%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP023^1 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:24:47 AM UTC 2026 % Result : Theorem 0.40s 0.70s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : ITP023^1 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n009.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 04:04:59 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.54 %----Proving TH0 % 0.40/0.70 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.70 % SZS status Theorem % 0.40/0.70 % SZS output start Proof % 0.40/0.70 ( % 0.40/0.70 (declare-sort tptp.mono_2Etyop_2Erealax_2Ereal 0) % 0.40/0.70 (declare-sort tptp.u 0) % 0.40/0.70 (declare-sort tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 0) % 0.40/0.70 (declare-sort tptp.du 0) % 0.40/0.70 (declare-sort tptp.d 0) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ebool_2EF Bool) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ebool_2ET Bool) % 0.40/0.70 (declare-const tptp.c_2Epred__set_2ESUBSET_2E2 (-> tptp.du tptp.du tptp.u)) % 0.40/0.70 (declare-const tptp.c_2Epair_2E_2C_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.c_2Ebool_2E_3F_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.c_2Emin_2E_3D_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Erealax_2Ereal (-> tptp.mono_2Etyop_2Erealax_2Ereal tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Erealax_2Ereal (-> tptp.du tptp.mono_2Etyop_2Erealax_2Ereal)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (-> tptp.du tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (-> tptp.du tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 (-> tptp.du tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) % 0.40/0.70 (declare-const tptp.c_2Epred__set_2ESUBSET_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Ebool (-> tptp.du Bool)) % 0.40/0.70 (declare-const tptp.tyop_2Emin_2Ebool tptp.d) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 (-> tptp.du tptp.mono_2Etyop_2Erealax_2Ereal Bool)) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ereal__topology_2Ecball (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Erealax_2Ereal Bool)) % 0.40/0.70 (declare-const tptp.combin_s_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Emin_2E_3D_3D_3E (-> Bool Bool Bool)) % 0.40/0.70 (declare-const tptp.tyop_2Erealax_2Ereal tptp.d) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ereal__topology_2Ebounded__def (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool)) % 0.40/0.70 (declare-const tptp.combin_k_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (-> tptp.du Bool Bool)) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ereal__topology_2Eball (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Erealax_2Ereal Bool)) % 0.40/0.70 (declare-const tptp.combin_i_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.app_2E2 (-> tptp.du tptp.du tptp.u)) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ebool_2E_5C_2F (-> Bool Bool Bool)) % 0.40/0.70 (declare-const tptp.c_2Ebool_2E_21_2E0 tptp.u) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ebool_2E_7E (-> Bool Bool)) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool)) % 0.40/0.70 (declare-const tptp.s (-> tptp.d tptp.u tptp.du)) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal (-> tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) % 0.40/0.70 (declare-const tptp.tyop_2Emin_2Efun (-> tptp.d tptp.d tptp.d)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 (-> tptp.du (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool)) % 0.40/0.70 (declare-const tptp.c_2Ebool_2E_21_2E1 (-> tptp.du tptp.u)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Ebool (-> Bool tptp.u)) % 0.40/0.70 (declare-const tptp.c_2Epair_2E_2C_2E2 (-> tptp.du tptp.du tptp.u)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (-> (-> Bool Bool) tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (-> tptp.du Bool Bool Bool)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (-> (-> Bool Bool Bool) tptp.u)) % 0.40/0.70 (declare-const tptp.c_2Emin_2E_3D_2E2 (-> tptp.du tptp.du tptp.u)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 (-> (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool) tptp.u)) % 0.40/0.70 (declare-const tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 (-> tptp.du (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool)) % 0.40/0.70 (declare-const tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 (-> (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool) tptp.u)) % 0.40/0.70 (declare-const tptp.mono_2Ec_2Ebool_2E_2F_5C (-> Bool Bool Bool)) % 0.40/0.70 (declare-const tptp.tyop_2Epair_2Eprod (-> tptp.d tptp.d tptp.d)) % 0.40/0.70 (declare-const tptp.j_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 (-> tptp.du tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Erealax_2Ereal Bool)) % 0.40/0.70 (declare-const tptp.c_2Ebool_2E_3F_2E1 (-> tptp.du tptp.u)) % 0.40/0.70 (declare-const tptp.i_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 (-> (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Erealax_2Ereal Bool) tptp.u)) % 0.40/0.70 (define @t1 () (@var "V1g_2E0" tptp.u)) % 0.40/0.70 (define @t2 () (@var "A_27b" tptp.d)) % 0.40/0.70 (define @t3 () (@var "A_27a" tptp.d)) % 0.40/0.70 (define @t4 () (_ tptp.tyop_2Emin_2Efun @t3)) % 0.40/0.70 (define @t5 () (_ @t4 @t2)) % 0.40/0.70 (define @t6 () (_ tptp.s @t5)) % 0.40/0.70 (define @t7 () (_ @t6 @t1)) % 0.40/0.70 (define @t8 () (@var "V0f_2E0" tptp.u)) % 0.40/0.70 (define @t9 () (_ @t6 @t8)) % 0.40/0.70 (define @t10 () (@var "V2x_2E0" tptp.u)) % 0.40/0.70 (define @t11 () (_ tptp.s @t3)) % 0.40/0.70 (define @t12 () (_ @t11 @t10)) % 0.40/0.70 (define @t13 () (_ tptp.s @t2)) % 0.40/0.70 (define @t14 () (_ @t13 (_ (_ tptp.app_2E2 @t7) @t12))) % 0.40/0.70 (define @t15 () (@list @t10)) % 0.40/0.70 (define @t16 () (@var "V0x_2E0" tptp.u)) % 0.40/0.70 (define @t17 () (_ @t11 @t16)) % 0.40/0.70 (define @t18 () (@var "V1y_2E0" tptp.u)) % 0.40/0.70 (define @t19 () (_ tptp.tyop_2Emin_2Efun @t2)) % 0.40/0.70 (define @t20 () (_ @t19 @t3)) % 0.40/0.70 (define @t21 () (@var "A_27c" tptp.d)) % 0.40/0.70 (define @t22 () (_ @t19 @t21)) % 0.40/0.70 (define @t23 () (_ @t4 @t22)) % 0.40/0.70 (define @t24 () (_ (_ tptp.s @t23) @t8)) % 0.40/0.70 (define @t25 () (_ tptp.s @t21)) % 0.40/0.70 (define @t26 () (_ @t4 @t21)) % 0.40/0.70 (define @t27 () (_ (_ tptp.tyop_2Emin_2Efun @t5) @t26)) % 0.40/0.70 (define @t28 () (@var "V1" Bool)) % 0.40/0.70 (define @t29 () (@var "V0" Bool)) % 0.40/0.70 (define @t30 () (@list @t29 @t28)) % 0.40/0.70 (define @t31 () (@list @t29)) % 0.40/0.70 (define @t32 () (@var "V1_2E0" tptp.u)) % 0.40/0.70 (define @t33 () (_ @t11 @t32)) % 0.40/0.70 (define @t34 () (@var "V0_2E0" tptp.u)) % 0.40/0.70 (define @t35 () (_ @t11 @t34)) % 0.40/0.70 (define @t36 () (_ tptp.s tptp.tyop_2Emin_2Ebool)) % 0.40/0.70 (define @t37 () (@var "V1x_2E0" tptp.u)) % 0.40/0.70 (define @t38 () (_ @t11 @t37)) % 0.40/0.70 (define @t39 () (_ @t4 tptp.tyop_2Emin_2Ebool)) % 0.40/0.70 (define @t40 () (_ tptp.s @t39)) % 0.40/0.70 (define @t41 () (_ @t40 @t8)) % 0.40/0.70 (define @t42 () (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ (_ tptp.app_2E2 @t41) @t38)))) % 0.40/0.70 (define @t43 () (@list @t37)) % 0.40/0.70 (define @t44 () (@list @t3 @t8)) % 0.40/0.70 (define @t45 () (_ @t36 @t34)) % 0.40/0.70 (define @t46 () (@list @t34)) % 0.40/0.70 (define @t47 () (_ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool)) % 0.40/0.70 (define @t48 () (_ @t47 tptp.tyop_2Emin_2Ebool)) % 0.40/0.70 (define @t49 () (_ tptp.s @t48)) % 0.40/0.70 (define @t50 () (_ @t49 @t34)) % 0.40/0.70 (define @t51 () (_ tptp.s (_ @t47 @t48))) % 0.40/0.70 (define @t52 () (_ @t51 @t34)) % 0.40/0.70 (define @t53 () (_ tptp.tyop_2Emin_2Efun tptp.tyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t54 () (_ @t53 tptp.tyop_2Emin_2Ebool)) % 0.40/0.70 (define @t55 () (_ tptp.tyop_2Emin_2Efun @t54)) % 0.40/0.70 (define @t56 () (_ @t55 tptp.tyop_2Emin_2Ebool)) % 0.40/0.70 (define @t57 () (_ tptp.s @t56)) % 0.40/0.70 (define @t58 () (_ @t57 @t34)) % 0.40/0.70 (define @t59 () (_ tptp.s (_ @t55 @t56))) % 0.40/0.70 (define @t60 () (_ @t59 @t34)) % 0.40/0.70 (define @t61 () (_ (_ tptp.tyop_2Epair_2Eprod tptp.tyop_2Erealax_2Ereal) tptp.tyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t62 () (_ tptp.s (_ (_ tptp.tyop_2Emin_2Efun @t61) @t54))) % 0.40/0.70 (define @t63 () (_ @t62 @t34)) % 0.40/0.70 (define @t64 () (_ tptp.s @t54)) % 0.40/0.70 (define @t65 () (_ @t64 @t34)) % 0.40/0.70 (define @t66 () (_ @t53 @t61)) % 0.40/0.70 (define @t67 () (_ tptp.s (_ @t53 @t66))) % 0.40/0.70 (define @t68 () (_ @t67 @t34)) % 0.40/0.70 (define @t69 () (_ tptp.s @t66)) % 0.40/0.70 (define @t70 () (_ @t69 @t34)) % 0.40/0.70 (define @t71 () (_ tptp.s @t61)) % 0.40/0.70 (define @t72 () (_ @t71 @t34)) % 0.40/0.70 (define @t73 () (_ tptp.s tptp.tyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t74 () (_ @t73 @t34)) % 0.40/0.70 (define @t75 () (@var "V0" (-> Bool Bool))) % 0.40/0.70 (define @t76 () (_ @t49 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t75))) % 0.40/0.70 (define @t77 () (@var "V0" (-> Bool Bool Bool))) % 0.40/0.70 (define @t78 () (_ @t51 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @t77))) % 0.40/0.70 (define @t79 () (@var "V0" (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool))) % 0.40/0.70 (define @t80 () (_ @t57 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @t79))) % 0.40/0.70 (define @t81 () (@var "V0" (-> (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool) Bool))) % 0.40/0.70 (define @t82 () (_ @t59 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @t81))) % 0.40/0.70 (define @t83 () (@var "V0" (-> tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 tptp.mono_2Etyop_2Erealax_2Ereal Bool))) % 0.40/0.70 (define @t84 () (_ @t62 (_ tptp.i_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 @t83))) % 