Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : ITP023_1 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% 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 : Sat Jun 21 05:11:34 AM UTC 2025

% Result   : Theorem 0.38s 0.57s
% Output   : Proof 0.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ITP023_1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Thu Jun 19 18:23:24 EDT 2025
% 0.11/0.33  % CPUTime    : 
% 0.38/0.57  % SZS status Theorem
% 0.38/0.57  % SZS output start Proof
% 0.38/0.57  tff(p_type, type, (
% 0.38/0.57     p: mono_2Etyop_2Emin_2Ebool > $o)).
% 0.38/0.57  tff(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1_type, type, (
% 0.38/0.57     mono_2Ec_2Ereal__topology_2Ebounded__def_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool)).
% 0.38/0.57  tff(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_type, type, (
% 0.38/0.57     mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29)).
% 0.38/0.57  tff(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_type, type, (
% 0.38/0.57     mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal * mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)).
% 0.38/0.57  tff(tptp_fun_V1e_2E0_4_type, type, (
% 0.38/0.57     tptp_fun_V1e_2E0_4: mono_2Etyop_2Erealax_2Ereal)).
% 0.38/0.57  tff(tptp_fun_V0x_2E0_5_type, type, (
% 0.38/0.57     tptp_fun_V0x_2E0_5: mono_2Etyop_2Erealax_2Ereal)).
% 0.38/0.57  tff(mono_2Ec_2Ereal__topology_2Eball_2E0_type, type, (
% 0.38/0.57     mono_2Ec_2Ereal__topology_2Eball_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29)).
% 0.38/0.57  tff(mono_2Ec_2Ebool_2EF_2E0_type, type, (
% 0.38/0.57     mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool)).
% 0.38/0.57  tff(mono_2Ec_2Ereal__topology_2Eball_2E1_type, type, (
% 0.38/0.57     mono_2Ec_2Ereal__topology_2Eball_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29)).
% 0.38/0.57  tff(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal_type, type, (
% 0.38/0.57     mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool)).
% 0.38/0.57  tff(mono_2Ec_2Ereal__topology_2Ecball_2E1_type, type, (
% 0.38/0.57     mono_2Ec_2Ereal__topology_2Ecball_2E1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29)).
% 0.38/0.57  tff(mono_2Ec_2Ebool_2ET_2E0_type, type, (
% 0.38/0.57     mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool)).
% 0.38/0.57  tff(j_mono_2Etyop_2Emin_2Ebool_type, type, (
% 0.38/0.57     j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool)).
% 0.38/0.57  tff(s_type, type, (
% 0.38/0.57     s: ( d * u ) > du)).
% 0.38/0.57  tff(c_2Emin_2E_3D_2E2_type, type, (
% 0.38/0.57     c_2Emin_2E_3D_2E2: ( du * du ) > u)).
% 0.38/0.57  tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29_type, type, (
% 0.38/0.57     i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 > u)).
% 0.38/0.57  tff(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_type, type, (
% 0.38/0.57     mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29)).
% 0.38/0.57  tff(tyop_2Emin_2Efun_type, type, (
% 0.38/0.57     tyop_2Emin_2Efun: ( d * d ) > d)).
% 0.38/0.57  tff(tyop_2Epair_2Eprod_type, type, (
% 0.38/0.57     tyop_2Epair_2Eprod: ( d * d ) > d)).
% 0.38/0.57  tff(tyop_2Erealax_2Ereal_type, type, (
% 0.38/0.57     tyop_2Erealax_2Ereal: d)).
% 0.38/0.57  tff(tyop_2Emin_2Ebool_type, type, (
% 0.38/0.57     tyop_2Emin_2Ebool: d)).
% 0.38/0.57  tff(1,plain,
% 0.38/0.57      ((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) <=> $false) <=> (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(2,plain,
% 0.38/0.57      ((~p(mono_2Ec_2Ebool_2EF_2E0)) <=> (~p(mono_2Ec_2Ebool_2EF_2E0))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(3,axiom,(~p(mono_2Ec_2Ebool_2EF_2E0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reserved_2Eho_2Enotfalse')).
