TSTP Solution File: ITP023_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP023_1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 Sep 17 04:15:30 EDT 2022
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ITP023_1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 03:47:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % SZS output start Proof
% 0.18/0.43 tff(p_type, type, (
% 0.18/0.43 p: mono_2Etyop_2Emin_2Ebool > $o)).
% 0.18/0.43 tff(mono_2Ec_2Ereal__topology_2Ebounded__def_2E1_type, type, (
% 0.18/0.43 mono_2Ec_2Ereal__topology_2Ebounded__def_2E1: mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool)).
% 0.18/0.43 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, (
% 0.18/0.43 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)).
% 0.18/0.43 tff(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_type, type, (
% 0.18/0.43 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)).
% 0.18/0.43 tff(tptp_fun_V1e_2E0_4_type, type, (
% 0.18/0.43 tptp_fun_V1e_2E0_4: mono_2Etyop_2Erealax_2Ereal)).
% 0.18/0.43 tff(tptp_fun_V0x_2E0_5_type, type, (
% 0.18/0.43 tptp_fun_V0x_2E0_5: mono_2Etyop_2Erealax_2Ereal)).
% 0.18/0.43 tff(mono_2Ec_2Ereal__topology_2Eball_2E0_type, type, (
% 0.18/0.43 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)).
% 0.18/0.43 tff(mono_2Ec_2Ereal__topology_2Eball_2E1_type, type, (
% 0.18/0.43 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)).
% 0.18/0.43 tff(mono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal_type, type, (
% 0.18/0.43 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)).
% 0.18/0.43 tff(mono_2Ec_2Ereal__topology_2Ecball_2E1_type, type, (
% 0.18/0.43 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)).
% 0.18/0.43 tff(mono_2Ec_2Ebool_2ET_2E0_type, type, (
% 0.18/0.43 mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool)).
% 0.18/0.43 tff(1,plain,
% 0.18/0.43 (^[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)))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(2,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.43 tff(3,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(4,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')).
% 0.18/0.43 tff(5,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.43 tff(6,plain,(
% 0.18/0.43 ![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))),
% 0.18/0.43 inference(skolemize,[status(sab)],[5])).
% 0.18/0.43 tff(7,plain,
% 0.18/0.43 (![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))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.43 tff(8,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(9,plain,
% 0.18/0.43 (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))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.43 tff(10,plain,
% 0.18/0.43 (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))),
% 0.18/0.43 inference(symmetry,[status(thm)],[9])).
% 0.18/0.43 tff(11,plain,
% 0.18/0.43 (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)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.43 tff(12,plain,
% 0.18/0.43 (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_2Eball_2E1(mono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal(V0x_2E0!5, V1e_2E0!4))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[11])).
% 0.18/0.43 tff(13,plain,
% 0.18/0.43 (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_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))))),
% 0.18/0.43 inference(symmetry,[status(thm)],[12])).
% 0.18/0.43 tff(14,plain,
% 0.18/0.43 ((~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_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)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[13])).
% 0.18/0.43 tff(15,plain,
% 0.18/0.43 ((~![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)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(16,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')).
% 0.18/0.43 tff(17,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.43 tff(18,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.18/0.43 tff(19,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.18/0.43 tff(20,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.43 tff(21,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.18/0.43 tff(22,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.18/0.43 tff(23,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.18/0.43 tff(24,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.18/0.43 tff(25,plain,
% 0.18/0.43 (~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.18/0.43 tff(26,plain,(
% 0.18/0.43 ~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))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[25])).
% 0.18/0.43 tff(27,plain,
% 0.18/0.43 (~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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[26, 14])).
% 0.18/0.43 tff(28,plain,
% 0.18/0.43 (p(mono_2Ec_2Ebool_2ET_2E0) <=> p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(29,axiom,(p(mono_2Ec_2Ebool_2ET_2E0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reserved_2Eho_2Etruth')).
% 0.18/0.43 tff(30,plain,
% 0.18/0.43 (p(mono_2Ec_2Ebool_2ET_2E0)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.43 tff(31,plain,
% 0.18/0.43 ((p(mono_2Ec_2Ebool_2ET_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)))))) | (~p(mono_2Ec_2Ebool_2ET_2E0))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(32,plain,
% 0.18/0.43 (p(mono_2Ec_2Ebool_2ET_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)))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.18/0.43 tff(33,plain,
% 0.18/0.43 (^[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)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(34,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.43 tff(35,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(36,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')).
% 0.18/0.43 tff(37,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.43 tff(38,plain,(
% 0.18/0.43 ![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))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[37])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 ((~![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))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (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))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 (((~p(mono_2Ec_2Ebool_2ET_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))))) | (~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)))))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 ((~p(mono_2Ec_2Ebool_2ET_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))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 (^[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))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(45,plain,
% 0.18/0.43 (![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)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 (![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)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(47,plain,
% 0.18/0.43 (^[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)))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 (![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)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.43 tff(49,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')).
% 0.18/0.44 tff(50,plain,
% 0.18/0.44 (![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)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.44 tff(51,plain,
% 0.18/0.44 (![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)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.18/0.44 tff(52,plain,(
% 0.18/0.44 ![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)))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[51])).
