%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP023+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:11:33 AM UTC 2025
% Result : Theorem 20.49s 20.75s
% Output : Proof 20.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP023+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 Jun 19 18:22:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 20.49/20.75 % SZS status Theorem
% 20.49/20.75 % SZS output start Proof
% 20.49/20.75 tff(p_type, type, (
% 20.49/20.75 p: $i > $o)).
% 20.49/20.75 tff(s_type, type, (
% 20.49/20.75 s: ( $i * $i ) > $i)).
% 20.49/20.75 tff(c_2Epred__set_2ESUBSET_2E2_type, type, (
% 20.49/20.75 c_2Epred__set_2ESUBSET_2E2: ( $i * $i ) > $i)).
% 20.49/20.75 tff(c_2Ereal__topology_2Ecball_2E1_type, type, (
% 20.49/20.75 c_2Ereal__topology_2Ecball_2E1: $i > $i)).
% 20.49/20.75 tff(c_2Epair_2E_2C_2E2_type, type, (
% 20.49/20.75 c_2Epair_2E_2C_2E2: ( $i * $i ) > $i)).
% 20.49/20.75 tff(tptp_fun_V1e_2E0_4_type, type, (
% 20.49/20.75 tptp_fun_V1e_2E0_4: $i)).
% 20.49/20.75 tff(tyop_2Erealax_2Ereal_type, type, (
% 20.49/20.75 tyop_2Erealax_2Ereal: $i)).
% 20.49/20.75 tff(tptp_fun_V0x_2E0_5_type, type, (
% 20.49/20.75 tptp_fun_V0x_2E0_5: $i)).
% 20.49/20.75 tff(tyop_2Epair_2Eprod_type, type, (
% 20.49/20.75 tyop_2Epair_2Eprod: ( $i * $i ) > $i)).
% 20.49/20.75 tff(tyop_2Emin_2Efun_type, type, (
% 20.49/20.75 tyop_2Emin_2Efun: ( $i * $i ) > $i)).
% 20.49/20.75 tff(tyop_2Emin_2Ebool_type, type, (
% 20.49/20.75 tyop_2Emin_2Ebool: $i)).
% 20.49/20.75 tff(c_2Ereal__topology_2Eball_2E1_type, type, (
% 20.49/20.75 c_2Ereal__topology_2Eball_2E1: $i > $i)).
% 20.49/20.75 tff(c_2Ereal__topology_2Ebounded__def_2E1_type, type, (
% 20.49/20.75 c_2Ereal__topology_2Ebounded__def_2E1: $i > $i)).
% 20.49/20.75 tff(1,plain,
% 20.49/20.75 (^[V0x_2E0: $i, V1e_2E0: $i] : refl(p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))))),
% 20.49/20.75 inference(bind,[status(th)],[])).
% 20.49/20.75 tff(2,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))) <=> ![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(quant_intro,[status(thm)],[1])).
% 20.49/20.75 tff(3,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))) <=> ![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(rewrite,[status(thm)],[])).
% 20.49/20.75 tff(4,axiom,(![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBALL__SUBSET__CBALL')).
% 20.49/20.75 tff(5,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 20.49/20.75 tff(6,plain,(
% 20.49/20.75 ![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(skolemize,[status(sab)],[5])).
% 20.49/20.75 tff(7,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 20.49/20.75 tff(8,plain,
% 20.49/20.75 ((~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))) | p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))),
% 20.49/20.75 inference(quant_inst,[status(thm)],[])).
% 20.49/20.75 tff(9,plain,
% 20.49/20.75 (p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))),
% 20.49/20.75 inference(unit_resolution,[status(thm)],[8, 7])).
% 20.49/20.75 tff(10,plain,
% 20.49/20.75 (^[V0x_2E0: $i, V1e_2E0: $i] : refl(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))) <=> p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))))),
% 20.49/20.75 inference(bind,[status(th)],[])).
% 20.49/20.75 tff(11,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))) <=> ![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(quant_intro,[status(thm)],[10])).
% 20.49/20.75 tff(12,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))) <=> ![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(rewrite,[status(thm)],[])).
% 20.49/20.75 tff(13,axiom,(![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBOUNDED__CBALL')).
% 20.49/20.75 tff(14,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(modus_ponens,[status(thm)],[13, 12])).
% 20.49/20.75 tff(15,plain,(
% 20.49/20.75 ![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(skolemize,[status(sab)],[14])).
% 20.49/20.75 tff(16,plain,
% 20.49/20.75 (![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(modus_ponens,[status(thm)],[15, 11])).
% 20.49/20.75 tff(17,plain,
% 20.49/20.75 ((~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))) | p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))),
% 20.49/20.75 inference(quant_inst,[status(thm)],[])).
% 20.49/20.75 tff(18,plain,
% 20.49/20.75 (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))),
% 20.49/20.75 inference(unit_resolution,[status(thm)],[17, 16])).
