 0.22/0.53 c_Inj0: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Unj_tp,type,
% 0.22/0.53 c_Unj: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_combine_funcs_tp,type,
% 0.22/0.53 c_combine_funcs: $i > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_setsum_tp,type,
% 0.22/0.53 c_setsum: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_proj0_tp,type,
% 0.22/0.53 c_proj0: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_proj1_tp,type,
% 0.22/0.53 c_proj1: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_binrep_tp,type,
% 0.22/0.53 c_binrep: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_lam_tp,type,
% 0.22/0.53 c_lam: $i > ( $i > $i ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_setprod_tp,type,
% 0.22/0.53 c_setprod: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_ap_tp,type,
% 0.22/0.53 c_ap: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_setsum_p_tp,type,
% 0.22/0.53 c_setsum_p: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_tuple_p_tp,type,
% 0.22/0.53 c_tuple_p: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_Pi_tp,type,
% 0.22/0.53 c_Pi: $i > ( $i > $i ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_setexp_tp,type,
% 0.22/0.53 c_setexp: $i > $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_Sep2_tp,type,
% 0.22/0.53 c_Sep2: $i > ( $i > $i ) > ( $i > $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_set_of_pairs_tp,type,
% 0.22/0.53 c_set_of_pairs: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_lam2_tp,type,
% 0.22/0.53 c_lam2: $i > ( $i > $i ) > ( $i > $i > $i ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_PNoEq__tp,type,
% 0.22/0.53 c_PNoEq_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_PNoLt__tp,type,
% 0.22/0.53 c_PNoLt_: $i > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_PNoLt_tp,type,
% 0.22/0.53 c_PNoLt: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_PNoLe_tp,type,
% 0.22/0.53 c_PNoLe: $i > ( $i > $o ) > $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_PNo_downc_tp,type,
% 0.22/0.53 c_PNo_downc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_PNo_upc_tp,type,
% 0.22/0.53 c_PNo_upc: ( $i > ( $i > $o ) > $o ) > $i > ( $i > $o ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNoElts__tp,type,
% 0.22/0.53 c_SNoElts_: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNo__tp,type,
% 0.22/0.53 c_SNo_: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_PSNo_tp,type,
% 0.22/0.53 c_PSNo: $i > ( $i > $o ) > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNo_tp,type,
% 0.22/0.53 c_SNo: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNoLev_tp,type,
% 0.22/0.53 c_SNoLev: $i > $i ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNoEq__tp,type,
% 0.22/0.53 c_SNoEq_: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNoLt_tp,type,
% 0.22/0.53 c_SNoLt: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_SNoLe_tp,type,
% 0.22/0.53 c_SNoLe: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_binop_on_tp,type,
% 0.22/0.53 c_binop_on: $i > ( $i > $i > $i ) > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_Loop_tp,type,
% 0.22/0.53 c_Loop: $i > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_Loop_with_defs_tp,type,
% 0.22/0.53 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 ).
% 0.22/0.53
% 0.22/0.53 thf(c_Loop_with_defs_cex1_tp,type,
% 0.22/0.53 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 ).
% 0.22/0.53
% 0.22/0.53 thf(c_Loop_with_defs_cex2_tp,type,
% 0.22/0.53 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 ).
% 0.22/0.53
% 0.22/0.53 thf(c_combinator_tp,type,
% 0.22/0.53 c_combinator: $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_combinator_equiv_tp,type,
% 0.22/0.53 c_combinator_equiv: $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(c_equip_mod_tp,type,
% 0.22/0.53 c_equip_mod: $i > $i > $i > $o ).
% 0.22/0.53
% 0.22/0.53 thf(ax1,axiom,
% 0.22/0.53 ! [X0: $i > $o,X1: $i] :
% 0.22/0.53 ( ( X0 @ X1 )
% 0.22/0.53 => ( X0 @ ( c_Eps_i @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax2,axiom,
% 0.22/0.53 ! [X0: $o] :
% 0.22/0.53 ( ( c_not @ ( c_not @ X0 ) )
% 0.22/0.53 => X0 ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax3,axiom,
% 0.22/0.53 ! [X0: $o,X1: $o] :
% 0.22/0.53 ( ( c_iff @ X0 @ X1 )
% 0.22/0.53 => ( X0 = X1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax4,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( ( c_Subq @ X0 @ X1 )
% 0.22/0.53 => ( ( c_Subq @ X1 @ X0 )
% 0.22/0.53 => ( X0 = X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax5,axiom,
% 0.22/0.53 ( c_not
% 0.22/0.53 @ ? [X0: $i] : ( c_In @ X0 @ c_Empty ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax6,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] :
% 0.22/0.53 ( c_iff @ ( c_In @ X1 @ ( c_Union @ X0 ) )
% 0.22/0.53 @ ? [X2: $i] : ( c_and @ ( c_In @ X1 @ X2 ) @ ( c_In @ X2 @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax7,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i] : ( c_iff @ ( c_In @ X1 @ ( c_Power @ X0 ) ) @ ( c_Subq @ X1 @ X0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax8,axiom,
% 0.22/0.53 ! [X0: $i,X1: $i > $i,X2: $i] :
% 0.22/0.53 ( c_iff
% 0.22/0.53 @ ( c_In @ X2
% 0.22/0.53 @ ( c_Repl @ X0
% 0.22/0.53 @ ^ [X3: $i] : ( X1 @ X3 ) ) )
% 0.22/0.53 @ ? [X3: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X3 @ X0 )
% 0.22/0.53 @ ( X2
% 0.22/0.53 = ( X1 @ X3 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax9,axiom,
% 0.22/0.53 ! [X0: $i > $o] :
% 0.22/0.53 ( ! [X1: $i] :
% 0.22/0.53 ( ( X0 @ X1 )
% 0.22/0.53 => ! [X2: $i] :
% 0.22/0.53 ( ( c_In @ X2 @ X1 )
% 0.22/0.53 => ( X0 @ X2 ) ) )
% 0.22/0.53 => ( ( X0 @ c_Empty )
% 0.22/0.53 => ( ! [X1: $i] :
% 0.22/0.53 ( ( X0 @ X1 )
% 0.22/0.53 => ( X0 @ ( c_Union @ X1 ) ) )
% 0.22/0.53 => ( ! [X1: $i] :
% 0.22/0.53 ( ( X0 @ X1 )
% 0.22/0.53 => ( X0 @ ( c_Power @ X1 ) ) )
% 0.22/0.53 => ( ! [X1: $i] :
% 0.22/0.53 ( ( X0 @ X1 )
% 0.22/0.53 => ! [X2: $i > $i] :
% 0.22/0.53 ( ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X1 )
% 0.22/0.53 => ( X0 @ ( X2 @ X3 ) ) )
% 0.22/0.53 => ( X0
% 0.22/0.53 @ ( c_Repl @ X1
% 0.22/0.53 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
% 0.22/0.53 => ! [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax10,axiom,
% 0.22/0.53 ! [X0: $i > $o] :
% 0.22/0.53 ( ! [X1: $i] :
% 0.22/0.53 ( ! [X2: $i] :
% 0.22/0.53 ( ( c_In @ X2 @ X1 )
% 0.22/0.53 => ( X0 @ X2 ) )
% 0.22/0.53 => ( X0 @ X1 ) )
% 0.22/0.53 => ! [X1: $i] : ( X0 @ X1 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax11,axiom,
% 0.22/0.53 ( c_False
% 0.22/0.53 = ( ! [X0: $o] : X0 ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax12,axiom,
% 0.22/0.53 ( c_True
% 0.22/0.53 = ( ! [X0: $o] :
% 0.22/0.53 ( X0
% 0.22/0.53 => X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax13,axiom,
% 0.22/0.53 ( c_not
% 0.22/0.53 = ( ^ [X0: $o] :
% 0.22/0.53 ( X0
% 0.22/0.53 => c_False ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax14,axiom,
% 0.22/0.53 ( c_and
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] :
% 0.22/0.53 ! [X2: $o] :
% 0.22/0.53 ( ( X0
% 0.22/0.53 => ( X1
% 0.22/0.53 => X2 ) )
% 0.22/0.53 => X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax15,axiom,
% 0.22/0.53 ( c_or
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] :
% 0.22/0.53 ! [X2: $o] :
% 0.22/0.53 ( ( X0
% 0.22/0.53 => X2 )
% 0.22/0.53 => ( ( X1
% 0.22/0.53 => X2 )
% 0.22/0.53 => X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax16,axiom,
% 0.22/0.53 ( c_iff
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] :
% 0.22/0.53 ( c_and
% 0.22/0.53 @ ( X0
% 0.22/0.53 => X1 )
% 0.22/0.53 @ ( X1
% 0.22/0.53 => X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax17,axiom,
% 0.22/0.53 ( c_Subq
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ! [X2: $i] :
% 0.22/0.53 ( ( c_In @ X2 @ X0 )
% 0.22/0.53 => ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax18,axiom,
% 0.22/0.53 ( c_TransSet
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ! [X1: $i] :
% 0.22/0.53 ( ( c_In @ X1 @ X0 )
% 0.22/0.53 => ( c_Subq @ X1 @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax19,axiom,
% 0.22/0.53 ( c_atleast2
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ? [X1: $i] : ( c_and @ ( c_In @ X1 @ X0 ) @ ( c_not @ ( c_Subq @ X0 @ ( c_Power @ X1 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax20,axiom,
% 0.22/0.53 ( c_atleast3
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast2 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax21,axiom,
% 0.22/0.53 ( c_atleast4
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast3 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax22,axiom,
% 0.22/0.53 ( c_atleast5
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast4 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax23,axiom,
% 0.22/0.53 ( c_atleast6
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ? [X1: $i] : ( c_and @ ( c_Subq @ X1 @ X0 ) @ ( c_and @ ( c_not @ ( c_Subq @ X0 @ X1 ) ) @ ( c_atleast5 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax24,axiom,
% 0.22/0.53 ( c_exactly2
% 0.22/0.53 = ( ^ [X0: $i] : ( c_and @ ( c_atleast2 @ X0 ) @ ( c_not @ ( c_atleast3 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax25,axiom,
% 0.22/0.53 ( c_exactly3
% 0.22/0.53 = ( ^ [X0: $i] : ( c_and @ ( c_atleast3 @ X0 ) @ ( c_not @ ( c_atleast4 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax26,axiom,
% 0.22/0.53 ( c_exactly4
% 0.22/0.53 = ( ^ [X0: $i] : ( c_and @ ( c_atleast4 @ X0 ) @ ( c_not @ ( c_atleast5 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax27,axiom,
% 0.22/0.53 ( c_exactly5
% 0.22/0.53 = ( ^ [X0: $i] : ( c_and @ ( c_atleast5 @ X0 ) @ ( c_not @ ( c_atleast6 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax28,axiom,
% 0.22/0.53 ( c_exu_i
% 0.22/0.53 = ( ^ [X0: $i > $o] :
% 0.22/0.53 ( c_and
% 0.22/0.53 @ ? [X1: $i] : ( X0 @ X1 )
% 0.22/0.53 @ ! [X1: $i,X2: $i] :
% 0.22/0.53 ( ( X0 @ X1 )
% 0.22/0.53 => ( ( X0 @ X2 )
% 0.22/0.53 => ( X1 = X2 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax29,axiom,
% 0.22/0.53 ( c_reflexive_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i] : ( X0 @ X1 @ X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax30,axiom,
% 0.22/0.53 ( c_irreflexive_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i] : ( c_not @ ( X0 @ X1 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax31,axiom,
% 0.22/0.53 ( c_symmetric_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i,X2: $i] :
% 0.22/0.53 ( ( X0 @ X1 @ X2 )
% 0.22/0.53 => ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax32,axiom,
% 0.22/0.53 ( c_antisymmetric_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i,X2: $i] :
% 0.22/0.53 ( ( X0 @ X1 @ X2 )
% 0.22/0.53 => ( ( X0 @ X2 @ X1 )
% 0.22/0.53 => ( X1 = X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax33,axiom,
% 0.22/0.53 ( c_transitive_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i,X2: $i,X3: $i] :
% 0.22/0.53 ( ( X0 @ X1 @ X2 )
% 0.22/0.53 => ( ( X0 @ X2 @ X3 )
% 0.22/0.53 => ( X0 @ X1 @ X3 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax34,axiom,
% 0.22/0.53 ( c_eqreln_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_symmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax35,axiom,
% 0.22/0.53 ( c_per_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_symmetric_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax36,axiom,
% 0.22/0.53 ( c_linear_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i,X2: $i] : ( c_or @ ( X0 @ X1 @ X2 ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax37,axiom,