% 0.18/0.44 tff(53,plain,
% 0.18/0.44 (![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)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.18/0.44 tff(54,plain,
% 0.18/0.44 (((~![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(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_2Ebool_2ET_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))))))) | (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))) = 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(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_2Ebool_2ET_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))))))) | (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))) = mono_2Ec_2Ebool_2ET_2E0))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(55,plain,
% 0.18/0.44 (((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))) = mono_2Ec_2Ebool_2ET_2E0) | (~((~p(mono_2Ec_2Ebool_2ET_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)))))) | (~(p(mono_2Ec_2Ebool_2ET_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)))))))) <=> ((~((~p(mono_2Ec_2Ebool_2ET_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)))))) | (~(p(mono_2Ec_2Ebool_2ET_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))))))) | (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))) = mono_2Ec_2Ebool_2ET_2E0))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(56,plain,
% 0.18/0.44 (((~![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_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) | (~((~p(mono_2Ec_2Ebool_2ET_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)))))) | (~(p(mono_2Ec_2Ebool_2ET_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))))))))) <=> ((~![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(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_2Ebool_2ET_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))))))) | (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))) = mono_2Ec_2Ebool_2ET_2E0)))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.18/0.44 tff(57,plain,
% 0.18/0.44 (((~![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_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) | (~((~p(mono_2Ec_2Ebool_2ET_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)))))) | (~(p(mono_2Ec_2Ebool_2ET_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))))))))) <=> ((~![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(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_2Ebool_2ET_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))))))) | (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))) = mono_2Ec_2Ebool_2ET_2E0))),
% 0.18/0.44 inference(transitivity,[status(thm)],[56, 54])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 ((~![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_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) | (~((~p(mono_2Ec_2Ebool_2ET_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)))))) | (~(p(mono_2Ec_2Ebool_2ET_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))))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(59,plain,
% 0.18/0.44 ((~![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(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_2Ebool_2ET_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))))))) | (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))) = mono_2Ec_2Ebool_2ET_2E0)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.44 tff(60,plain,
% 0.18/0.44 (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))) = mono_2Ec_2Ebool_2ET_2E0),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[59, 53, 43, 32])).
% 0.18/0.44 tff(61,plain,
% 0.18/0.44 ((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_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_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)))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 (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_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)))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[61, 41])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (^[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)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(66,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')).
% 0.18/0.44 tff(67,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.44 tff(68,plain,(
% 0.18/0.44 ![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))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[67])).
% 0.18/0.44 tff(69,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.44 tff(70,plain,
% 0.18/0.44 ((~![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))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 (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))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.18/0.44 tff(72,plain,
% 0.18/0.44 ((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(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_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)))))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(73,plain,
% 0.18/0.44 (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(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)))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 (((~![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(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_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_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))))))) | (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))) = 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)))))) <=> ((~![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(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_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_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))))))) | (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))) = 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)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(75,plain,
% 0.18/0.44 (((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))) = 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_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_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(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_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_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_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_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))))))) | (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))) = 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)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 ((~((~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(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_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_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)))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(77,plain,
% 0.18/0.44 (((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))) = 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(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_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_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)))))))) <=> ((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))) = 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_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_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(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))))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[76])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (((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))) = 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(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_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_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_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_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_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_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))))))) | (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))) = 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)))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[77, 75])).
% 0.18/0.44 tff(79,plain,
% 0.18/0.44 (((~![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_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)))) | (~((~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(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_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_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))))))))) <=> ((~![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(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_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_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))))))) | (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))) = 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))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[78])).
% 0.18/0.44 tff(80,plain,
% 0.18/0.44 (((~![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_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)))) | (~((~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(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_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_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))))))))) <=> ((~![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(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_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_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))))))) | (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))) = 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)))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[79, 74])).
% 0.18/0.45 tff(81,plain,
% 0.18/0.45 ((~![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_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)))) | (~((~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(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_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_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))))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(82,plain,
% 0.18/0.45 ((~![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(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_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_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))))))) | (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))) = 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))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.45 tff(83,plain,
% 0.18/0.45 (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))) = 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)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[82, 53, 73, 62])).
% 0.18/0.45 tff(84,plain,
% 0.18/0.45 (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))) = 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)))),
% 0.18/0.45 inference(symmetry,[status(thm)],[83])).
% 0.18/0.45 tff(85,plain,
% 0.18/0.45 (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)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[10])).
% 0.18/0.45 tff(86,plain,
% 0.18/0.45 (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),
% 0.18/0.45 inference(transitivity,[status(thm)],[85, 84, 60])).
% 0.18/0.45 tff(87,plain,
% 0.18/0.45 (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)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[86])).
% 0.18/0.45 tff(88,plain,
% 0.18/0.45 (p(mono_2Ec_2Ebool_2ET_2E0) <=> 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))))),
% 0.18/0.45 inference(symmetry,[status(thm)],[87])).
% 0.18/0.45 tff(89,plain,
% 0.18/0.45 (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))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[30, 88])).
% 0.18/0.45 tff(90,plain,
% 0.18/0.45 (^[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)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(91,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.45 tff(92,plain,
% 0.18/0.45 (^[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))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(93,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.45 tff(94,plain,
% 0.18/0.45 (![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)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(95,plain,
% 0.18/0.45 (^[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))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(96,plain,
% 0.18/0.45 (![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)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.45 tff(97,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')).
% 0.18/0.45 tff(98,plain,
% 0.18/0.45 (![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)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.18/0.45 tff(99,plain,
% 0.18/0.45 (![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)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.18/0.45 tff(100,plain,(
% 0.18/0.45 ![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)))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[99])).
% 0.18/0.45 tff(101,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.18/0.45 tff(102,plain,
% 0.18/0.45 (![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))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.18/0.45 tff(103,plain,
% 0.18/0.45 (((~![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))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(104,plain,
% 0.18/0.45 ((~![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))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 ((~![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)))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 (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)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[105, 102, 41])).
% 0.18/0.46 tff(107,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[106, 89, 27])).
% 0.18/0.46 % SZS output end Proof
%------------------------------------------------------------------------------