% 0.38/0.57  tff(4,plain,
% 0.38/0.57      (~p(mono_2Ec_2Ebool_2EF_2E0)),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.38/0.57  tff(5,plain,
% 0.38/0.57      (p(mono_2Ec_2Ebool_2EF_2E0) <=> $false),
% 0.38/0.57      inference(iff_false,[status(thm)],[4])).
% 0.38/0.57  tff(6,plain,
% 0.38/0.57      ((~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))) <=> (~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(7,axiom,(~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBOUNDED__BALL')).
% 0.38/0.57  tff(8,plain,
% 0.38/0.57      (~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.38/0.57  tff(9,plain,
% 0.38/0.57      (~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[8, 6])).
% 0.38/0.57  tff(10,plain,
% 0.38/0.57      (~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[9, 6])).
% 0.38/0.57  tff(11,plain,
% 0.38/0.57      (~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[10, 6])).
% 0.38/0.57  tff(12,plain,(
% 0.38/0.57      ~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.57      inference(skolemize,[status(sab)],[11])).
% 0.38/0.57  tff(13,plain,
% 0.38/0.57      ((p(mono_2Ec_2Ebool_2EF_2E0) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.57      inference(tautology,[status(thm)],[])).
% 0.38/0.57  tff(14,plain,
% 0.38/0.57      (p(mono_2Ec_2Ebool_2EF_2E0) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))),
% 0.38/0.57      inference(unit_resolution,[status(thm)],[13, 12])).
% 0.38/0.57  tff(15,plain,
% 0.38/0.57      (((~p(mono_2Ec_2Ebool_2EF_2E0)) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(mono_2Ec_2Ebool_2EF_2E0)),
% 0.38/0.57      inference(tautology,[status(thm)],[])).
% 0.38/0.57  tff(16,plain,
% 0.38/0.57      ((~p(mono_2Ec_2Ebool_2EF_2E0)) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.57      inference(unit_resolution,[status(thm)],[15, 4])).
% 0.38/0.57  tff(17,plain,
% 0.38/0.57      (^[V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : refl(((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0))))) <=> ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0))))))),
% 0.38/0.57      inference(bind,[status(th)],[])).
% 0.38/0.57  tff(18,plain,
% 0.38/0.57      (![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0))))) <=> ![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(quant_intro,[status(thm)],[17])).
% 0.38/0.57  tff(19,plain,
% 0.38/0.57      (![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0))))) <=> ![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(20,plain,
% 0.38/0.57      (^[V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : trans(monotonicity(rewrite((p(V0t1_2E0) => p(V1t2_2E0)) <=> (p(V1t2_2E0) | (~p(V0t1_2E0)))), trans(monotonicity(rewrite((p(V1t2_2E0) => p(V0t1_2E0)) <=> ((~p(V1t2_2E0)) | p(V0t1_2E0))), (((p(V1t2_2E0) => p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0)) <=> (((~p(V1t2_2E0)) | p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0)))), rewrite((((~p(V1t2_2E0)) | p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0)) <=> ((~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (V0t1_2E0 = V1t2_2E0))), (((p(V1t2_2E0) => p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0)) <=> ((~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (V0t1_2E0 = V1t2_2E0)))), (((p(V0t1_2E0) => p(V1t2_2E0)) => ((p(V1t2_2E0) => p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0))) <=> ((p(V1t2_2E0) | (~p(V0t1_2E0))) => ((~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (V0t1_2E0 = V1t2_2E0))))), rewrite(((p(V1t2_2E0) | (~p(V0t1_2E0))) => ((~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (V0t1_2E0 = V1t2_2E0))) <=> ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))), (((p(V0t1_2E0) => p(V1t2_2E0)) => ((p(V1t2_2E0) => p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0))) <=> ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))))),
% 0.38/0.57      inference(bind,[status(th)],[])).