% 0.22/0.53 ( c_trichotomous_or_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] :
% 0.22/0.53 ! [X1: $i,X2: $i] : ( c_or @ ( c_or @ ( X0 @ X1 @ X2 ) @ ( X1 = X2 ) ) @ ( X0 @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax38,axiom,
% 0.22/0.53 ( c_partialorder_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_and @ ( c_reflexive_i @ X0 ) @ ( c_antisymmetric_i @ X0 ) ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax39,axiom,
% 0.22/0.53 ( c_totalorder_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_partialorder_i @ X0 ) @ ( c_linear_i @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax40,axiom,
% 0.22/0.53 ( c_strictpartialorder_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_irreflexive_i @ X0 ) @ ( c_transitive_i @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax41,axiom,
% 0.22/0.53 ( c_stricttotalorder_i
% 0.22/0.53 = ( ^ [X0: $i > $i > $o] : ( c_and @ ( c_strictpartialorder_i @ X0 ) @ ( c_trichotomous_or_i @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax42,axiom,
% 0.22/0.53 ( c_If_i
% 0.22/0.53 = ( ^ [X0: $o,X1: $i,X2: $i] :
% 0.22/0.53 ( c_Eps_i
% 0.22/0.53 @ ^ [X3: $i] : ( c_or @ ( c_and @ X0 @ ( X3 = X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ ( X3 = X2 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax43,axiom,
% 0.22/0.53 ( c_exactly1of2
% 0.22/0.53 = ( ^ [X0: $o,X1: $o] : ( c_or @ ( c_and @ X0 @ ( c_not @ X1 ) ) @ ( c_and @ ( c_not @ X0 ) @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax44,axiom,
% 0.22/0.53 ( c_exactly1of3
% 0.22/0.53 = ( ^ [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 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax45,axiom,
% 0.22/0.53 ( c_nIn
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_In @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax46,axiom,
% 0.22/0.53 ( c_nSubq
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ( c_not @ ( c_Subq @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax47,axiom,
% 0.22/0.53 ( c_UPair
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_Repl @ ( c_Power @ ( c_Power @ c_Empty ) )
% 0.22/0.53 @ ^ [X2: $i] : ( c_If_i @ ( c_In @ c_Empty @ X2 ) @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax48,axiom,
% 0.22/0.53 ( c_Sing
% 0.22/0.53 = ( ^ [X0: $i] : ( c_UPair @ X0 @ X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax49,axiom,
% 0.22/0.53 ( c_binunion
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ( c_Union @ ( c_UPair @ X0 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax50,axiom,
% 0.22/0.53 ( c_SetAdjoin
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ( c_binunion @ X0 @ ( c_Sing @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax51,axiom,
% 0.22/0.53 ( c_famunion
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i] :
% 0.22/0.53 ( c_Union
% 0.22/0.53 @ ( c_Repl @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax52,axiom,
% 0.22/0.53 ( c_Sep
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( c_If_i
% 0.22/0.53 @ ? [X2: $i] : ( c_and @ ( c_In @ X2 @ X0 ) @ ( X1 @ X2 ) )
% 0.22/0.53 @ ( c_Repl @ X0
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ^ [X3: $i] :
% 0.22/0.53 ( c_If_i @ ( X1 @ X3 ) @ X3
% 0.22/0.53 @ ( c_Eps_i
% 0.22/0.53 @ ^ [X4: $i] : ( c_and @ ( c_In @ X4 @ X0 ) @ ( X1 @ X4 ) ) ) )
% 0.22/0.53 @ X2 ) )
% 0.22/0.53 @ c_Empty ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax53,axiom,
% 0.22/0.53 ( c_ReplSep
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $i] :
% 0.22/0.53 ( c_Repl
% 0.22/0.53 @ ( c_Sep @ X0
% 0.22/0.53 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.22/0.53 @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax54,axiom,
% 0.22/0.53 ( c_binintersect
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_Sep @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax55,axiom,
% 0.22/0.53 ( c_setminus
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_Sep @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( c_nIn @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax56,axiom,
% 0.22/0.53 ( c_inj
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.22/0.53 ( c_and
% 0.22/0.53 @ ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X0 )
% 0.22/0.53 => ( c_In @ ( X2 @ X3 ) @ X1 ) )
% 0.22/0.53 @ ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X0 )
% 0.22/0.53 => ! [X4: $i] :
% 0.22/0.53 ( ( c_In @ X4 @ X0 )
% 0.22/0.53 => ( ( ( X2 @ X3 )
% 0.22/0.53 = ( X2 @ X4 ) )
% 0.22/0.53 => ( X3 = X4 ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax57,axiom,
% 0.22/0.53 ( c_bij
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i > $i] :
% 0.22/0.53 ( c_and @ ( c_inj @ X0 @ X1 @ X2 )
% 0.22/0.53 @ ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X1 )
% 0.22/0.53 => ? [X4: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X4 @ X0 )
% 0.22/0.53 @ ( ( X2 @ X4 )
% 0.22/0.53 = X3 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax58,axiom,
% 0.22/0.53 ( c_atleastp
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ? [X2: $i > $i] : ( c_inj @ X0 @ X1 @ X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax59,axiom,
% 0.22/0.53 ( c_equip
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ? [X2: $i > $i] : ( c_bij @ X0 @ X1 @ X2 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax60,axiom,
% 0.22/0.53 ( c_In_rec_poly_G_i
% 0.22/0.53 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i,X2: $i] :
% 0.22/0.53 ! [X3: $i > $i > $o] :
% 0.22/0.53 ( ! [X4: $i,X5: $i > $i] :
% 0.22/0.53 ( ! [X6: $i] :
% 0.22/0.53 ( ( c_In @ X6 @ X4 )
% 0.22/0.53 => ( X3 @ X6 @ ( X5 @ X6 ) ) )
% 0.22/0.53 => ( X3 @ X4 @ ( X0 @ X4 @ X5 ) ) )
% 0.22/0.53 => ( X3 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax61,axiom,
% 0.22/0.53 ( c_In_rec_poly_i
% 0.22/0.53 = ( ^ [X0: $i > ( $i > $i ) > $i,X1: $i] :
% 0.22/0.53 ( c_Eps_i
% 0.22/0.53 @ ^ [X2: $i] : ( c_In_rec_poly_G_i @ X0 @ X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax62,axiom,
% 0.22/0.53 ( c_ordsucc
% 0.22/0.53 = ( ^ [X0: $i] : ( c_binunion @ X0 @ ( c_Sing @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax63,axiom,
% 0.22/0.53 ( c_nat_p
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ! [X1: $i > $o] :
% 0.22/0.53 ( ( X1 @ c_Empty )
% 0.22/0.53 => ( ! [X2: $i] :
% 0.22/0.53 ( ( X1 @ X2 )
% 0.22/0.53 => ( X1 @ ( c_ordsucc @ X2 ) ) )
% 0.22/0.53 => ( X1 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax64,axiom,
% 0.22/0.53 ( c_nat_primrec
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.22/0.53 ( c_In_rec_poly_i
% 0.22/0.53 @ ^ [X2: $i,X3: $i > $i] : ( c_If_i @ ( c_In @ ( c_Union @ X2 ) @ X2 ) @ ( X1 @ ( c_Union @ X2 ) @ ( X3 @ ( c_Union @ X2 ) ) ) @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax65,axiom,
% 0.22/0.53 ( c_add_nat
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_nat_primrec @ X0
% 0.22/0.53 @ ^ [X2: $i,X3: $i] : ( c_ordsucc @ X3 )
% 0.22/0.53 @ X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax66,axiom,
% 0.22/0.53 ( c_mul_nat
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_nat_primrec @ c_Empty
% 0.22/0.53 @ ^ [X2: $i,X3: $i] : ( c_add_nat @ X0 @ X3 )
% 0.22/0.53 @ X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax67,axiom,
% 0.22/0.53 ( c_ordinal
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( c_and @ ( c_TransSet @ X0 )
% 0.22/0.53 @ ! [X1: $i] :
% 0.22/0.53 ( ( c_In @ X1 @ X0 )
% 0.22/0.53 => ( c_TransSet @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax68,axiom,
% 0.22/0.53 ( c_V_
% 0.22/0.53 = ( c_In_rec_poly_i
% 0.22/0.53 @ ^ [X0: $i,X1: $i > $i] :
% 0.22/0.53 ( c_famunion @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( c_Power @ ( X1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax69,axiom,
% 0.22/0.53 ( c_Inj1
% 0.22/0.53 = ( c_In_rec_poly_i
% 0.22/0.53 @ ^ [X0: $i,X1: $i > $i] :
% 0.22/0.53 ( c_binunion @ ( c_Sing @ c_Empty )
% 0.22/0.53 @ ( c_Repl @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax70,axiom,
% 0.22/0.53 ( c_Inj0
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( c_Repl @ X0
% 0.22/0.53 @ ^ [X1: $i] : ( c_Inj1 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax71,axiom,
% 0.22/0.53 ( c_Unj
% 0.22/0.53 = ( c_In_rec_poly_i
% 0.22/0.53 @ ^ [X0: $i,X1: $i > $i] :
% 0.22/0.53 ( c_Repl @ ( c_setminus @ X0 @ ( c_Sing @ c_Empty ) )
% 0.22/0.53 @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax72,axiom,
% 0.22/0.53 ( c_combine_funcs
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i > $i,X3: $i > $i,X4: $i] :
% 0.22/0.53 ( c_If_i
% 0.22/0.53 @ ( X4
% 0.22/0.53 = ( c_Inj0 @ ( c_Unj @ X4 ) ) )
% 0.22/0.53 @ ( X2 @ ( c_Unj @ X4 ) )
% 0.22/0.53 @ ( X3 @ ( c_Unj @ X4 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax73,axiom,
% 0.22/0.53 ( c_setsum
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_binunion
% 0.22/0.53 @ ( c_Repl @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( c_Inj0 @ X2 ) )
% 0.22/0.53 @ ( c_Repl @ X1
% 0.22/0.53 @ ^ [X2: $i] : ( c_Inj1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax74,axiom,
% 0.22/0.53 ( c_proj0
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( c_ReplSep @ X0
% 0.22/0.53 @ ^ [X1: $i] :
% 0.22/0.53 ? [X2: $i] :
% 0.22/0.53 ( ( c_Inj0 @ X2 )
% 0.22/0.53 = X1 )
% 0.22/0.53 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax75,axiom,
% 0.22/0.53 ( c_proj1
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( c_ReplSep @ X0
% 0.22/0.53 @ ^ [X1: $i] :
% 0.22/0.53 ? [X2: $i] :
% 0.22/0.53 ( ( c_Inj1 @ X2 )
% 0.22/0.53 = X1 )
% 0.22/0.53 @ ^ [X1: $i] : ( c_Unj @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax76,axiom,
% 0.22/0.53 ( c_binrep
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] : ( c_setsum @ X0 @ ( c_Power @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax77,axiom,
% 0.22/0.53 ( c_lam
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i] :
% 0.22/0.53 ( c_famunion @ X0
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( c_Repl @ ( X1 @ X2 )
% 0.22/0.53 @ ^ [X3: $i] : ( c_setsum @ X2 @ X3 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax78,axiom,
% 0.22/0.53 ( c_setprod
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_lam @ X0
% 0.22/0.53 @ ^ [X2: $i] : X1 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax79,axiom,
% 0.22/0.53 ( c_ap
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_ReplSep @ X0
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ? [X3: $i] :
% 0.22/0.53 ( X2
% 0.22/0.53 = ( c_setsum @ X1 @ X3 ) )
% 0.22/0.53 @ ^ [X2: $i] : ( c_proj1 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax80,axiom,
% 0.22/0.53 ( c_setsum_p
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( ( c_setsum @ ( c_ap @ X0 @ c_Empty ) @ ( c_ap @ X0 @ ( c_ordsucc @ c_Empty ) ) )
% 0.22/0.53 = X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax81,axiom,
% 0.22/0.53 ( c_tuple_p
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ! [X2: $i] :
% 0.22/0.53 ( ( c_In @ X2 @ X1 )
% 0.22/0.53 => ? [X3: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X3 @ X0 )
% 0.22/0.53 @ ? [X4: $i] :
% 0.22/0.53 ( X2
% 0.22/0.53 = ( c_setsum @ X3 @ X4 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax82,axiom,
% 0.22/0.53 ( c_Pi
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i] :
% 0.22/0.53 ( c_Sep
% 0.22/0.53 @ ( c_Power
% 0.22/0.53 @ ( c_lam @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( c_Union @ ( X1 @ X2 ) ) ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X0 )
% 0.22/0.53 => ( c_In @ ( c_ap @ X2 @ X3 ) @ ( X1 @ X3 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax83,axiom,
% 0.22/0.53 ( c_setexp