% 20.49/20.75 tff(19,plain,
% 20.49/20.75 ((~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))) <=> (~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0)))))))))),
% 20.49/20.75 inference(rewrite,[status(thm)],[])).
% 20.49/20.75 tff(20,axiom,(~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBOUNDED__BALL')).
% 20.49/20.75 tff(21,plain,
% 20.49/20.75 (~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(modus_ponens,[status(thm)],[20, 19])).
% 20.49/20.75 tff(22,plain,
% 20.49/20.75 (~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.75 inference(modus_ponens,[status(thm)],[21, 19])).
% 20.49/20.75 tff(23,plain,
% 20.49/20.75 (~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.76 inference(modus_ponens,[status(thm)],[22, 19])).
% 20.49/20.76 tff(24,plain,
% 20.49/20.76 (~![V0x_2E0: $i, V1e_2E0: $i] : p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0), s(tyop_2Erealax_2Ereal, V1e_2E0))))))))),
% 20.49/20.76 inference(modus_ponens,[status(thm)],[23, 19])).
% 20.49/20.76 tff(25,plain,(
% 20.49/20.76 ~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))),
% 20.49/20.76 inference(skolemize,[status(sab)],[24])).
% 20.49/20.76 tff(26,plain,
% 20.49/20.76 (^[V0s_2E0: $i, V1t_2E0: $i] : refl((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))),
% 20.49/20.76 inference(bind,[status(th)],[])).
% 20.49/20.76 tff(27,plain,
% 20.49/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))) <=> ![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))),
% 20.49/20.76 inference(quant_intro,[status(thm)],[26])).
% 20.49/20.76 tff(28,plain,
% 20.49/20.76 (^[V0s_2E0: $i, V1t_2E0: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) <=> (~((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))), ((~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))) <=> (~(~((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))))), rewrite((~(~((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))) <=> ((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))), ((~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))) <=> ((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))), ((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | ((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))))), rewrite((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | ((~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))), ((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))))),
% 20.59/20.76 inference(bind,[status(th)],[])).
% 20.59/20.76 tff(29,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> ![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))),
% 20.59/20.76 inference(quant_intro,[status(thm)],[28])).
% 20.59/20.76 tff(30,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) <=> ![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))),
% 20.59/20.76 inference(rewrite,[status(thm)],[])).
% 20.59/20.76 tff(31,plain,
% 20.59/20.76 (^[V0s_2E0: $i, V1t_2E0: $i] : rewrite(((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) => p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0))))) <=> (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))))),
% 20.59/20.76 inference(bind,[status(th)],[])).
% 20.59/20.76 tff(32,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : ((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) => p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0))))) <=> ![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))),
% 20.59/20.76 inference(quant_intro,[status(thm)],[31])).
% 20.59/20.76 tff(33,axiom,(![V0s_2E0: $i, V1t_2E0: $i] : ((p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) => p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Ereal__topology_2EBOUNDED__SUBSET')).
% 20.59/20.76 tff(34,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))),
% 20.59/20.76 inference(modus_ponens,[status(thm)],[33, 32])).
% 20.59/20.76 tff(35,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))),
% 20.59/20.76 inference(modus_ponens,[status(thm)],[34, 30])).
% 20.59/20.76 tff(36,plain,(
% 20.59/20.76 ![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~(p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))) & p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0)))))))),
% 20.59/20.76 inference(skolemize,[status(sab)],[35])).
% 20.59/20.76 tff(37,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))),
% 20.59/20.76 inference(modus_ponens,[status(thm)],[36, 29])).
% 20.59/20.76 tff(38,plain,
% 20.59/20.76 (![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))),
% 20.59/20.76 inference(modus_ponens,[status(thm)],[37, 27])).
% 20.59/20.76 tff(39,plain,
% 20.59/20.76 (((~![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) | (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))))) <=> ((~![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) | p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))))),
% 20.59/20.76 inference(rewrite,[status(thm)],[])).
% 20.59/20.76 tff(40,plain,
% 20.59/20.76 ((~![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) | (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))))),
% 20.66/20.88 inference(quant_inst,[status(thm)],[])).
% 20.66/20.88 tff(41,plain,
% 20.66/20.88 ((~![V0s_2E0: $i, V1t_2E0: $i] : (p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0)))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V0s_2E0), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), V1t_2E0))))))) | p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4)))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))))))) | (~p(s(tyop_2Emin_2Ebool, c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4))))), s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal, tyop_2Emin_2Ebool), c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal, V0x_2E0!5), s(tyop_2Erealax_2Ereal, V1e_2E0!4)))))))))),
% 20.66/20.88 inference(modus_ponens,[status(thm)],[40, 39])).
% 20.66/20.88 tff(42,plain,
% 20.66/20.88 ($false),
% 20.66/20.88 inference(unit_resolution,[status(thm)],[41, 38, 25, 18, 9])).
% 20.66/20.88 % SZS output end Proof
% 20.66/20.88 % E exiting
%------------------------------------------------------------------------------