% 0.38/0.57  tff(21,plain,
% 0.38/0.57      (![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((p(V0t1_2E0) => p(V1t2_2E0)) => ((p(V1t2_2E0) => p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0))) <=> ![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(quant_intro,[status(thm)],[20])).
% 0.38/0.57  tff(22,axiom,(![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((p(V0t1_2E0) => p(V1t2_2E0)) => ((p(V1t2_2E0) => p(V0t1_2E0)) => (V0t1_2E0 = V1t2_2E0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ebool_2EIMP__ANTISYM__AX')).
% 0.38/0.57  tff(23,plain,
% 0.38/0.57      (![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.38/0.57  tff(24,plain,
% 0.38/0.57      (![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[23, 19])).
% 0.38/0.57  tff(25,plain,(
% 0.38/0.57      ![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(skolemize,[status(sab)],[24])).
% 0.38/0.57  tff(26,plain,
% 0.38/0.57      (![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[25, 18])).
% 0.38/0.57  tff(27,plain,
% 0.38/0.57      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2EF_2E0) | (~((~p(mono_2Ec_2Ebool_2EF_2E0)) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))) | (~(p(mono_2Ec_2Ebool_2EF_2E0) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))))))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2EF_2E0) | (~((~p(mono_2Ec_2Ebool_2EF_2E0)) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))) | (~(p(mono_2Ec_2Ebool_2EF_2E0) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))))))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(28,plain,
% 0.38/0.57      ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2EF_2E0) | (~((~p(mono_2Ec_2Ebool_2EF_2E0)) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))) | (~(p(mono_2Ec_2Ebool_2EF_2E0) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))))))),
% 0.38/0.57      inference(quant_inst,[status(thm)],[])).
% 0.38/0.57  tff(29,plain,
% 0.38/0.57      ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2EF_2E0) | (~((~p(mono_2Ec_2Ebool_2EF_2E0)) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))) | (~(p(mono_2Ec_2Ebool_2EF_2E0) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[28, 27])).
% 0.38/0.57  tff(30,plain,
% 0.38/0.57      (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2EF_2E0),
% 0.38/0.57      inference(unit_resolution,[status(thm)],[29, 26, 16, 14])).
% 0.38/0.57  tff(31,plain,
% 0.38/0.57      (^[X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : refl((mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0)) <=> (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0)))),
% 0.38/0.57      inference(bind,[status(th)],[])).
% 0.38/0.57  tff(32,plain,
% 0.38/0.57      (![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0)) <=> ![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))),
% 0.38/0.57      inference(quant_intro,[status(thm)],[31])).
% 0.38/0.57  tff(33,plain,
% 0.38/0.57      (![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0)) <=> ![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(34,axiom,(![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','arityeq1_2Ec_2Ereal__topology_2Eball_2E1')).
% 0.38/0.57  tff(35,plain,
% 0.38/0.57      (![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[34, 33])).
% 0.38/0.57  tff(36,plain,(
% 0.38/0.57      ![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))),
% 0.38/0.57      inference(skolemize,[status(sab)],[35])).
% 0.38/0.57  tff(37,plain,
% 0.38/0.57      (![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[36, 32])).
% 0.38/0.57  tff(38,plain,
% 0.38/0.57      ((~![X0_2E0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] : (mono_2Ec_2Ereal__topology_2Eball_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, X0_2E0))) | (mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))),
% 0.38/0.57      inference(quant_inst,[status(thm)],[])).
% 0.38/0.57  tff(39,plain,
% 0.38/0.57      (mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)) = mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))),
% 0.38/0.57      inference(unit_resolution,[status(thm)],[38, 37])).
% 0.38/0.57  tff(40,plain,
% 0.38/0.57      (mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)) = mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))),
% 0.38/0.57      inference(symmetry,[status(thm)],[39])).