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_Pi @ X1
% 0.22/0.53 @ ^ [X2: $i] : X0 ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax84,axiom,
% 0.22/0.53 ( c_Sep2
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $o] :
% 0.22/0.53 ( c_Sep
% 0.22/0.53 @ ( c_lam @ X0
% 0.22/0.53 @ ^ [X3: $i] : ( X1 @ X3 ) )
% 0.22/0.53 @ ^ [X3: $i] : ( X2 @ ( c_ap @ X3 @ c_Empty ) @ ( c_ap @ X3 @ ( c_ordsucc @ c_Empty ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax85,axiom,
% 0.22/0.53 ( c_set_of_pairs
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ! [X1: $i] :
% 0.22/0.53 ( ( c_In @ X1 @ X0 )
% 0.22/0.53 => ? [X2: $i,X3: $i] :
% 0.22/0.53 ( X1
% 0.22/0.53 = ( c_lam @ ( c_ordsucc @ ( c_ordsucc @ c_Empty ) )
% 0.22/0.53 @ ^ [X4: $i] : ( c_If_i @ ( X4 = c_Empty ) @ X2 @ X3 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax86,axiom,
% 0.22/0.53 ( c_lam2
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i,X2: $i > $i > $i] :
% 0.22/0.53 ( c_lam @ X0
% 0.22/0.53 @ ^ [X3: $i] :
% 0.22/0.53 ( c_lam @ ( X1 @ X3 )
% 0.22/0.53 @ ^ [X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax87,axiom,
% 0.22/0.53 ( c_PNoEq_
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.22/0.53 ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X0 )
% 0.22/0.53 => ( c_iff @ ( X1 @ X3 ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax88,axiom,
% 0.22/0.53 ( c_PNoLt_
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o,X2: $i > $o] :
% 0.22/0.53 ? [X3: $i] : ( c_and @ ( c_In @ X3 @ X0 ) @ ( c_and @ ( c_and @ ( c_PNoEq_ @ X3 @ X1 @ X2 ) @ ( c_not @ ( X1 @ X3 ) ) ) @ ( X2 @ X3 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax89,axiom,
% 0.22/0.53 ( c_PNoLt
% 0.22/0.53 = ( ^ [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 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax90,axiom,
% 0.22/0.53 ( c_PNoLe
% 0.22/0.53 = ( ^ [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 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax91,axiom,
% 0.22/0.53 ( c_PNo_downc
% 0.22/0.53 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.22/0.53 ? [X3: $i] :
% 0.22/0.53 ( c_and @ ( c_ordinal @ X3 )
% 0.22/0.53 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X1 @ X2 @ X3 @ X4 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax92,axiom,
% 0.22/0.53 ( c_PNo_upc
% 0.22/0.53 = ( ^ [X0: $i > ( $i > $o ) > $o,X1: $i,X2: $i > $o] :
% 0.22/0.53 ? [X3: $i] :
% 0.22/0.53 ( c_and @ ( c_ordinal @ X3 )
% 0.22/0.53 @ ? [X4: $i > $o] : ( c_and @ ( X0 @ X3 @ X4 ) @ ( c_PNoLe @ X3 @ X4 @ X1 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax93,axiom,
% 0.22/0.53 ( c_SNoElts_
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( c_binunion @ X0
% 0.22/0.53 @ ( c_Repl @ X0
% 0.22/0.53 @ ^ [X1: $i] :
% 0.22/0.53 ( ^ [X2: $i] : ( c_SetAdjoin @ X2 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.22/0.53 @ X1 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax94,axiom,
% 0.22/0.53 ( c_SNo_
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_and @ ( c_Subq @ X1 @ ( c_SNoElts_ @ X0 ) )
% 0.22/0.53 @ ! [X2: $i] :
% 0.22/0.53 ( ( c_In @ X2 @ X0 )
% 0.22/0.53 => ( c_exactly1of2
% 0.22/0.53 @ ( c_In
% 0.22/0.53 @ ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.22/0.53 @ X2 )
% 0.22/0.53 @ X1 )
% 0.22/0.53 @ ( c_In @ X2 @ X1 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax95,axiom,
% 0.22/0.53 ( c_PSNo
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $o] :
% 0.22/0.53 ( c_binunion
% 0.22/0.53 @ ( c_Sep @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( X1 @ X2 ) )
% 0.22/0.53 @ ( c_ReplSep @ X0
% 0.22/0.53 @ ^ [X2: $i] : ( c_not @ ( X1 @ X2 ) )
% 0.22/0.53 @ ^ [X2: $i] :
% 0.22/0.53 ( ^ [X3: $i] : ( c_SetAdjoin @ X3 @ ( c_Sing @ ( c_ordsucc @ c_Empty ) ) )
% 0.22/0.53 @ X2 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax96,axiom,
% 0.22/0.53 ( c_SNo
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ? [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax97,axiom,
% 0.22/0.53 ( c_SNoLev
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ( c_Eps_i
% 0.22/0.53 @ ^ [X1: $i] : ( c_and @ ( c_ordinal @ X1 ) @ ( c_SNo_ @ X1 @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax98,axiom,
% 0.22/0.53 ( c_SNoEq_
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ( c_PNoEq_ @ X0
% 0.22/0.53 @ ^ [X3: $i] : ( c_In @ X3 @ X1 )
% 0.22/0.53 @ ^ [X3: $i] : ( c_In @ X3 @ X2 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax99,axiom,
% 0.22/0.53 ( c_SNoLt
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_PNoLt @ ( c_SNoLev @ X0 )
% 0.22/0.53 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.22/0.53 @ ( c_SNoLev @ X1 )
% 0.22/0.53 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax100,axiom,
% 0.22/0.53 ( c_SNoLe
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ( c_PNoLe @ ( c_SNoLev @ X0 )
% 0.22/0.53 @ ^ [X2: $i] : ( c_In @ X2 @ X0 )
% 0.22/0.53 @ ( c_SNoLev @ X1 )
% 0.22/0.53 @ ^ [X2: $i] : ( c_In @ X2 @ X1 ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax101,axiom,
% 0.22/0.53 ( c_binop_on
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $i] :
% 0.22/0.53 ! [X2: $i] :
% 0.22/0.53 ( ( c_In @ X2 @ X0 )
% 0.22/0.53 => ! [X3: $i] :
% 0.22/0.53 ( ( c_In @ X3 @ X0 )
% 0.22/0.53 => ( c_In @ ( X1 @ X2 @ X3 ) @ X0 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax102,axiom,
% 0.22/0.53 ( c_Loop
% 0.22/0.53 = ( ^ [X0: $i,X1: $i > $i > $i,X2: $i > $i > $i,X3: $i > $i > $i,X4: $i] :
% 0.22/0.53 ( c_and
% 0.22/0.53 @ ( c_and @ ( c_and @ ( c_and @ ( c_binop_on @ X0 @ X1 ) @ ( c_binop_on @ X0 @ X2 ) ) @ ( c_binop_on @ X0 @ X3 ) )
% 0.22/0.53 @ ! [X5: $i] :
% 0.22/0.53 ( ( c_In @ X5 @ X0 )
% 0.22/0.53 => ( c_and
% 0.22/0.53 @ ( ( X1 @ X4 @ X5 )
% 0.22/0.53 = X5 )
% 0.22/0.53 @ ( ( X1 @ X5 @ X4 )
% 0.22/0.53 = X5 ) ) ) )
% 0.22/0.53 @ ! [X5: $i] :
% 0.22/0.53 ( ( c_In @ X5 @ X0 )
% 0.22/0.53 => ! [X6: $i] :
% 0.22/0.53 ( ( c_In @ X6 @ X0 )
% 0.22/0.53 => ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( ( X2 @ X5 @ ( X1 @ X5 @ X6 ) )
% 0.22/0.53 = X6 )
% 0.22/0.53 @ ( ( X1 @ X5 @ ( X2 @ X5 @ X6 ) )
% 0.22/0.53 = X6 ) )
% 0.22/0.53 @ ( ( X3 @ ( X1 @ X5 @ X6 ) @ X6 )
% 0.22/0.53 = X5 ) )
% 0.22/0.53 @ ( ( X1 @ ( X3 @ X5 @ X6 ) @ X6 )
% 0.22/0.53 = X5 ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax103,axiom,
% 0.22/0.53 ( c_Loop_with_defs
% 0.22/0.53 = ( ^ [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] :
% 0.22/0.53 ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( c_and @ ( c_Loop @ X0 @ X1 @ X2 @ X3 @ X4 )
% 0.22/0.53 @ ! [X14: $i] :
% 0.22/0.53 ( ( c_In @ X14 @ X0 )
% 0.22/0.53 => ! [X15: $i] :
% 0.22/0.53 ( ( c_In @ X15 @ X0 )
% 0.22/0.53 => ( ( X5 @ X14 @ X15 )
% 0.22/0.53 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) )
% 0.22/0.53 @ ! [X14: $i] :
% 0.22/0.53 ( ( c_In @ X14 @ X0 )
% 0.22/0.53 => ! [X15: $i] :
% 0.22/0.53 ( ( c_In @ X15 @ X0 )
% 0.22/0.53 => ! [X16: $i] :
% 0.22/0.53 ( ( c_In @ X16 @ X0 )
% 0.22/0.53 => ( ( X6 @ X14 @ X15 @ X16 )
% 0.22/0.53 = ( X2 @ ( X1 @ X14 @ ( X1 @ X15 @ X16 ) ) @ ( X1 @ ( X1 @ X14 @ X15 ) @ X16 ) ) ) ) ) ) )
% 0.22/0.53 @ ! [X14: $i] :
% 0.22/0.53 ( ( c_In @ X14 @ X0 )
% 0.22/0.53 => ! [X15: $i] :
% 0.22/0.53 ( ( c_In @ X15 @ X0 )
% 0.22/0.53 => ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( c_and
% 0.22/0.53 @ ( ( X7 @ X14 @ X15 )
% 0.22/0.53 = ( X2 @ X14 @ ( X1 @ X15 @ X14 ) ) )
% 0.22/0.53 @ ( ( X10 @ X14 @ X15 )
% 0.22/0.53 = ( X1 @ X14 @ ( X1 @ X15 @ ( X2 @ X14 @ X4 ) ) ) ) )
% 0.22/0.53 @ ( ( X11 @ X14 @ X15 )
% 0.22/0.53 = ( X1 @ ( X1 @ ( X3 @ X4 @ X14 ) @ X15 ) @ X14 ) ) )
% 0.22/0.53 @ ( ( X12 @ X14 @ X15 )
% 0.22/0.53 = ( X1 @ ( X2 @ X14 @ X15 ) @ ( X2 @ ( X2 @ X14 @ X4 ) @ X4 ) ) ) )
% 0.22/0.53 @ ( ( X13 @ X14 @ X15 )
% 0.22/0.53 = ( X1 @ ( X3 @ X4 @ ( X3 @ X4 @ X14 ) ) @ ( X3 @ X15 @ X14 ) ) ) ) ) ) )
% 0.22/0.53 @ ! [X14: $i] :
% 0.22/0.53 ( ( c_In @ X14 @ X0 )
% 0.22/0.53 => ! [X15: $i] :
% 0.22/0.53 ( ( c_In @ X15 @ X0 )
% 0.22/0.53 => ! [X16: $i] :
% 0.22/0.53 ( ( c_In @ X16 @ X0 )
% 0.22/0.53 => ( c_and
% 0.22/0.53 @ ( ( X8 @ X14 @ X15 @ X16 )
% 0.22/0.53 = ( X2 @ ( X1 @ X15 @ X14 ) @ ( X1 @ X15 @ ( X1 @ X14 @ X16 ) ) ) )
% 0.22/0.53 @ ( ( X9 @ X14 @ X15 @ X16 )
% 0.22/0.53 = ( X3 @ ( X1 @ ( X1 @ X16 @ X14 ) @ X15 ) @ ( X1 @ X14 @ X15 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax104,axiom,
% 0.22/0.53 ( c_Loop_with_defs_cex1
% 0.22/0.53 = ( ^ [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] :
% 0.22/0.53 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.22/0.53 @ ? [X14: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X14 @ X0 )
% 0.22/0.53 @ ? [X15: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X15 @ X0 )
% 0.22/0.53 @ ? [X16: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X16 @ X0 )
% 0.22/0.53 @ ? [X17: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X17 @ X0 )
% 0.22/0.53 @ ( c_not
% 0.22/0.53 @ ( ( X5 @ ( X1 @ ( X2 @ ( X8 @ X15 @ X16 @ X14 ) @ X4 ) @ X14 ) @ X17 )
% 0.22/0.53 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax105,axiom,
% 0.22/0.53 ( c_Loop_with_defs_cex2
% 0.22/0.53 = ( ^ [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] :
% 0.22/0.53 ( c_and @ ( c_Loop_with_defs @ X0 @ X1 @ X2 @ X3 @ X4 @ X5 @ X6 @ X7 @ X8 @ X9 @ X10 @ X11 @ X12 @ X13 )
% 0.22/0.53 @ ? [X14: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X14 @ X0 )
% 0.22/0.53 @ ? [X15: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X15 @ X0 )
% 0.22/0.53 @ ? [X16: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X16 @ X0 )
% 0.22/0.53 @ ? [X17: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X17 @ X0 )
% 0.22/0.53 @ ? [X18: $i] :
% 0.22/0.53 ( c_and @ ( c_In @ X18 @ X0 )
% 0.22/0.53 @ ( c_not
% 0.22/0.53 @ ( ( X6 @ X18 @ ( X1 @ ( X3 @ X4 @ X14 ) @ ( X9 @ X15 @ X16 @ X14 ) ) @ X17 )
% 0.22/0.53 = X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax106,axiom,
% 0.22/0.53 ( c_combinator
% 0.22/0.53 = ( ^ [X0: $i] :
% 0.22/0.53 ! [X1: $i > $o] :
% 0.22/0.53 ( ( X1 @ ( c_Inj0 @ c_Empty ) )
% 0.22/0.53 => ( ( X1 @ ( c_Inj0 @ ( c_Power @ c_Empty ) ) )
% 0.22/0.53 => ( ! [X2: $i,X3: $i] :
% 0.22/0.53 ( ( X1 @ X2 )
% 0.22/0.53 => ( ( X1 @ X3 )
% 0.22/0.53 => ( X1 @ ( c_Inj1 @ ( c_setsum @ X2 @ X3 ) ) ) ) )
% 0.22/0.53 => ( X1 @ X0 ) ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax107,axiom,
% 0.22/0.53 ( c_combinator_equiv
% 0.22/0.53 = ( ^ [X0: $i,X1: $i] :
% 0.22/0.53 ! [X2: $i > $i > $o] :
% 0.22/0.53 ( ^ [X3: $i,X4: $i,X5: $i > $i > $i] :
% 0.22/0.53 ( ( c_per_i @ X2 )
% 0.22/0.53 => ( ! [X6: $i] :
% 0.22/0.53 ( ( c_combinator @ X6 )
% 0.22/0.53 => ( X2 @ X6 @ X6 ) )
% 0.22/0.53 => ( ! [X6: $i,X7: $i,X8: $i,X9: $i] :
% 0.22/0.53 ( ( c_combinator @ X6 )
% 0.22/0.53 => ( ( c_combinator @ X7 )
% 0.22/0.53 => ( ( c_combinator @ X8 )
% 0.22/0.53 => ( ( c_combinator @ X9 )
% 0.22/0.53 => ( ( X2 @ X6 @ X8 )
% 0.22/0.53 => ( ( X2 @ X7 @ X9 )
% 0.22/0.53 => ( X2 @ ( X5 @ X6 @ X7 ) @ ( X5 @ X8 @ X9 ) ) ) ) ) ) ) )
% 0.22/0.53 => ( ! [X6: $i,X7: $i] : ( X2 @ ( X5 @ ( X5 @ X3 @ X6 ) @ X7 ) @ X6 )
% 0.22/0.53 => ( ! [X6: $i,X7: $i,X8: $i] : ( X2 @ ( X5 @ ( X5 @ ( X5 @ X4 @ X6 ) @ X7 ) @ X8 ) @ ( X5 @ ( X5 @ X6 @ X8 ) @ ( X5 @ X7 @ X8 ) ) )
% 0.22/0.53 => ( X2 @ X0 @ X1 ) ) ) ) ) )
% 0.22/0.53 @ ( c_Inj0 @ c_Empty )
% 0.22/0.53 @ ( c_Inj0 @ ( c_Power @ c_Empty ) )
% 0.22/0.53 @ ^ [X3: $i,X4: $i] : ( c_Inj1 @ ( c_setsum @ X3 @ X4 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(ax108,axiom,
% 0.22/0.53 ( c_equip_mod
% 0.22/0.53 = ( ^ [X0: $i,X1: $i,X2: $i] :
% 0.22/0.53 ? [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 ) ) ) ) ) ).
% 0.22/0.53
% 0.22/0.53 thf(conj,conjecture,
% 0.22/0.53 ! [X0: ( $i > $i ) > ( $i > $i > $i ) > ( ( ( $i > $i ) > $i ) > $i ) > $o,X1: ( ( ( ( ( $i > $i ) > $i > $i ) > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i ) > $i > $i > $i ) > ( $i > ( ( $i > $i ) > $i ) > $i ) > $i > $i > $o,X2: ( ( $i > ( ( $i > $i ) > $i ) > $i > $i ) > $i > ( $i > $i ) > ( $i > $i ) > $i > $i ) > $i > ( ( ( $i > $i ) > $i ) > $i ) > $o,X3: ( $i > ( ( $i > $i ) > $i > $i > $i ) > $i > $i > $i ) > $i > $o] :
% 0.22/0.53 ( ! [X4: $i,X5: $i,X6: $i,X7: $i] :
% 0.22/0.53 ( ( c_In @ ( c_Inj0 @ X4 ) @ ( c_Inj1 @ ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 0.22/0.53 => ( ( X0
% 0.22/0.53 @ ^ [X8: $i] : ( c_Inj0 @ ( c_setsum @ c_Empty @ ( c_Inj0 @ ( c_Inj0 @ c_Empty ) ) ) )
% 0.22/0.53 @ ^ [X8: $i,X9: $i] : ( c_Inj0 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ X8 ) ) )
% 0.22/0.53 @ ^ [X8: ( $i > $i ) > $i] : c_Empty )
% 0.22/0.53 => ( X3
% 0.22/0.53 @ ^ [X8: $i,X9: ( $i > $i ) > $i > $i > $i,X10: $i,X11: $i] : X8
% 0.22/0.53 @ c_Empty ) ) )
% 0.22/0.53 => ( ! [X4: $i,X5: $i,X6: $i > $i > $i > $i,X7: $i > ( ( $i > $i ) > $i ) > $i] :
% 0.22/0.53 ( ( X3
% 0.22/0.53 @ ^ [X8: $i,X9: ( $i > $i ) > $i > $i > $i,X10: $i,X11: $i] : c_Empty
% 0.22/0.53 @ ( c_Inj0
% 0.22/0.53 @ ( c_Inj0
% 0.22/0.53 @ ( c_setsum
% 0.22/0.53 @ ( X7 @ c_Empty
% 0.22/0.53 @ ^ [X8: $i > $i] : c_Empty )
% 0.22/0.53 @ c_Empty ) ) ) )
% 0.22/0.53 => ( X3
% 0.22/0.53 @ ^ [X8: $i,X9: ( $i > $i ) > $i > $i > $i,X10: $i,X11: $i] : ( c_setsum @ c_Empty @ ( c_setsum @ ( c_Inj1 @ X11 ) @ c_Empty ) )
% 0.22/0.53 @ X5 ) )
% 0.22/0.53 => ( ! [X4: ( ( $i > $i > $i ) > ( $i > $i ) > $i ) > $i,X5: $i,X6: $i > $i,X7: $i] :
% 0.22/0.53 ( X2
% 0.22/0.53 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i > $i,X9: $i,X10: $i > $i,X11: $i > $i,X12: $i] : ( c_Inj1 @ ( c_setsum @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ ( c_setsum @ c_Empty @ c_Empty ) ) ) )
% 0.22/0.53 @ ( c_Inj0
% 0.22/0.53 @ ( X4
% 0.22/0.53 @ ^ [X8: $i > $i > $i,X9: $i > $i] : ( X9 @ ( c_Inj1 @ c_Empty ) ) ) )
% 0.22/0.53 @ ^ [X8: ( $i > $i ) > $i] :
% 0.22/0.53 ( c_setsum
% 0.22/0.53 @ ( c_Inj1
% 0.22/0.53 @ ( c_Inj1
% 0.22/0.53 @ ( X8
% 0.22/0.53 @ ^ [X9: $i] : c_Empty ) ) )
% 0.22/0.53 @ X5 ) )
% 0.22/0.53 => ( ! [X4: $i,X5: $i > $i,X6: $i > $i,X7: $i > ( $i > $i ) > $i] :
% 0.22/0.53 ( ( X2
% 0.22/0.53 @ ^ [X8: $i > ( ( $i > $i ) > $i ) > $i > $i,X9: $i,X10: $i > $i,X11: $i > $i,X12: $i] : ( c_Inj1 @ ( c_Inj0 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ X12 ) ) )
% 0.22/0.53 @ ( c_setsum @ c_Empty @ c_Empty )
% 0.22/0.53 @ ^ [X8: ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ ( X6 @ ( X6 @ c_Empty ) ) ) ) )
% 0.22/0.53 => ( c_In
% 0.22/0.53 @ ( c_Inj1
% 0.22/0.53 @ ( X5
% 0.22/0.53 @ ( c_setsum
% 0.22/0.53 @ ( X7 @ c_Empty
% 0.22/0.53 @ ^ [X8: $i] : c_Empty )
% 0.22/0.53 @ ( c_Inj1 @ c_Empty ) ) ) )
% 0.22/0.53 @ ( c_Inj1 @ c_Empty ) ) )
% 0.22/0.53 => ( ! [X4: $i,X5: $i,X6: $i > $i,X7: $i] :
% 0.22/0.53 ( ( X0
% 0.22/0.53 @ ^ [X8: $i] : ( X6 @ X5 )
% 0.22/0.53 @ ^ [X8: $i,X9: $i] : c_Empty
% 0.22/0.53 @ ^ [X8: ( $i > $i ) > $i] : c_Empty )
% 0.22/0.53 => ( X1
% 0.22/0.53 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i,X9: $i,X10: $i] : X7
% 0.22/0.53 @ ^ [X8: $i,X9: ( $i > $i ) > $i] : c_Empty
% 0.22/0.53 @ c_Empty
% 0.22/0.53 @ ( c_Inj0 @ ( X6 @ c_Empty ) ) ) )
% 0.22/0.53 => ( ! [X4: $i,X5: $i,X6: $i,X7: $i > $i] :
% 0.22/0.53 ( ( c_In @ ( c_Inj1 @ c_Empty ) @ ( c_Inj0 @ ( c_setsum @ ( c_Inj0 @ ( c_setsum @ c_Empty @ c_Empty ) ) @ ( c_Inj1 @ ( c_setsum @ c_Empty @ c_Empty ) ) ) ) )
% 0.22/0.53 => ( ( X1
% 0.22/0.53 @ ^ [X8: ( ( ( $i > $i ) > $i > $i ) > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i,X9: $i,X10: $i] : ( c_setsum @ c_Empty @ ( c_setsum @ c_Empty @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) )
% 0.22/0.53 @ ^ [X8: $i,X9: ( $i > $i ) > $i] :
% 0.22/0.53 ( X9
% 0.22/0.53 @ ^ [X10: $i] : X8 )
% 0.22/0.53 @ ( X7 @ ( c_setsum @ ( c_Inj1 @ X5 ) @ X6 ) )
% 0.22/0.53 @ ( c_setsum @ ( c_setsum @ c_Empty @ ( c_Inj0 @ ( c_Inj1 @ c_Empty ) ) ) @ c_Empty ) )
% 0.22/0.53 => ( X0
% 0.22/0.53 @ ^ [X8: $i] : c_Empty
% 0.22/0.53 @ ^ [X8: $i,X9: $i] : ( c_Inj1 @ ( c_Inj0 @ ( c_setsum @ c_Empty @ ( X7 @ c_Empty ) ) ) )
% 0.22/0.53 @ ^ [X8: ( $i > $i ) > $i] :
% 0.22/0.53 ( c_Inj0
% 0.22/0.53 @ ( c_setsum
% 0.22/0.53 @ ( c_setsum @ c_Empty
% 0.22/0.53 @ ( X8
% 0.22/0.53 @ ^ [X9: $i] : c_Empty ) )
% 0.22/0.53 @ ( X7 @ ( c_Inj0 @ c_Empty ) ) ) ) ) ) )
% 0.22/0.53 => ( ! [X4: $i > ( ( $i > $i ) > $i > $i ) > $i > $i > $i,X5: $i,X6: ( $i > $i > $i > $i ) > $i,X7: ( $i > $i ) > ( $i > $i ) > $i] :
% 0.22/0.53 ( ( c_In
% 0.22/0.53 @ ( c_setsum @ c_Empty
% 0.22/0.53 @ ( X7
% 0.22/0.53 @ ^ [X8: $i] :
% 0.22/0.53 ( c_Inj0
% 0.22/0.53 @ ( X6
% 0.22/0.53 @ ^ [X9: $i,X10: $i,X11: $i] : c_Empty ) )
% 0.22/0.58 @ ^ [X8: $i] :
% 0.22/0.58 ( c_Inj0
% 0.22/0.58 @ ( X7
% 0.22/0.58 @ ^ [X9: $i] : c_Empty
% 0.22/0.58 @ ^ [X9: $i] : c_Empty ) ) ) )
% 0.22/0.58 @ ( c_setsum
% 0.22/0.58 @ ( c_setsum @ c_Empty
% 0.22/0.58 @ ( c_Inj0
% 0.22/0.58 @ ( X4 @ c_Empty
% 0.22/0.58 @ ^ [X8: $i > $i,X9: $i] : c_Empty
% 0.22/0.58 @ c_Empty
% 0.22/0.58 @ c_Empty ) ) )
% 0.22/0.58 @ c_Empty ) )
% 0.22/0.58 => ( ( X3
% 0.22/0.58 @ ^ [X8: $i,X9: ( $i > $i ) > $i > $i > $i,X10: $i,X11: $i] :
% 0.22/0.58 ( X9
% 0.22/0.58 @ ^ [X12: $i] : ( c_setsum @ X10 @ ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) ) )
% 0.22/0.58 @ c_Empty
% 0.22/0.58 @ X10 )
% 0.22/0.58 @ ( c_setsum @ ( c_Inj0 @ c_Empty ) @ c_Empty ) )
% 0.22/0.58 => ( X0
% 0.22/0.58 @ ^ [X8: $i] : ( c_Inj1 @ ( c_Inj1 @ ( c_Inj1 @ X8 ) ) )
% 0.22/0.58 @ ^ [X8: $i,X9: $i] : c_Empty
% 0.22/0.58 @ ^ [X8: ( $i > $i ) > $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ ( c_setsum @ ( c_setsum @ c_Empty @ c_Empty ) @ c_Empty ) ) ) ) ) )
% 0.22/0.58 => ( ! [X4: $i,X5: ( $i > ( $i > $i ) > $i ) > $i,X6: $i,X7: $i > $i > $i] :
% 0.22/0.58 ( ( X0
% 0.22/0.58 @ ^ [X8: $i] : ( c_setsum @ c_Empty @ ( c_Inj1 @ c_Empty ) )
% 0.22/0.58 @ ^ [X8: $i,X9: $i] : ( X7 @ ( c_Inj0 @ X9 ) @ ( c_Inj0 @ X8 ) )
% 0.22/0.58 @ ^ [X8: ( $i > $i ) > $i] : X6 )
% 0.22/0.58 => ( c_In
% 0.22/0.58 @ ( c_setsum
% 0.22/0.58 @ ( c_setsum
% 0.22/0.58 @ ( c_setsum @ ( X7 @ c_Empty @ c_Empty )
% 0.22/0.58 @ ( X5
% 0.22/0.58 @ ^ [X8: $i,X9: $i > $i] : c_Empty ) )
% 0.22/0.58 @ c_Empty )
% 0.22/0.58 @ ( c_setsum
% 0.22/0.58 @ ( X5
% 0.22/0.58 @ ^ [X8: $i,X9: $i > $i] : ( X7 @ c_Empty @ c_Empty ) )
% 0.22/0.58 @ ( X5
% 0.22/0.58 @ ^ [X8: $i,X9: $i > $i] : ( X9 @ c_Empty ) ) ) )
% 0.22/0.58 @ ( c_Inj0 @ c_Empty ) ) )
% 0.22/0.58 => c_False ) ) ) ) ) ) ) ) ).