% 0.38/0.57  tff(41,plain,
% 0.38/0.57      (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))),
% 0.38/0.57      inference(monotonicity,[status(thm)],[40])).
% 0.38/0.57  tff(42,plain,
% 0.38/0.57      (mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2EF_2E0),
% 0.38/0.57      inference(transitivity,[status(thm)],[41, 30])).
% 0.38/0.57  tff(43,plain,
% 0.38/0.57      (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) <=> p(mono_2Ec_2Ebool_2EF_2E0)),
% 0.38/0.57      inference(monotonicity,[status(thm)],[42])).
% 0.38/0.57  tff(44,plain,
% 0.38/0.57      (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) <=> $false),
% 0.38/0.57      inference(transitivity,[status(thm)],[43, 5])).
% 0.38/0.57  tff(45,plain,
% 0.38/0.57      (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[44, 1])).
% 0.38/0.57  tff(46,plain,
% 0.38/0.57      ((p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) <=> $true) <=> p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(47,plain,
% 0.38/0.57      (p(mono_2Ec_2Ebool_2ET_2E0) <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.38/0.57      inference(rewrite,[status(thm)],[])).
% 0.38/0.57  tff(48,axiom,(p(mono_2Ec_2Ebool_2ET_2E0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reserved_2Eho_2Etruth')).
% 0.38/0.57  tff(49,plain,
% 0.38/0.57      (p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.38/0.57      inference(modus_ponens,[status(thm)],[48, 47])).
% 0.38/0.57  tff(50,plain,
% 0.38/0.57      (p(mono_2Ec_2Ebool_2ET_2E0) <=> $true),
% 0.38/0.57      inference(iff_true,[status(thm)],[49])).
% 0.38/0.57  tff(51,plain,
% 0.38/0.57      ((p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~p(mono_2Ec_2Ebool_2ET_2E0))),
% 0.38/0.57      inference(tautology,[status(thm)],[])).
% 0.38/0.57  tff(52,plain,
% 0.38/0.57      (p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.58      inference(unit_resolution,[status(thm)],[51, 49])).
% 0.38/0.58  tff(53,plain,
% 0.38/0.58      (^[A_27a: d, V0_2E0: u, V1_2E0: u] : refl((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))))),
% 0.38/0.58      inference(bind,[status(th)],[])).
% 0.38/0.58  tff(54,plain,
% 0.38/0.58      (![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))) <=> ![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 0.38/0.58      inference(quant_intro,[status(thm)],[53])).
% 0.38/0.58  tff(55,plain,
% 0.38/0.58      (![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0))) <=> ![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(56,axiom,(![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reserved_2Elogic_2E_3D')).
% 0.38/0.58  tff(57,plain,
% 0.38/0.58      (![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 0.38/0.58      inference(modus_ponens,[status(thm)],[56, 55])).
% 0.38/0.58  tff(58,plain,(
% 0.38/0.58      ![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 0.38/0.58      inference(skolemize,[status(sab)],[57])).
% 0.38/0.58  tff(59,plain,
% 0.38/0.58      (![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))),
% 0.38/0.58      inference(modus_ponens,[status(thm)],[58, 54])).
% 0.38/0.58  tff(60,plain,
% 0.38/0.58      (((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))) <=> ((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(61,plain,
% 0.38/0.58      ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> $true) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(62,plain,
% 0.38/0.58      ((s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))) <=> $true),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(63,plain,
% 0.38/0.58      ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> (s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))) <=> (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> $true)),
% 0.38/0.58      inference(monotonicity,[status(thm)],[62])).
% 0.38/0.58  tff(64,plain,
% 0.38/0.58      ((p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> (s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))) <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))),
% 0.38/0.58      inference(transitivity,[status(thm)],[63, 61])).
% 0.38/0.58  tff(65,plain,
% 0.38/0.58      (((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> (s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) <=> ((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.58      inference(monotonicity,[status(thm)],[64])).
% 0.38/0.58  tff(66,plain,
% 0.38/0.58      (((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> (s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) <=> ((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.58      inference(transitivity,[status(thm)],[65, 60])).