% 0.22/0.58
% 0.22/0.58 %------------------------------------------------------------------------------
% 0.22/0.58 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.px16MMHSKA/cvc5---1.0.5_26673.p...
% 0.22/0.58 (declare-sort $$unsorted 0)
% 0.22/0.58 (declare-fun tptp.c_Eps_i ((-> $$unsorted Bool)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_False () Bool)
% 0.22/0.58 (declare-fun tptp.c_True () Bool)
% 0.22/0.58 (declare-fun tptp.c_not (Bool) Bool)
% 0.22/0.58 (declare-fun tptp.c_and (Bool Bool) Bool)
% 0.22/0.58 (declare-fun tptp.c_or (Bool Bool) Bool)
% 0.22/0.58 (declare-fun tptp.c_iff (Bool Bool) Bool)
% 0.22/0.58 (declare-fun tptp.c_In ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_Subq ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_Empty () $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Union ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Power ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Repl ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_TransSet ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_atleast2 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_atleast3 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_atleast4 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_atleast5 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_atleast6 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_exactly2 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_exactly3 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_exactly4 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_exactly5 ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_exu_i ((-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_reflexive_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_irreflexive_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_symmetric_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_antisymmetric_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_transitive_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_eqreln_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_per_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_linear_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_trichotomous_or_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_partialorder_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_totalorder_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_strictpartialorder_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_stricttotalorder_i ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_If_i (Bool $$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_exactly1of2 (Bool Bool) Bool)
% 0.22/0.58 (declare-fun tptp.c_exactly1of3 (Bool Bool Bool) Bool)
% 0.22/0.58 (declare-fun tptp.c_nIn ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_nSubq ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_UPair ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Sing ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_binunion ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_SetAdjoin ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_famunion ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Sep ($$unsorted (-> $$unsorted Bool)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_ReplSep ($$unsorted (-> $$unsorted Bool) (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_binintersect ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_setminus ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_inj ($$unsorted $$unsorted (-> $$unsorted $$unsorted)) Bool)
% 0.22/0.58 (declare-fun tptp.c_bij ($$unsorted $$unsorted (-> $$unsorted $$unsorted)) Bool)
% 0.22/0.58 (declare-fun tptp.c_atleastp ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_equip ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_In_rec_poly_G_i ((-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_In_rec_poly_i ((-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted) $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_ordsucc ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_nat_p ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_nat_primrec ($$unsorted (-> $$unsorted $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_add_nat ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_mul_nat ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_ordinal ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_V_ ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Inj1 ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Inj0 ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Unj ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_combine_funcs ($$unsorted $$unsorted (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_setsum ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_proj0 ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_proj1 ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_binrep ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_lam ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_setprod ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_ap ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_setsum_p ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_tuple_p ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_Pi ($$unsorted (-> $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_setexp ($$unsorted $$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_Sep2 ($$unsorted (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted Bool)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_set_of_pairs ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_lam2 ($$unsorted (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_PNoEq_ ($$unsorted (-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_PNoLt_ ($$unsorted (-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_PNoLt ($$unsorted (-> $$unsorted Bool) $$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_PNoLe ($$unsorted (-> $$unsorted Bool) $$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_PNo_downc ((-> $$unsorted (-> $$unsorted Bool) Bool) $$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_PNo_upc ((-> $$unsorted (-> $$unsorted Bool) Bool) $$unsorted (-> $$unsorted Bool)) Bool)
% 0.22/0.58 (declare-fun tptp.c_SNoElts_ ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_SNo_ ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_PSNo ($$unsorted (-> $$unsorted Bool)) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_SNo ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_SNoLev ($$unsorted) $$unsorted)
% 0.22/0.58 (declare-fun tptp.c_SNoEq_ ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_SNoLt ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_SNoLe ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_binop_on ($$unsorted (-> $$unsorted $$unsorted $$unsorted)) Bool)
% 0.22/0.58 (declare-fun tptp.c_Loop ($$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_Loop_with_defs ($$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) $$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted)) Bool)
% 0.22/0.58 (declare-fun tptp.c_Loop_with_defs_cex1 ($$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) $$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted)) Bool)
% 0.22/0.58 (declare-fun tptp.c_Loop_with_defs_cex2 ($$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) $$unsorted (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted)) Bool)
% 0.22/0.58 (declare-fun tptp.c_combinator ($$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_combinator_equiv ($$unsorted $$unsorted) Bool)
% 0.22/0.58 (declare-fun tptp.c_equip_mod ($$unsorted $$unsorted $$unsorted) Bool)
% 0.22/0.58 (assert (forall ((X0 (-> $$unsorted Bool)) (X1 $$unsorted)) (=> (@ X0 X1) (@ X0 (@ tptp.c_Eps_i X0)))))
% 0.22/0.58 (assert (forall ((X0 Bool)) (=> (@ tptp.c_not (@ tptp.c_not X0)) X0)))
% 0.22/0.58 (assert (forall ((X0 Bool) (X1 Bool)) (=> (@ (@ tptp.c_iff X0) X1) (= X0 X1))))
% 0.22/0.58 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (=> (@ (@ tptp.c_Subq X0) X1) (=> (@ (@ tptp.c_Subq X1) X0) (= X0 X1)))))
% 0.22/0.58 (assert (@ tptp.c_not (exists ((X0 $$unsorted)) (@ (@ tptp.c_In X0) tptp.c_Empty))))
% 0.22/0.58 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_iff (@ (@ tptp.c_In X1) (@ tptp.c_Union X0))) (exists ((X2 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X1) X2)) (@ (@ tptp.c_In X2) X0))))))
% 0.22/0.58 (assert (forall ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_iff (@ (@ tptp.c_In X1) (@ tptp.c_Power X0))) (@ (@ tptp.c_Subq X1) X0))))
% 0.22/0.58 (assert (forall ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 $$unsorted)) (@ (@ tptp.c_iff (@ (@ tptp.c_In X2) (@ (@ tptp.c_Repl X0) (lambda ((X3 $$unsorted)) (@ X1 X3))))) (exists ((X3 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X3) X0)) (= X2 (@ X1 X3)))))))
% 0.22/0.58 (assert (forall ((X0 (-> $$unsorted Bool))) (=> (forall ((X1 $$unsorted)) (=> (@ X0 X1) (forall ((X2 $$unsorted)) (=> (@ (@ tptp.c_In X2) X1) (@ X0 X2))))) (=> (@ X0 tptp.c_Empty) (=> (forall ((X1 $$unsorted)) (=> (@ X0 X1) (@ X0 (@ tptp.c_Union X1)))) (=> (forall ((X1 $$unsorted)) (=> (@ X0 X1) (@ X0 (@ tptp.c_Power X1)))) (=> (forall ((X1 $$unsorted)) (=> (@ X0 X1) (forall ((X2 (-> $$unsorted $$unsorted))) (=> (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X1) (@ X0 (@ X2 X3)))) (@ X0 (@ (@ tptp.c_Repl X1) (lambda ((X3 $$unsorted)) (@ X2 X3)))))))) (forall ((X1 $$unsorted)) (@ X0 X1)))))))))
% 0.22/0.58 (assert (forall ((X0 (-> $$unsorted Bool))) (=> (forall ((X1 $$unsorted)) (=> (forall ((X2 $$unsorted)) (=> (@ (@ tptp.c_In X2) X1) (@ X0 X2))) (@ X0 X1))) (forall ((X1 $$unsorted)) (@ X0 X1)))))
% 0.22/0.58 (assert (= tptp.c_False (forall ((X0 Bool)) X0)))
% 0.22/0.58 (assert (= tptp.c_True (forall ((X0 Bool)) (=> X0 X0))))
% 0.22/0.58 (assert (= tptp.c_not (lambda ((X0 Bool)) (=> X0 tptp.c_False))))
% 0.22/0.58 (assert (= tptp.c_and (lambda ((X0 Bool) (X1 Bool)) (forall ((X2 Bool)) (=> (=> X0 (=> X1 X2)) X2)))))
% 0.22/0.58 (assert (= tptp.c_or (lambda ((X0 Bool) (X1 Bool)) (forall ((X2 Bool)) (=> (=> X0 X2) (=> (=> X1 X2) X2))))))
% 0.22/0.58 (assert (= tptp.c_iff (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.c_and (=> X0 X1)) (=> X1 X0)))))
% 0.22/0.58 (assert (= tptp.c_Subq (lambda ((X0 $$unsorted) (X1 $$unsorted)) (forall ((X2 $$unsorted)) (let ((_let_1 (@ tptp.c_In X2))) (=> (@ _let_1 X0) (@ _let_1 X1)))))))
% 0.22/0.58 (assert (= tptp.c_TransSet (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.c_In X1) X0) (@ (@ tptp.c_Subq X1) X0))))))
% 0.22/0.58 (assert (= tptp.c_atleast2 (lambda ((X0 $$unsorted)) (exists ((X1 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X1) X0)) (@ tptp.c_not (@ (@ tptp.c_Subq X0) (@ tptp.c_Power X1))))))))
% 0.22/0.58 (assert (= tptp.c_atleast3 (lambda ((X0 $$unsorted)) (exists ((X1 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_Subq X1) X0)) (@ (@ tptp.c_and (@ tptp.c_not (@ (@ tptp.c_Subq X0) X1))) (@ tptp.c_atleast2 X1)))))))
% 0.22/0.58 (assert (= tptp.c_atleast4 (lambda ((X0 $$unsorted)) (exists ((X1 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_Subq X1) X0)) (@ (@ tptp.c_and (@ tptp.c_not (@ (@ tptp.c_Subq X0) X1))) (@ tptp.c_atleast3 X1)))))))
% 0.22/0.58 (assert (= tptp.c_atleast5 (lambda ((X0 $$unsorted)) (exists ((X1 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_Subq X1) X0)) (@ (@ tptp.c_and (@ tptp.c_not (@ (@ tptp.c_Subq X0) X1))) (@ tptp.c_atleast4 X1)))))))
% 0.22/0.58 (assert (= tptp.c_atleast6 (lambda ((X0 $$unsorted)) (exists ((X1 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_Subq X1) X0)) (@ (@ tptp.c_and (@ tptp.c_not (@ (@ tptp.c_Subq X0) X1))) (@ tptp.c_atleast5 X1)))))))
% 0.22/0.58 (assert (= tptp.c_exactly2 (lambda ((X0 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_atleast2 X0)) (@ tptp.c_not (@ tptp.c_atleast3 X0))))))
% 0.22/0.58 (assert (= tptp.c_exactly3 (lambda ((X0 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_atleast3 X0)) (@ tptp.c_not (@ tptp.c_atleast4 X0))))))
% 0.22/0.58 (assert (= tptp.c_exactly4 (lambda ((X0 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_atleast4 X0)) (@ tptp.c_not (@ tptp.c_atleast5 X0))))))
% 0.22/0.58 (assert (= tptp.c_exactly5 (lambda ((X0 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_atleast5 X0)) (@ tptp.c_not (@ tptp.c_atleast6 X0))))))
% 0.22/0.58 (assert (= tptp.c_exu_i (lambda ((X0 (-> $$unsorted Bool))) (@ (@ tptp.c_and (exists ((X1 $$unsorted)) (@ X0 X1))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (@ X0 X1) (=> (@ X0 X2) (= X1 X2))))))))
% 0.22/0.58 (assert (= tptp.c_reflexive_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted)) (@ (@ X0 X1) X1)))))
% 0.22/0.58 (assert (= tptp.c_irreflexive_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted)) (@ tptp.c_not (@ (@ X0 X1) X1))))))
% 0.22/0.58 (assert (= tptp.c_symmetric_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (@ (@ X0 X1) X2) (@ (@ X0 X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_antisymmetric_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (=> (@ (@ X0 X1) X2) (=> (@ (@ X0 X2) X1) (= X1 X2)))))))
% 0.22/0.58 (assert (= tptp.c_transitive_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted) (X2 $$unsorted) (X3 $$unsorted)) (let ((_let_1 (@ X0 X1))) (=> (@ _let_1 X2) (=> (@ (@ X0 X2) X3) (@ _let_1 X3))))))))
% 0.22/0.58 (assert (= tptp.c_eqreln_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ tptp.c_reflexive_i X0)) (@ tptp.c_symmetric_i X0))) (@ tptp.c_transitive_i X0)))))
% 0.22/0.58 (assert (= tptp.c_per_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_and (@ tptp.c_symmetric_i X0)) (@ tptp.c_transitive_i X0)))))
% 0.22/0.58 (assert (= tptp.c_linear_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.c_or (@ (@ X0 X1) X2)) (@ (@ X0 X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_trichotomous_or_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (forall ((X1 $$unsorted) (X2 $$unsorted)) (@ (@ tptp.c_or (@ (@ tptp.c_or (@ (@ X0 X1) X2)) (= X1 X2))) (@ (@ X0 X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_partialorder_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ tptp.c_reflexive_i X0)) (@ tptp.c_antisymmetric_i X0))) (@ tptp.c_transitive_i X0)))))
% 0.22/0.58 (assert (= tptp.c_totalorder_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_and (@ tptp.c_partialorder_i X0)) (@ tptp.c_linear_i X0)))))
% 0.22/0.58 (assert (= tptp.c_strictpartialorder_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_and (@ tptp.c_irreflexive_i X0)) (@ tptp.c_transitive_i X0)))))
% 0.22/0.58 (assert (= tptp.c_stricttotalorder_i (lambda ((X0 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_and (@ tptp.c_strictpartialorder_i X0)) (@ tptp.c_trichotomous_or_i X0)))))
% 0.22/0.58 (assert (= tptp.c_If_i (lambda ((X0 Bool) (X1 $$unsorted) (X2 $$unsorted)) (@ tptp.c_Eps_i (lambda ((X3 $$unsorted)) (@ (@ tptp.c_or (@ (@ tptp.c_and X0) (= X3 X1))) (@ (@ tptp.c_and (@ tptp.c_not X0)) (= X3 X2))))))))
% 0.22/0.58 (assert (= tptp.c_exactly1of2 (lambda ((X0 Bool) (X1 Bool)) (@ (@ tptp.c_or (@ (@ tptp.c_and X0) (@ tptp.c_not X1))) (@ (@ tptp.c_and (@ tptp.c_not X0)) X1)))))
% 0.22/0.58 (assert (= tptp.c_exactly1of3 (lambda ((X0 Bool) (X1 Bool) (X2 Bool)) (@ (@ tptp.c_or (@ (@ tptp.c_and (@ (@ tptp.c_exactly1of2 X0) X1)) (@ tptp.c_not X2))) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ tptp.c_not X0)) (@ tptp.c_not X1))) X2)))))
% 0.22/0.58 (assert (= tptp.c_nIn (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.c_not (@ (@ tptp.c_In X0) X1)))))
% 0.22/0.58 (assert (= tptp.c_nSubq (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.c_not (@ (@ tptp.c_Subq X0) X1)))))
% 0.22/0.58 (assert (= tptp.c_UPair (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_Repl (@ tptp.c_Power (@ tptp.c_Power tptp.c_Empty))) (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.c_If_i (@ (@ tptp.c_In tptp.c_Empty) X2)) X0) X1))))))
% 0.22/0.58 (assert (= tptp.c_Sing (lambda ((X0 $$unsorted)) (@ (@ tptp.c_UPair X0) X0))))
% 0.22/0.58 (assert (= tptp.c_binunion (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ tptp.c_Union (@ (@ tptp.c_UPair X0) X1)))))
% 0.22/0.58 (assert (= tptp.c_SetAdjoin (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_binunion X0) (@ tptp.c_Sing X1)))))
% 0.22/0.58 (assert (= tptp.c_famunion (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ tptp.c_Union (@ (@ tptp.c_Repl X0) (lambda ((X2 $$unsorted)) (@ X1 X2)))))))
% 0.22/0.58 (assert (= tptp.c_Sep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ (@ tptp.c_If_i (exists ((X2 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X2) X0)) (@ X1 X2)))) (@ (@ tptp.c_Repl X0) (lambda ((X2 $$unsorted)) (@ (lambda ((X3 $$unsorted)) (@ (@ (@ tptp.c_If_i (@ X1 X3)) X3) (@ tptp.c_Eps_i (lambda ((X4 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X4) X0)) (@ X1 X4)))))) X2)))) tptp.c_Empty))))
% 0.22/0.58 (assert (= tptp.c_ReplSep (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_Repl (@ (@ tptp.c_Sep X0) (lambda ((X3 $$unsorted)) (@ X1 X3)))) (lambda ((X3 $$unsorted)) (@ X2 X3))))))
% 0.22/0.58 (assert (= tptp.c_binintersect (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_Sep X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_In X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_setminus (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_Sep X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_nIn X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_inj (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_and (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X0) (@ (@ tptp.c_In (@ X2 X3)) X1)))) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X0) (forall ((X4 $$unsorted)) (=> (@ (@ tptp.c_In X4) X0) (=> (= (@ X2 X3) (@ X2 X4)) (= X3 X4))))))))))
% 0.22/0.58 (assert (= tptp.c_bij (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_and (@ (@ (@ tptp.c_inj X0) X1) X2)) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X1) (exists ((X4 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X4) X0)) (= (@ X2 X4) X3)))))))))
% 0.22/0.58 (assert (= tptp.c_atleastp (lambda ((X0 $$unsorted) (X1 $$unsorted)) (exists ((X2 (-> $$unsorted $$unsorted))) (@ (@ (@ tptp.c_inj X0) X1) X2)))))
% 0.22/0.58 (assert (= tptp.c_equip (lambda ((X0 $$unsorted) (X1 $$unsorted)) (exists ((X2 (-> $$unsorted $$unsorted))) (@ (@ (@ tptp.c_bij X0) X1) X2)))))
% 0.22/0.58 (assert (= tptp.c_In_rec_poly_G_i (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted) (X2 $$unsorted)) (forall ((X3 (-> $$unsorted $$unsorted Bool))) (=> (forall ((X4 $$unsorted) (X5 (-> $$unsorted $$unsorted))) (=> (forall ((X6 $$unsorted)) (=> (@ (@ tptp.c_In X6) X4) (@ (@ X3 X6) (@ X5 X6)))) (@ (@ X3 X4) (@ (@ X0 X4) X5)))) (@ (@ X3 X1) X2))))))
% 0.22/0.58 (assert (= tptp.c_In_rec_poly_i (lambda ((X0 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) (X1 $$unsorted)) (@ tptp.c_Eps_i (lambda ((X2 $$unsorted)) (@ (@ (@ tptp.c_In_rec_poly_G_i X0) X1) X2))))))
% 0.22/0.58 (assert (= tptp.c_ordsucc (lambda ((X0 $$unsorted)) (@ (@ tptp.c_binunion X0) (@ tptp.c_Sing X0)))))
% 0.22/0.58 (assert (= tptp.c_nat_p (lambda ((X0 $$unsorted)) (forall ((X1 (-> $$unsorted Bool))) (=> (@ X1 tptp.c_Empty) (=> (forall ((X2 $$unsorted)) (=> (@ X1 X2) (@ X1 (@ tptp.c_ordsucc X2)))) (@ X1 X0)))))))
% 0.22/0.58 (assert (= tptp.c_nat_primrec (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted $$unsorted)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.c_In_rec_poly_i (lambda ((X2 $$unsorted) (X3 (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.c_Union X2))) (@ (@ (@ tptp.c_If_i (@ (@ tptp.c_In _let_1) X2)) (@ (@ X1 _let_1) (@ X3 _let_1))) X0)))) __flatten_var_0))))
% 0.22/0.58 (assert (= tptp.c_add_nat (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.c_nat_primrec X0) (lambda ((X2 $$unsorted) (X3 $$unsorted)) (@ tptp.c_ordsucc X3))) X1))))
% 0.22/0.58 (assert (= tptp.c_mul_nat (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.c_nat_primrec tptp.c_Empty) (lambda ((X2 $$unsorted) (X3 $$unsorted)) (@ (@ tptp.c_add_nat X0) X3))) X1))))
% 0.22/0.58 (assert (= tptp.c_ordinal (lambda ((X0 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_TransSet X0)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.c_In X1) X0) (@ tptp.c_TransSet X1)))))))
% 0.22/0.58 (assert (= tptp.c_V_ (@ tptp.c_In_rec_poly_i (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_famunion X0) (lambda ((X2 $$unsorted)) (@ tptp.c_Power (@ X1 X2))))))))
% 0.22/0.58 (assert (= tptp.c_Inj1 (@ tptp.c_In_rec_poly_i (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_binunion (@ tptp.c_Sing tptp.c_Empty)) (@ (@ tptp.c_Repl X0) (lambda ((X2 $$unsorted)) (@ X1 X2))))))))
% 0.22/0.58 (assert (= tptp.c_Inj0 (lambda ((X0 $$unsorted)) (@ (@ tptp.c_Repl X0) (lambda ((X1 $$unsorted)) (@ tptp.c_Inj1 X1))))))
% 0.22/0.58 (assert (= tptp.c_Unj (@ tptp.c_In_rec_poly_i (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_Repl (@ (@ tptp.c_setminus X0) (@ tptp.c_Sing tptp.c_Empty))) (lambda ((X2 $$unsorted)) (@ X1 X2)))))))
% 0.22/0.58 (assert (= tptp.c_combine_funcs (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 (-> $$unsorted $$unsorted)) (X3 (-> $$unsorted $$unsorted)) (X4 $$unsorted)) (let ((_let_1 (@ tptp.c_Unj X4))) (@ (@ (@ tptp.c_If_i (= X4 (@ tptp.c_Inj0 _let_1))) (@ X2 _let_1)) (@ X3 _let_1))))))
% 0.22/0.58 (assert (= tptp.c_setsum (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_binunion (@ (@ tptp.c_Repl X0) (lambda ((X2 $$unsorted)) (@ tptp.c_Inj0 X2)))) (@ (@ tptp.c_Repl X1) (lambda ((X2 $$unsorted)) (@ tptp.c_Inj1 X2)))))))