% 0.38/0.58  tff(67,plain,
% 0.38/0.58      ((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))) <=> (s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) = s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))),
% 0.38/0.58      inference(quant_inst,[status(thm)],[])).
% 0.38/0.58  tff(68,plain,
% 0.38/0.58      ((~![A_27a: d, V0_2E0: u, V1_2E0: u] : (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(A_27a, V0_2E0), s(A_27a, V1_2E0))))) <=> (s(A_27a, V0_2E0) = s(A_27a, V1_2E0)))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))),
% 0.38/0.58      inference(modus_ponens,[status(thm)],[67, 66])).
% 0.38/0.58  tff(69,plain,
% 0.38/0.58      (p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))),
% 0.38/0.58      inference(unit_resolution,[status(thm)],[68, 59])).
% 0.38/0.58  tff(70,plain,
% 0.38/0.58      (((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.58      inference(tautology,[status(thm)],[])).
% 0.38/0.58  tff(71,plain,
% 0.38/0.58      ((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))),
% 0.38/0.58      inference(unit_resolution,[status(thm)],[70, 69])).
% 0.38/0.58  tff(72,plain,
% 0.38/0.58      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0))),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(73,plain,
% 0.38/0.58      (((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))))) <=> ((~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0))),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(74,plain,
% 0.38/0.58      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0)))),
% 0.38/0.58      inference(monotonicity,[status(thm)],[73])).
% 0.38/0.58  tff(75,plain,
% 0.38/0.58      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0))),
% 0.38/0.58      inference(transitivity,[status(thm)],[74, 72])).
% 0.38/0.58  tff(76,plain,
% 0.38/0.58      ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))),
% 0.38/0.58      inference(quant_inst,[status(thm)],[])).
% 0.38/0.58  tff(77,plain,
% 0.38/0.58      ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (~((~p(mono_2Ec_2Ebool_2ET_2E0)) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Ebool_2ET_2E0) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0)),
% 0.38/0.58      inference(modus_ponens,[status(thm)],[76, 75])).
% 0.38/0.58  tff(78,plain,
% 0.38/0.58      (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Ebool_2ET_2E0),
% 0.38/0.58      inference(unit_resolution,[status(thm)],[77, 26, 71, 52])).
% 0.38/0.58  tff(79,plain,
% 0.38/0.58      (((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.58      inference(tautology,[status(thm)],[])).
% 0.38/0.58  tff(80,plain,
% 0.38/0.58      ((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))),
% 0.38/0.58      inference(unit_resolution,[status(thm)],[79, 69])).
% 0.38/0.58  tff(81,plain,
% 0.38/0.58      (^[V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : refl(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))) <=> p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))))),
% 0.38/0.58      inference(bind,[status(th)],[])).
% 0.38/0.58  tff(82,plain,
% 0.38/0.58      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))) <=> ![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.58      inference(quant_intro,[status(thm)],[81])).
% 0.38/0.58  tff(83,plain,
% 0.38/0.58      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))) <=> ![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.58      inference(rewrite,[status(thm)],[])).
% 0.38/0.58  tff(84,axiom,(![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBALL__SUBSET__CBALL')).
% 0.38/0.58  tff(85,plain,
% 0.38/0.58      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.58      inference(modus_ponens,[status(thm)],[84, 83])).
% 0.38/0.58  tff(86,plain,(
% 0.38/0.58      ![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.58      inference(skolemize,[status(sab)],[85])).
% 0.38/0.58  tff(87,plain,
% 0.38/0.58      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.58      inference(modus_ponens,[status(thm)],[86, 82])).
% 0.38/0.58  tff(88,plain,
% 0.38/0.58      ((~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))) | p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.59      inference(quant_inst,[status(thm)],[])).
% 0.38/0.59  tff(89,plain,
% 0.38/0.59      (p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.59      inference(unit_resolution,[status(thm)],[88, 87])).