% 0.22/0.58 (assert (= tptp.c_proj0 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.c_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.c_Inj0 X2) X1)))) (lambda ((X1 $$unsorted)) (@ tptp.c_Unj X1))))))
% 0.22/0.58 (assert (= tptp.c_proj1 (lambda ((X0 $$unsorted)) (@ (@ (@ tptp.c_ReplSep X0) (lambda ((X1 $$unsorted)) (exists ((X2 $$unsorted)) (= (@ tptp.c_Inj1 X2) X1)))) (lambda ((X1 $$unsorted)) (@ tptp.c_Unj X1))))))
% 0.22/0.58 (assert (= tptp.c_binrep (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_setsum X0) (@ tptp.c_Power X1)))))
% 0.22/0.58 (assert (= tptp.c_lam (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_famunion X0) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_Repl (@ X1 X2)) (lambda ((X3 $$unsorted)) (@ (@ tptp.c_setsum X2) X3))))))))
% 0.22/0.58 (assert (= tptp.c_setprod (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_lam X0) (lambda ((X2 $$unsorted)) X1)))))
% 0.22/0.58 (assert (= tptp.c_ap (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ tptp.c_ReplSep X0) (lambda ((X2 $$unsorted)) (exists ((X3 $$unsorted)) (= X2 (@ (@ tptp.c_setsum X1) X3))))) (lambda ((X2 $$unsorted)) (@ tptp.c_proj1 X2))))))
% 0.22/0.58 (assert (= tptp.c_setsum_p (lambda ((X0 $$unsorted)) (let ((_let_1 (@ tptp.c_ap X0))) (= (@ (@ tptp.c_setsum (@ _let_1 tptp.c_Empty)) (@ _let_1 (@ tptp.c_ordsucc tptp.c_Empty))) X0)))))
% 0.22/0.58 (assert (= tptp.c_tuple_p (lambda ((X0 $$unsorted) (X1 $$unsorted)) (forall ((X2 $$unsorted)) (=> (@ (@ tptp.c_In X2) X1) (exists ((X3 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X3) X0)) (exists ((X4 $$unsorted)) (= X2 (@ (@ tptp.c_setsum X3) X4))))))))))
% 0.22/0.58 (assert (= tptp.c_Pi (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted))) (@ (@ tptp.c_Sep (@ tptp.c_Power (@ (@ tptp.c_lam X0) (lambda ((X2 $$unsorted)) (@ tptp.c_Union (@ X1 X2)))))) (lambda ((X2 $$unsorted)) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X0) (@ (@ tptp.c_In (@ (@ tptp.c_ap X2) X3)) (@ X1 X3)))))))))
% 0.22/0.58 (assert (= tptp.c_setexp (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_Pi X1) (lambda ((X2 $$unsorted)) X0)))))
% 0.22/0.58 (assert (= tptp.c_Sep2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.c_Sep (@ (@ tptp.c_lam X0) (lambda ((X3 $$unsorted)) (@ X1 X3)))) (lambda ((X3 $$unsorted)) (let ((_let_1 (@ tptp.c_ap X3))) (@ (@ X2 (@ _let_1 tptp.c_Empty)) (@ _let_1 (@ tptp.c_ordsucc tptp.c_Empty)))))))))
% 0.22/0.58 (assert (= tptp.c_set_of_pairs (lambda ((X0 $$unsorted)) (forall ((X1 $$unsorted)) (=> (@ (@ tptp.c_In X1) X0) (exists ((X2 $$unsorted) (X3 $$unsorted)) (= X1 (@ (@ tptp.c_lam (@ tptp.c_ordsucc (@ tptp.c_ordsucc tptp.c_Empty))) (lambda ((X4 $$unsorted)) (@ (@ (@ tptp.c_If_i (= X4 tptp.c_Empty)) X2) X3))))))))))
% 0.22/0.58 (assert (= tptp.c_lam2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted $$unsorted))) (@ (@ tptp.c_lam X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.c_lam (@ X1 X3)) (lambda ((X4 $$unsorted)) (@ (@ X2 X3) X4))))))))
% 0.22/0.58 (assert (= tptp.c_PNoEq_ (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 (-> $$unsorted Bool))) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X0) (@ (@ tptp.c_iff (@ X1 X3)) (@ X2 X3)))))))
% 0.22/0.58 (assert (= tptp.c_PNoLt_ (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 (-> $$unsorted Bool))) (exists ((X3 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X3) X0)) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ (@ tptp.c_PNoEq_ X3) X1) X2)) (@ tptp.c_not (@ X1 X3)))) (@ X2 X3)))))))
% 0.22/0.58 (assert (= tptp.c_PNoLt (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted) (X3 (-> $$unsorted Bool))) (@ (@ tptp.c_or (@ (@ tptp.c_or (@ (@ (@ tptp.c_PNoLt_ (@ (@ tptp.c_binintersect X0) X2)) X1) X3)) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_In X0) X2)) (@ (@ (@ tptp.c_PNoEq_ X0) X1) X3))) (@ X3 X0)))) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_In X2) X0)) (@ (@ (@ tptp.c_PNoEq_ X2) X1) X3))) (@ tptp.c_not (@ X1 X2)))))))
% 0.22/0.58 (assert (= tptp.c_PNoLe (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool)) (X2 $$unsorted) (X3 (-> $$unsorted Bool))) (@ (@ tptp.c_or (@ (@ (@ (@ tptp.c_PNoLt X0) X1) X2) X3)) (@ (@ tptp.c_and (= X0 X2)) (@ (@ (@ tptp.c_PNoEq_ X0) X1) X3))))))
% 0.22/0.58 (assert (= tptp.c_PNo_downc (lambda ((X0 (-> $$unsorted (-> $$unsorted Bool) Bool)) (X1 $$unsorted) (X2 (-> $$unsorted Bool))) (exists ((X3 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_ordinal X3)) (exists ((X4 (-> $$unsorted Bool))) (@ (@ tptp.c_and (@ (@ X0 X3) X4)) (@ (@ (@ (@ tptp.c_PNoLe X1) X2) X3) X4))))))))
% 0.22/0.58 (assert (= tptp.c_PNo_upc (lambda ((X0 (-> $$unsorted (-> $$unsorted Bool) Bool)) (X1 $$unsorted) (X2 (-> $$unsorted Bool))) (exists ((X3 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_ordinal X3)) (exists ((X4 (-> $$unsorted Bool))) (@ (@ tptp.c_and (@ (@ X0 X3) X4)) (@ (@ (@ (@ tptp.c_PNoLe X3) X4) X1) X2))))))))
% 0.22/0.58 (assert (= tptp.c_SNoElts_ (lambda ((X0 $$unsorted)) (@ (@ tptp.c_binunion X0) (@ (@ tptp.c_Repl X0) (lambda ((X1 $$unsorted)) (@ (lambda ((X2 $$unsorted)) (@ (@ tptp.c_SetAdjoin X2) (@ tptp.c_Sing (@ tptp.c_ordsucc tptp.c_Empty)))) X1)))))))
% 0.22/0.58 (assert (= tptp.c_SNo_ (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_Subq X1) (@ tptp.c_SNoElts_ X0))) (forall ((X2 $$unsorted)) (let ((_let_1 (@ tptp.c_In X2))) (=> (@ _let_1 X0) (@ (@ tptp.c_exactly1of2 (@ (@ tptp.c_In (@ (lambda ((X3 $$unsorted)) (@ (@ tptp.c_SetAdjoin X3) (@ tptp.c_Sing (@ tptp.c_ordsucc tptp.c_Empty)))) X2)) X1)) (@ _let_1 X1)))))))))
% 0.22/0.58 (assert (= tptp.c_PSNo (lambda ((X0 $$unsorted) (X1 (-> $$unsorted Bool))) (@ (@ tptp.c_binunion (@ (@ tptp.c_Sep X0) (lambda ((X2 $$unsorted)) (@ X1 X2)))) (@ (@ (@ tptp.c_ReplSep X0) (lambda ((X2 $$unsorted)) (@ tptp.c_not (@ X1 X2)))) (lambda ((X2 $$unsorted)) (@ (lambda ((X3 $$unsorted)) (@ (@ tptp.c_SetAdjoin X3) (@ tptp.c_Sing (@ tptp.c_ordsucc tptp.c_Empty)))) X2)))))))
% 0.22/0.58 (assert (= tptp.c_SNo (lambda ((X0 $$unsorted)) (exists ((X1 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_ordinal X1)) (@ (@ tptp.c_SNo_ X1) X0))))))
% 0.22/0.58 (assert (= tptp.c_SNoLev (lambda ((X0 $$unsorted)) (@ tptp.c_Eps_i (lambda ((X1 $$unsorted)) (@ (@ tptp.c_and (@ tptp.c_ordinal X1)) (@ (@ tptp.c_SNo_ X1) X0)))))))
% 0.22/0.58 (assert (= tptp.c_SNoEq_ (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (@ (@ (@ tptp.c_PNoEq_ X0) (lambda ((X3 $$unsorted)) (@ (@ tptp.c_In X3) X1))) (lambda ((X3 $$unsorted)) (@ (@ tptp.c_In X3) X2))))))
% 0.22/0.58 (assert (= tptp.c_SNoLt (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ (@ tptp.c_PNoLt (@ tptp.c_SNoLev X0)) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_In X2) X0))) (@ tptp.c_SNoLev X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_In X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_SNoLe (lambda ((X0 $$unsorted) (X1 $$unsorted)) (@ (@ (@ (@ tptp.c_PNoLe (@ tptp.c_SNoLev X0)) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_In X2) X0))) (@ tptp.c_SNoLev X1)) (lambda ((X2 $$unsorted)) (@ (@ tptp.c_In X2) X1))))))
% 0.22/0.58 (assert (= tptp.c_binop_on (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted $$unsorted))) (forall ((X2 $$unsorted)) (=> (@ (@ tptp.c_In X2) X0) (forall ((X3 $$unsorted)) (=> (@ (@ tptp.c_In X3) X0) (@ (@ tptp.c_In (@ (@ X1 X2) X3)) X0))))))))
% 0.22/0.58 (assert (= tptp.c_Loop (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted $$unsorted)) (X3 (-> $$unsorted $$unsorted $$unsorted)) (X4 $$unsorted)) (let ((_let_1 (@ tptp.c_binop_on X0))) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (@ _let_1 X1)) (@ _let_1 X2))) (@ _let_1 X3))) (forall ((X5 $$unsorted)) (=> (@ (@ tptp.c_In X5) X0) (@ (@ tptp.c_and (= (@ (@ X1 X4) X5) X5)) (= (@ (@ X1 X5) X4) X5)))))) (forall ((X5 $$unsorted)) (=> (@ (@ tptp.c_In X5) X0) (forall ((X6 $$unsorted)) (let ((_let_1 (@ X1 X5))) (let ((_let_2 (@ _let_1 X6))) (let ((_let_3 (@ X2 X5))) (=> (@ (@ tptp.c_In X6) X0) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (= (@ _let_3 _let_2) X6)) (= (@ _let_1 (@ _let_3 X6)) X6))) (= (@ (@ X3 _let_2) X6) X5))) (= (@ (@ X1 (@ (@ X3 X5) X6)) X6) X5))))))))))))))
% 0.22/0.58 (assert (= tptp.c_Loop_with_defs (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted $$unsorted)) (X3 (-> $$unsorted $$unsorted $$unsorted)) (X4 $$unsorted) (X5 (-> $$unsorted $$unsorted $$unsorted)) (X6 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X7 (-> $$unsorted $$unsorted $$unsorted)) (X8 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X9 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X10 (-> $$unsorted $$unsorted $$unsorted)) (X11 (-> $$unsorted $$unsorted $$unsorted)) (X12 (-> $$unsorted $$unsorted $$unsorted)) (X13 (-> $$unsorted $$unsorted $$unsorted))) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ (@ (@ (@ tptp.c_Loop X0) X1) X2) X3) X4)) (forall ((X14 $$unsorted)) (=> (@ (@ tptp.c_In X14) X0) (forall ((X15 $$unsorted)) (=> (@ (@ tptp.c_In X15) X0) (= (@ (@ X5 X14) X15) (@ (@ X2 (@ (@ X1 X15) X14)) (@ (@ X1 X14) X15))))))))) (forall ((X14 $$unsorted)) (=> (@ (@ tptp.c_In X14) X0) (forall ((X15 $$unsorted)) (=> (@ (@ tptp.c_In X15) X0) (forall ((X16 $$unsorted)) (let ((_let_1 (@ X1 X14))) (=> (@ (@ tptp.c_In X16) X0) (= (@ (@ (@ X6 X14) X15) X16) (@ (@ X2 (@ _let_1 (@ (@ X1 X15) X16))) (@ (@ X1 (@ _let_1 X15)) X16)))))))))))) (forall ((X14 $$unsorted)) (=> (@ (@ tptp.c_In X14) X0) (forall ((X15 $$unsorted)) (let ((_let_1 (@ X3 X4))) (let ((_let_2 (@ _let_1 X14))) (let ((_let_3 (@ X2 X14))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ X1 X15))) (=> (@ (@ tptp.c_In X15) X0) (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (@ (@ tptp.c_and (= (@ (@ X7 X14) X15) (@ _let_3 (@ _let_5 X14)))) (= (@ (@ X10 X14) X15) (@ (@ X1 X14) (@ _let_5 _let_4))))) (= (@ (@ X11 X14) X15) (@ (@ X1 (@ (@ X1 _let_2) X15)) X14)))) (= (@ (@ X12 X14) X15) (@ (@ X1 (@ _let_3 X15)) (@ (@ X2 _let_4) X4))))) (= (@ (@ X13 X14) X15) (@ (@ X1 (@ _let_1 _let_2)) (@ (@ X3 X15) X14))))))))))))))) (forall ((X14 $$unsorted)) (=> (@ (@ tptp.c_In X14) X0) (forall ((X15 $$unsorted)) (=> (@ (@ tptp.c_In X15) X0) (forall ((X16 $$unsorted)) (let ((_let_1 (@ X1 X14))) (let ((_let_2 (@ X1 X15))) (=> (@ (@ tptp.c_In X16) X0) (@ (@ tptp.c_and (= (@ (@ (@ X8 X14) X15) X16) (@ (@ X2 (@ _let_2 X14)) (@ _let_2 (@ _let_1 X16))))) (= (@ (@ (@ X9 X14) X15) X16) (@ (@ X3 (@ (@ X1 (@ (@ X1 X16) X14)) X15)) (@ _let_1 X15))))))))))))))))