% 0.38/0.59  tff(90,plain,
% 0.38/0.59      ((p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))),
% 0.38/0.59      inference(tautology,[status(thm)],[])).
% 0.38/0.59  tff(91,plain,
% 0.38/0.59      (p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))),
% 0.38/0.59      inference(unit_resolution,[status(thm)],[90, 89])).
% 0.38/0.59  tff(92,plain,
% 0.38/0.59      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))))),
% 0.38/0.59      inference(rewrite,[status(thm)],[])).
% 0.38/0.59  tff(93,plain,
% 0.38/0.59      (((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))))) <=> ((~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))))),
% 0.38/0.59      inference(rewrite,[status(thm)],[])).
% 0.38/0.59  tff(94,plain,
% 0.38/0.59      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))),
% 0.38/0.59      inference(monotonicity,[status(thm)],[93])).
% 0.38/0.59  tff(95,plain,
% 0.38/0.59      (((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))) <=> ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))))),
% 0.38/0.59      inference(transitivity,[status(thm)],[94, 92])).
% 0.38/0.59  tff(96,plain,
% 0.38/0.59      ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | ((j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))))),
% 0.38/0.59      inference(quant_inst,[status(thm)],[])).
% 0.38/0.59  tff(97,plain,
% 0.38/0.59      ((~![V0t1_2E0: mono_2Etyop_2Emin_2Ebool, V1t2_2E0: mono_2Etyop_2Emin_2Ebool] : ((V0t1_2E0 = V1t2_2E0) | (~((~p(V1t2_2E0)) | p(V0t1_2E0))) | (~(p(V1t2_2E0) | (~p(V0t1_2E0)))))) | (~(p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))) | (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~((~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[96, 95])).
% 0.38/0.59  tff(98,plain,
% 0.38/0.59      (j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal))))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))),
% 0.38/0.59      inference(unit_resolution,[status(thm)],[97, 26, 91, 80])).
% 0.38/0.59  tff(99,plain,
% 0.38/0.59      (mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool, c_2Emin_2E_3D_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal))), i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29(mono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)))))),
% 0.38/0.59      inference(symmetry,[status(thm)],[98])).
% 0.38/0.59  tff(100,plain,
% 0.38/0.59      (mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Ec_2Ereal__topology_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))),
% 0.38/0.59      inference(monotonicity,[status(thm)],[40])).
% 0.38/0.59  tff(101,plain,
% 0.38/0.59      (mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))) = mono_2Ec_2Ebool_2ET_2E0),
% 0.38/0.59      inference(transitivity,[status(thm)],[100, 99, 78])).
% 0.38/0.59  tff(102,plain,
% 0.38/0.59      (p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.38/0.59      inference(monotonicity,[status(thm)],[101])).
% 0.38/0.59  tff(103,plain,
% 0.38/0.59      (p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) <=> $true),
% 0.38/0.59      inference(transitivity,[status(thm)],[102, 50])).
% 0.38/0.59  tff(104,plain,
% 0.38/0.59      (p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[103, 46])).
% 0.38/0.59  tff(105,plain,
% 0.38/0.59      (^[V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : refl(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))) <=> p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))))),
% 0.38/0.59      inference(bind,[status(th)],[])).
% 0.38/0.59  tff(106,plain,
% 0.38/0.59      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))) <=> ![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.59      inference(quant_intro,[status(thm)],[105])).
% 0.38/0.59  tff(107,plain,
% 0.38/0.59      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0)))) <=> ![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.59      inference(rewrite,[status(thm)],[])).
% 0.38/0.59  tff(108,axiom,(![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBOUNDED__CBALL')).
% 0.38/0.59  tff(109,plain,
% 0.38/0.59      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[108, 107])).
% 0.38/0.59  tff(110,plain,(
% 0.38/0.59      ![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.59      inference(skolemize,[status(sab)],[109])).
% 0.38/0.59  tff(111,plain,
% 0.38/0.59      (![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[110, 106])).
% 0.38/0.59  tff(112,plain,
% 0.38/0.59      ((~![V0x_2E0: mono_2Etyop_2Erealax_2Ereal, V1e_2E0: mono_2Etyop_2Erealax_2Ereal] : p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0, V1e_2E0))))) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.59      inference(quant_inst,[status(thm)],[])).
% 0.38/0.59  tff(113,plain,
% 0.38/0.59      (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.38/0.59      inference(unit_resolution,[status(thm)],[112, 111])).
% 0.38/0.59  tff(114,plain,
% 0.38/0.59      (^[V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : refl((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))) <=> (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))),
% 0.38/0.59      inference(bind,[status(th)],[])).
% 0.38/0.59  tff(115,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))) <=> ![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))),
% 0.38/0.59      inference(quant_intro,[status(thm)],[114])).
% 0.38/0.59  tff(116,plain,
% 0.38/0.59      (^[V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : trans(monotonicity(trans(monotonicity(rewrite((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))) <=> (~((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))), ((~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))) <=> (~(~((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))))), rewrite((~(~((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))) <=> ((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))), ((~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))) <=> ((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))), ((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) <=> (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | ((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))))), rewrite((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | ((~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) <=> (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))), ((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) <=> (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))))),
% 0.38/0.59      inference(bind,[status(th)],[])).
% 0.38/0.59  tff(117,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) <=> ![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))),
% 0.38/0.59      inference(quant_intro,[status(thm)],[116])).
% 0.38/0.59  tff(118,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) <=> ![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))),
% 0.38/0.59      inference(rewrite,[status(thm)],[])).
% 0.38/0.59  tff(119,plain,
% 0.38/0.59      (^[V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : rewrite(((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))) => p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0))) <=> (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))))),
% 0.38/0.59      inference(bind,[status(th)],[])).
% 0.38/0.59  tff(120,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))) => p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0))) <=> ![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))),
% 0.38/0.59      inference(quant_intro,[status(thm)],[119])).
% 0.38/0.59  tff(121,axiom,(![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : ((p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))) => p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBOUNDED__SUBSET')).
% 0.38/0.59  tff(122,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.38/0.59  tff(123,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[122, 118])).
% 0.38/0.59  tff(124,plain,(
% 0.38/0.59      ![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~(p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0)) & p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0)))))),
% 0.38/0.59      inference(skolemize,[status(sab)],[123])).
% 0.38/0.59  tff(125,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[124, 117])).
% 0.38/0.59  tff(126,plain,
% 0.38/0.59      (![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[125, 115])).
% 0.38/0.59  tff(127,plain,
% 0.38/0.59      (((~![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) | (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))))) <=> ((~![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))))),
% 0.38/0.59      inference(rewrite,[status(thm)],[])).
% 0.38/0.59  tff(128,plain,
% 0.38/0.59      ((~![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) | (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))))),
% 0.38/0.59      inference(quant_inst,[status(thm)],[])).
% 0.38/0.59  tff(129,plain,
% 0.38/0.59      ((~![V0s_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, V1t_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] : (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V0s_2E0)) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(V1t_2E0))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(V0s_2E0, V1t_2E0))))) | p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))),
% 0.38/0.59      inference(modus_ponens,[status(thm)],[128, 127])).
% 0.38/0.59  tff(130,plain,
% 0.38/0.59      (p(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))) | (~p(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal(mono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ereal__topology_2Eball_2E0, mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)), mono_2Ec_2Ereal__topology_2Ecball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4)))))),
% 0.38/0.60      inference(unit_resolution,[status(thm)],[129, 126, 113])).
% 0.38/0.60  tff(131,plain,
% 0.38/0.60      ($false),
% 0.38/0.60      inference(unit_resolution,[status(thm)],[130, 104, 45])).
% 0.38/0.60  % SZS output end Proof
% 0.38/0.60  % E exiting
%------------------------------------------------------------------------------