% 0.22/0.58 (assert (= tptp.c_Loop_with_defs_cex1 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted $$unsorted)) (X3 (-> $$unsorted $$unsorted $$unsorted)) (X4 $$unsorted) (X5 (-> $$unsorted $$unsorted $$unsorted)) (X6 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X7 (-> $$unsorted $$unsorted $$unsorted)) (X8 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X9 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X10 (-> $$unsorted $$unsorted $$unsorted)) (X11 (-> $$unsorted $$unsorted $$unsorted)) (X12 (-> $$unsorted $$unsorted $$unsorted)) (X13 (-> $$unsorted $$unsorted $$unsorted))) (@ (@ tptp.c_and (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) (exists ((X14 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X14) X0)) (exists ((X15 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X15) X0)) (exists ((X16 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X16) X0)) (exists ((X17 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X17) X0)) (@ tptp.c_not (= (@ (@ X5 (@ (@ X1 (@ (@ X2 (@ (@ (@ X8 X15) X16) X14)) X4)) X14)) X17) X4))))))))))))))
% 0.22/0.58 (assert (= tptp.c_Loop_with_defs_cex2 (lambda ((X0 $$unsorted) (X1 (-> $$unsorted $$unsorted $$unsorted)) (X2 (-> $$unsorted $$unsorted $$unsorted)) (X3 (-> $$unsorted $$unsorted $$unsorted)) (X4 $$unsorted) (X5 (-> $$unsorted $$unsorted $$unsorted)) (X6 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X7 (-> $$unsorted $$unsorted $$unsorted)) (X8 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X9 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X10 (-> $$unsorted $$unsorted $$unsorted)) (X11 (-> $$unsorted $$unsorted $$unsorted)) (X12 (-> $$unsorted $$unsorted $$unsorted)) (X13 (-> $$unsorted $$unsorted $$unsorted))) (@ (@ tptp.c_and (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ (@ tptp.c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) (exists ((X14 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X14) X0)) (exists ((X15 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X15) X0)) (exists ((X16 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X16) X0)) (exists ((X17 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X17) X0)) (exists ((X18 $$unsorted)) (@ (@ tptp.c_and (@ (@ tptp.c_In X18) X0)) (@ tptp.c_not (= (@ (@ (@ X6 X18) (@ (@ X1 (@ (@ X3 X4) X14)) (@ (@ (@ X9 X15) X16) X14))) X17) X4))))))))))))))))
% 0.22/0.58 (assert (= tptp.c_combinator (lambda ((X0 $$unsorted)) (forall ((X1 (-> $$unsorted Bool))) (=> (@ X1 (@ tptp.c_Inj0 tptp.c_Empty)) (=> (@ X1 (@ tptp.c_Inj0 (@ tptp.c_Power tptp.c_Empty))) (=> (forall ((X2 $$unsorted) (X3 $$unsorted)) (=> (@ X1 X2) (=> (@ X1 X3) (@ X1 (@ tptp.c_Inj1 (@ (@ tptp.c_setsum X2) X3)))))) (@ X1 X0))))))))
% 0.22/0.58 (assert (= tptp.c_combinator_equiv (lambda ((X0 $$unsorted) (X1 $$unsorted)) (forall ((X2 (-> $$unsorted $$unsorted Bool))) (@ (@ (@ (lambda ((X3 $$unsorted) (X4 $$unsorted) (X5 (-> $$unsorted $$unsorted $$unsorted))) (=> (@ tptp.c_per_i X2) (=> (forall ((X6 $$unsorted)) (=> (@ tptp.c_combinator X6) (@ (@ X2 X6) X6))) (=> (forall ((X6 $$unsorted) (X7 $$unsorted) (X8 $$unsorted) (X9 $$unsorted)) (=> (@ tptp.c_combinator X6) (=> (@ tptp.c_combinator X7) (=> (@ tptp.c_combinator X8) (=> (@ tptp.c_combinator X9) (=> (@ (@ X2 X6) X8) (=> (@ (@ X2 X7) X9) (@ (@ X2 (@ (@ X5 X6) X7)) (@ (@ X5 X8) X9))))))))) (=> (forall ((X6 $$unsorted) (X7 $$unsorted)) (@ (@ X2 (@ (@ X5 (@ (@ X5 X3) X6)) X7)) X6)) (=> (forall ((X6 $$unsorted) (X7 $$unsorted) (X8 $$unsorted)) (@ (@ X2 (@ (@ X5 (@ (@ X5 (@ (@ X5 X4) X6)) X7)) X8)) (@ (@ X5 (@ (@ X5 X6) X8)) (@ (@ X5 X7) X8)))) (@ (@ X2 X0) X1))))))) (@ tptp.c_Inj0 tptp.c_Empty)) (@ tptp.c_Inj0 (@ tptp.c_Power tptp.c_Empty))) (lambda ((X3 $$unsorted) (X4 $$unsorted)) (@ tptp.c_Inj1 (@ (@ tptp.c_setsum X3) X4))))))))
% 0.22/0.58 (assert (= tptp.c_equip_mod (lambda ((X0 $$unsorted) (X1 $$unsorted) (X2 $$unsorted)) (exists ((X3 $$unsorted) (X4 $$unsorted)) (let ((_let_1 (@ (@ tptp.c_equip (@ (@ tptp.c_setprod X4) X3)) X2))) (@ (@ tptp.c_or (@ (@ tptp.c_and (@ (@ tptp.c_equip (@ (@ tptp.c_setsum X0) X3)) X1)) _let_1)) (@ (@ tptp.c_and (@ (@ tptp.c_equip (@ (@ tptp.c_setsum X1) X3)) X0)) _let_1)))))))
% 0.22/0.58 (assert (not (forall ((X0 (-> (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted $$unsorted) (-> (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted) Bool)) (X1 (-> (-> (-> (-> (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) $$unsorted) (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted $$unsorted) (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted) $$unsorted $$unsorted Bool)) (X2 (-> (-> (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted) $$unsorted (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted $$unsorted) $$unsorted (-> (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted) Bool)) (X3 (-> (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted $$unsorted) $$unsorted $$unsorted $$unsorted) $$unsorted Bool))) (=> (forall ((X4 $$unsorted) (X5 $$unsorted) (X6 $$unsorted) (X7 $$unsorted)) (let ((_let_1 (@ tptp.c_setsum tptp.c_Empty))) (=> (@ (@ tptp.c_In (@ tptp.c_Inj0 X4)) (@ tptp.c_Inj1 (@ _let_1 (@ (@ tptp.c_setsum (@ tptp.c_Inj0 tptp.c_Empty)) (@ _let_1 tptp.c_Empty))))) (=> (@ (@ (@ X0 (lambda ((X8 $$unsorted)) (@ tptp.c_Inj0 (@ (@ tptp.c_setsum tptp.c_Empty) (@ tptp.c_Inj0 (@ tptp.c_Inj0 tptp.c_Empty)))))) (lambda ((X8 $$unsorted) (X9 $$unsorted)) (@ tptp.c_Inj0 (@ tptp.c_Inj0 (@ (@ tptp.c_setsum tptp.c_Empty) X8))))) (lambda ((X8 (-> (-> $$unsorted $$unsorted) $$unsorted))) tptp.c_Empty)) (@ (@ X3 (lambda ((X8 $$unsorted) (X9 (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted $$unsorted)) (X10 $$unsorted) (X11 $$unsorted)) X8)) tptp.c_Empty))))) (=> (forall ((X4 $$unsorted) (X5 $$unsorted) (X6 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) (X7 (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted))) (=> (@ (@ X3 (lambda ((X8 $$unsorted) (X9 (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted $$unsorted)) (X10 $$unsorted) (X11 $$unsorted)) tptp.c_Empty)) (@ tptp.c_Inj0 (@ tptp.c_Inj0 (@ (@ tptp.c_setsum (@ (@ X7 tptp.c_Empty) (lambda ((X8 (-> $$unsorted $$unsorted))) tptp.c_Empty))) tptp.c_Empty)))) (@ (@ X3 (lambda ((X8 $$unsorted) (X9 (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted $$unsorted)) (X10 $$unsorted) (X11 $$unsorted)) (@ (@ tptp.c_setsum tptp.c_Empty) (@ (@ tptp.c_setsum (@ tptp.c_Inj1 X11)) tptp.c_Empty)))) X5))) (=> (forall ((X4 (-> (-> (-> $$unsorted $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted) $$unsorted)) (X5 $$unsorted) (X6 (-> $$unsorted $$unsorted)) (X7 $$unsorted)) (@ (@ (@ X2 (lambda ((X8 (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted)) (X9 $$unsorted) (X10 (-> $$unsorted $$unsorted)) (X11 (-> $$unsorted $$unsorted)) (X12 $$unsorted)) (let ((_let_1 (@ tptp.c_setsum (@ tptp.c_Inj0 tptp.c_Empty)))) (@ tptp.c_Inj1 (@ (@ tptp.c_setsum (@ _let_1 tptp.c_Empty)) (@ _let_1 (@ (@ tptp.c_setsum tptp.c_Empty) tptp.c_Empty))))))) (@ tptp.c_Inj0 (@ X4 (lambda ((X8 (-> $$unsorted $$unsorted $$unsorted)) (X9 (-> $$unsorted $$unsorted))) (@ X9 (@ tptp.c_Inj1 tptp.c_Empty)))))) (lambda ((X8 (-> (-> $$unsorted $$unsorted) $$unsorted))) (@ (@ tptp.c_setsum (@ tptp.c_Inj1 (@ tptp.c_Inj1 (@ X8 (lambda ((X9 $$unsorted)) tptp.c_Empty))))) X5)))) (=> (forall ((X4 $$unsorted) (X5 (-> $$unsorted $$unsorted)) (X6 (-> $$unsorted $$unsorted)) (X7 (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted))) (let ((_let_1 (@ tptp.c_Inj1 tptp.c_Empty))) (=> (@ (@ (@ X2 (lambda ((X8 (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted) $$unsorted $$unsorted)) (X9 $$unsorted) (X10 (-> $$unsorted $$unsorted)) (X11 (-> $$unsorted $$unsorted)) (X12 $$unsorted)) (@ tptp.c_Inj1 (@ tptp.c_Inj0 (@ (@ tptp.c_setsum (@ (@ tptp.c_setsum tptp.c_Empty) tptp.c_Empty)) X12))))) (@ (@ tptp.c_setsum tptp.c_Empty) tptp.c_Empty)) (lambda ((X8 (-> (-> $$unsorted $$unsorted) $$unsorted))) (@ (@ tptp.c_setsum tptp.c_Empty) (@ tptp.c_Inj1 (@ X6 (@ X6 tptp.c_Empty)))))) (@ (@ tptp.c_In (@ tptp.c_Inj1 (@ X5 (@ (@ tptp.c_setsum (@ (@ X7 tptp.c_Empty) (lambda ((X8 $$unsorted)) tptp.c_Empty))) _let_1)))) _let_1)))) (=> (forall ((X4 $$unsorted) (X5 $$unsorted) (X6 (-> $$unsorted $$unsorted)) (X7 $$unsorted)) (=> (@ (@ (@ X0 (lambda ((X8 $$unsorted)) (@ X6 X5))) (lambda ((X8 $$unsorted) (X9 $$unsorted)) tptp.c_Empty)) (lambda ((X8 (-> (-> $$unsorted $$unsorted) $$unsorted))) tptp.c_Empty)) (@ (@ (@ (@ X1 (lambda ((X8 (-> (-> (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) $$unsorted) (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted)) (X9 $$unsorted) (X10 $$unsorted)) X7)) (lambda ((X8 $$unsorted) (X9 (-> (-> $$unsorted $$unsorted) $$unsorted))) tptp.c_Empty)) tptp.c_Empty) (@ tptp.c_Inj0 (@ X6 tptp.c_Empty))))) (=> (forall ((X4 $$unsorted) (X5 $$unsorted) (X6 $$unsorted) (X7 (-> $$unsorted $$unsorted))) (let ((_let_1 (@ tptp.c_Inj1 tptp.c_Empty))) (let ((_let_2 (@ tptp.c_setsum tptp.c_Empty))) (let ((_let_3 (@ _let_2 tptp.c_Empty))) (=> (@ (@ tptp.c_In _let_1) (@ tptp.c_Inj0 (@ (@ tptp.c_setsum (@ tptp.c_Inj0 _let_3)) (@ tptp.c_Inj1 _let_3)))) (=> (@ (@ (@ (@ X1 (lambda ((X8 (-> (-> (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) $$unsorted) (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted)) (X9 $$unsorted) (X10 $$unsorted)) (let ((_let_1 (@ tptp.c_setsum tptp.c_Empty))) (@ _let_1 (@ _let_1 (@ tptp.c_Inj0 (@ tptp.c_Inj1 tptp.c_Empty))))))) (lambda ((X8 $$unsorted) (X9 (-> (-> $$unsorted $$unsorted) $$unsorted))) (@ X9 (lambda ((X10 $$unsorted)) X8)))) (@ X7 (@ (@ tptp.c_setsum (@ tptp.c_Inj1 X5)) X6))) (@ (@ tptp.c_setsum (@ _let_2 (@ tptp.c_Inj0 _let_1))) tptp.c_Empty)) (@ (@ (@ X0 (lambda ((X8 $$unsorted)) tptp.c_Empty)) (lambda ((X8 $$unsorted) (X9 $$unsorted)) (@ tptp.c_Inj1 (@ tptp.c_Inj0 (@ (@ tptp.c_setsum tptp.c_Empty) (@ X7 tptp.c_Empty)))))) (lambda ((X8 (-> (-> $$unsorted $$unsorted) $$unsorted))) (@ tptp.c_Inj0 (@ (@ tptp.c_setsum (@ (@ tptp.c_setsum tptp.c_Empty) (@ X8 (lambda ((X9 $$unsorted)) tptp.c_Empty)))) (@ X7 (@ tptp.c_Inj0 tptp.c_Empty)))))))))))) (=> (forall ((X4 (-> $$unsorted (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted) $$unsorted $$unsorted $$unsorted)) (X5 $$unsorted) (X6 (-> (-> $$unsorted $$unsorted $$unsorted $$unsorted) $$unsorted)) (X7 (-> (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) $$unsorted))) (let ((_let_1 (@ tptp.c_setsum tptp.c_Empty))) (=> (@ (@ tptp.c_In (@ _let_1 (@ (@ X7 (lambda ((X8 $$unsorted)) (@ tptp.c_Inj0 (@ X6 (lambda ((X9 $$unsorted) (X10 $$unsorted) (X11 $$unsorted)) tptp.c_Empty)/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 6576 Alarm clock ( read result; case "$result" in
% 299.75/300.21 unsat)
% 299.75/300.21 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.75/300.21 ;;
% 299.75/300.21 sat)
% 299.75/300.21 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.75/300.21 ;;
% 299.75/300.21 esac; exit 1 )
% 299.75/300.21 Alarm clock
% 299.75/300.21 % cvc5---1.0.5 exiting
% 299.75/300.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------