0.40/0.70 (define @t85 () (@var "V0" (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool))) % 0.40/0.70 (define @t86 () (_ @t64 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @t85))) % 0.40/0.70 (define @t87 () (@var "V0" (-> tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29))) % 0.40/0.70 (define @t88 () (_ @t67 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @t87))) % 0.40/0.70 (define @t89 () (@var "V0" (-> tptp.mono_2Etyop_2Erealax_2Ereal tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29))) % 0.40/0.70 (define @t90 () (_ @t69 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @t89))) % 0.40/0.70 (define @t91 () (@var "V0" tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) % 0.40/0.70 (define @t92 () (@var "V0" tptp.mono_2Etyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t93 () (_ @t73 (_ tptp.i_mono_2Etyop_2Erealax_2Ereal @t92))) % 0.40/0.70 (define @t94 () (@var "X0_2E0" tptp.u)) % 0.40/0.70 (define @t95 () (_ @t40 @t94)) % 0.40/0.70 (define @t96 () (_ tptp.s (_ (_ tptp.tyop_2Emin_2Efun @t39) tptp.tyop_2Emin_2Ebool))) % 0.40/0.70 (define @t97 () (@list @t3 @t94)) % 0.40/0.70 (define @t98 () (@var "X1_2E0" tptp.u)) % 0.40/0.70 (define @t99 () (_ @t11 @t98)) % 0.40/0.70 (define @t100 () (_ @t11 @t94)) % 0.40/0.70 (define @t101 () (_ @t36 (_ tptp.i_mono_2Etyop_2Emin_2Ebool @t28))) % 0.40/0.70 (define @t102 () (_ @t75 @t28)) % 0.40/0.70 (define @t103 () (@list @t75 @t28)) % 0.40/0.70 (define @t104 () (_ @t77 @t28)) % 0.40/0.70 (define @t105 () (@list @t77 @t28)) % 0.40/0.70 (define @t106 () (@var "V1" (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool))) % 0.40/0.70 (define @t107 () (_ @t64 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @t106))) % 0.40/0.70 (define @t108 () (_ @t79 @t106)) % 0.40/0.70 (define @t109 () (@list @t79 @t106)) % 0.40/0.70 (define @t110 () (_ @t81 @t106)) % 0.40/0.70 (define @t111 () (@list @t81 @t106)) % 0.40/0.70 (define @t112 () (@var "V1" tptp.mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29)) % 0.40/0.70 (define @t113 () (_ @t83 @t112)) % 0.40/0.70 (define @t114 () (@list @t83 @t112)) % 0.40/0.70 (define @t115 () (@var "V1" tptp.mono_2Etyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t116 () (_ @t73 (_ tptp.i_mono_2Etyop_2Erealax_2Ereal @t115))) % 0.40/0.70 (define @t117 () (_ @t87 @t115)) % 0.40/0.70 (define @t118 () (@list @t87 @t115)) % 0.40/0.70 (define @t119 () (_ @t89 @t115)) % 0.40/0.70 (define @t120 () (@list @t89 @t115)) % 0.40/0.70 (define @t121 () (@var "V1t2" Bool)) % 0.40/0.70 (define @t122 () (@var "V0t1" Bool)) % 0.40/0.70 (define @t123 () (@var "V0t" Bool)) % 0.40/0.70 (define @t124 () (not @t123)) % 0.40/0.70 (define @t125 () (=> @t123 tptp.mono_2Ec_2Ebool_2EF)) % 0.40/0.70 (define @t126 () (@list @t123)) % 0.40/0.70 (define @t127 () (forall @t126 (= (not @t124) @t123))) % 0.40/0.70 (define @t128 () (_ @t11 @t18)) % 0.40/0.70 (define @t129 () (@var "V0P_2E0" tptp.u)) % 0.40/0.70 (define @t130 () (_ tptp.app_2E2 (_ @t40 @t129))) % 0.40/0.70 (define @t131 () (@var "V2C" Bool)) % 0.40/0.70 (define @t132 () (@var "V1B" Bool)) % 0.40/0.70 (define @t133 () (@var "V0A" Bool)) % 0.40/0.70 (define @t134 () (or @t133 @t132 @t131)) % 0.40/0.70 (define @t135 () (or @t133 @t132)) % 0.40/0.70 (define @t136 () (@list @t133 @t132)) % 0.40/0.70 (define @t137 () (not @t132)) % 0.40/0.70 (define @t138 () (not @t133)) % 0.40/0.70 (define @t139 () (@var "V1e" tptp.mono_2Etyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t140 () (@var "V0x" tptp.mono_2Etyop_2Erealax_2Ereal)) % 0.40/0.70 (define @t141 () (_ (_ tptp.mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @t140) @t139)) % 0.40/0.70 (define @t142 () (_ tptp.mono_2Ec_2Ereal__topology_2Ecball @t141)) % 0.40/0.70 (define @t143 () (_ tptp.mono_2Ec_2Ereal__topology_2Eball @t141)) % 0.40/0.70 (define @t144 () (_ (_ tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t143) @t142)) % 0.40/0.70 (define @t145 () (@list @t140 @t139)) % 0.40/0.70 (define @t146 () (forall @t145 @t144)) % 0.40/0.70 (define @t147 () (@var "V0s" (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool))) % 0.40/0.70 (define @t148 () (_ tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t147)) % 0.40/0.70 (define @t149 () (@var "V1t" (-> tptp.mono_2Etyop_2Erealax_2Ereal Bool))) % 0.40/0.70 (define @t150 () (_ (_ tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t147) @t149)) % 0.40/0.70 (define @t151 () (_ tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t149)) % 0.40/0.70 (define @t152 () (and @t151 @t150)) % 0.40/0.70 (define @t153 () (@list @t147 @t149)) % 0.40/0.70 (define @t154 () (forall @t153 (=> @t152 @t148))) % 0.40/0.70 (define @t155 () (_ tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t142)) % 0.40/0.70 (define @t156 () (forall @t145 @t155)) % 0.40/0.70 (define @t157 () (=> @t138 tptp.mono_2Ec_2Ebool_2EF)) % 0.40/0.70 (define @t158 () (@list @t133)) % 0.40/0.70 (define @t159 () (@var "V0B" Bool)) % 0.40/0.70 (define @t160 () (=> (not @t159) tptp.mono_2Ec_2Ebool_2EF)) % 0.40/0.70 (define @t161 () (@var "V1A" Bool)) % 0.40/0.70 (define @t162 () (@list @t159 @t161)) % 0.40/0.70 (define @t163 () (@var "V2p" Bool)) % 0.40/0.70 (define @t164 () (not @t163)) % 0.40/0.70 (define @t165 () (@var "V1q" Bool)) % 0.40/0.70 (define @t166 () (not @t165)) % 0.40/0.70 (define @t167 () (@var "V0r" Bool)) % 0.40/0.70 (define @t168 () (not @t167)) % 0.40/0.70 (define @t169 () (@list @t167 @t165 @t163)) % 0.40/0.70 (define @t170 () (or @t163 @t168)) % 0.40/0.70 (define @t171 () (@var "V1p" Bool)) % 0.40/0.70 (define @t172 () (@var "V0q" Bool)) % 0.40/0.70 (define @t173 () (not @t172)) % 0.40/0.70 (define @t174 () (_ tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t143)) % 0.40/0.70 (define @t175 () (forall @t145 @t174)) % 0.40/0.70 (define @t176 () (not @t175)) % 0.40/0.70 (define @t177 () (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t147)) % 0.40/0.70 (define @t178 () (tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t147 @t149)) % 0.40/0.70 (define @t179 () (not @t150)) % 0.40/0.70 (define @t180 () (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t149)) % 0.40/0.70 (define @t181 () (not @t151)) % 0.40/0.70 (define @t182 () (or @t181 @t179 @t148)) % 0.40/0.70 (define @t183 () (tptp.mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @t140 @t139)) % 0.40/0.70 (define @t184 () (_ tptp.mono_2Ec_2Ereal__topology_2Ecball @t183)) % 0.40/0.70 (define @t185 () (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t184)) % 0.40/0.70 (define @t186 () (_ tptp.mono_2Ec_2Ereal__topology_2Eball @t183)) % 0.40/0.70 (define @t187 () (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t186)) % 0.40/0.70 (define @t188 () (forall @t145 @t187)) % 0.40/0.70 (define @t189 () (@quantifiers_skolemize @t188 1)) % 0.40/0.70 (define @t190 () (@quantifiers_skolemize @t188 0)) % 0.40/0.70 (define @t191 () (@list @t190 @t189)) % 0.40/0.70 (define @t192 () (tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t186 @t184)) % 0.40/0.70 (define @t193 () (tptp.mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @t190 @t189)) % 0.40/0.70 (define @t194 () (_ tptp.mono_2Ec_2Ereal__topology_2Eball @t193)) % 0.40/0.70 (define @t195 () (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t194)) % 0.40/0.70 (define @t196 () (_ tptp.mono_2Ec_2Ereal__topology_2Ecball @t193)) % 0.40/0.70 (define @t197 () (tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t194 @t196)) % 0.40/0.70 (define @t198 () (not @t197)) % 0.40/0.70 (define @t199 () (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t196)) % 0.40/0.70 (define @t200 () (not @t199)) % 0.40/0.70 (define @t201 () (or @t200 @t198 @t195)) % 0.40/0.70 (define @t202 () (not @t201)) % 0.40/0.70 (define @t203 () (forall @t153 (or (not @t180) (not @t178) @t177))) % 0.40/0.70 (assume @p1 (forall (@list @t3 @t2 @t8 @t1) (=> (forall @t15 (= (_ @t13 (_ (_ tptp.app_2E2 @t9) @t12)) @t14)) (= @t9 @t7)))) % 0.40/0.70 (assume @p2 (forall (@list @t3 @t16) (= (_ @t11 (_ (_ tptp.app_2E2 (_ (_ tptp.s (_ @t4 @t3)) tptp.combin_i_2E0)) @t17)) @t17))) % 0.40/0.70 (assume @p3 (forall (@list @t3 @t2 @t16 @t18) (= (_ @t11 (_ (_ tptp.app_2E2 (_ (_ tptp.s @t20) (_ (_ tptp.app_2E2 (_ (_ tptp.s (_ @t4 @t20)) tptp.combin_k_2E0)) @t17))) (_ @t13 @t18))) @t17))) % 0.40/0.70 (assume @p4 (forall (@list @t3 @t2 @t21 @t8 @t1 @t10) (= (_ @t25 (_ (_ tptp.app_2E2 (_ (_ tptp.s @t26) (_ (_ tptp.app_2E2 (_ (_ tptp.s @t27) (_ (_ tptp.app_2E2 (_ (_ tptp.s (_ (_ tptp.tyop_2Emin_2Efun @t23) @t27)) tptp.combin_s_2E0)) @t24))) @t7))) @t12)) (_ @t25 (_ (_ tptp.app_2E2 (_ (_ tptp.s @t22) (_ (_ tptp.app_2E2 @t24) @t12))) @t14))))) % 0.40/0.70 (assume @p5 (forall @t30 (= (_ (_ tptp.mono_2Ec_2Ebool_2E_2F_5C @t29) @t28) (and @t29 @t28)))) % 0.40/0.70 (assume @p6 (forall @t30 (= (_ (_ tptp.mono_2Ec_2Ebool_2E_5C_2F @t29) @t28) (or @t29 @t28)))) % 0.40/0.70 (assume @p7 (forall @t31 (= (_ tptp.mono_2Ec_2Ebool_2E_7E @t29) (not @t29)))) % 0.40/0.70 (assume @p8 (forall @t30 (= (_ (_ tptp.mono_2Ec_2Emin_2E_3D_3D_3E @t29) @t28) (=> @t29 @t28)))) % 0.40/0.70 (assume @p9 (forall (@list @t3 @t34 @t32) (= (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ (_ tptp.c_2Emin_2E_3D_2E2 @t35) @t33))) (= @t35 @t33)))) % 0.40/0.70 (assume @p10 (forall @t44 (= (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ tptp.c_2Ebool_2E_21_2E1 @t41))) (forall @t43 @t42)))) % 0.40/0.70 (assume @p11 (forall @t44 (= (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ tptp.c_2Ebool_2E_3F_2E1 @t41))) (exists @t43 @t42)))) % 0.40/0.70 (assume @p12 (forall @t46 (= (_ @t36 (_ tptp.i_mono_2Etyop_2Emin_2Ebool (_ tptp.j_mono_2Etyop_2Emin_2Ebool @t45))) @t45))) % 0.40/0.70 (assume @p13 (forall @t46 (= (_ @t49 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t50))) @t50))) % 0.40/0.70 (assume @p14 (forall @t46 (= (_ @t51 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @t52))) @t52))) % 0.40/0.70 (assume @p15 (forall @t46 (= (_ @t57 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @t58))) @t58))) % 0.40/0.70 (assume @p16 (forall @t46 (= (_ @t59 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @t60))) @t60))) % 0.40/0.70 (assume @p17 (forall @t46 (= (_ @t62 (_ tptp.i_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 (_ tptp.j_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 @t63))) @t63))) % 0.40/0.70 (assume @p18 (forall @t46 (= (_ @t64 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @t65))) @t65))) % 0.40/0.70 (assume @p19 (forall @t46 (= (_ @t67 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @t68))) @t68))) % 0.40/0.70 (assume @p20 (forall @t46 (= (_ @t69 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @t70))) @t70))) % 0.40/0.70 (assume @p21 (forall @t46 (= (_ @t71 (_ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (_ tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @t72))) @t72))) % 0.40/0.70 (assume @p22 (forall @t46 (= (_ @t73 (_ tptp.i_mono_2Etyop_2Erealax_2Ereal (_ tptp.j_mono_2Etyop_2Erealax_2Ereal @t74))) @t74))) % 0.40/0.70 (assume @p23 (forall @t31 (= (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ tptp.i_mono_2Etyop_2Emin_2Ebool @t29))) @t29))) % 0.40/0.70 (assume @p24 (forall (@list @t75) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t76) @t75))) % 0.40/0.70 (assume @p25 (forall (@list @t77) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @t78) @t77))) % 0.40/0.70 (assume @p26 (forall (@list @t79) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @t80) @t79))) % 0.40/0.70 (assume @p27 (forall (@list @t81) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @t82) @t81))) % 0.40/0.70 (assume @p28 (forall (@list @t83) (= (_ tptp.j_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 @t84) @t83))) % 0.40/0.70 (assume @p29 (forall (@list @t85) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @t86) @t85))) % 0.40/0.70 (assume @p30 (forall (@list @t87) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 @t88) @t87))) % 0.40/0.70 (assume @p31 (forall (@list @t89) (= (_ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @t90) @t89))) % 0.40/0.70 (assume @p32 (forall (@list @t91) (= (_ tptp.j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (_ @t71 (_ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @t91))) @t91))) % 0.40/0.70 (assume @p33 (forall (@list @t92) (= (_ tptp.j_mono_2Etyop_2Erealax_2Ereal @t93) @t92))) % 0.40/0.70 (assume @p34 (forall @t97 (= (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ tptp.c_2Ebool_2E_21_2E1 @t95))) (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ (_ tptp.app_2E2 (_ @t96 tptp.c_2Ebool_2E_21_2E0)) @t95)))))) % 0.40/0.70 (assume @p35 (forall (@list @t3 @t94 @t98) (= (= @t100 @t99) (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ (_ tptp.app_2E2 (_ @t40 (_ (_ tptp.app_2E2 (_ (_ tptp.s (_ @t4 @t39)) tptp.c_2Emin_2E_3D_2E0)) @t100))) @t99)))))) % 0.40/0.70 (assume @p36 (forall @t97 (= (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ tptp.c_2Ebool_2E_3F_2E1 @t95))) (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ (_ tptp.app_2E2 (_ @t96 tptp.c_2Ebool_2E_3F_2E0)) @t95)))))) % 0.40/0.70 (assume @p37 (forall @t103 (= (_ @t36 (_ tptp.i_mono_2Etyop_2Emin_2Ebool @t102)) (_ @t36 (_ (_ tptp.app_2E2 @t76) @t101))))) % 0.40/0.70 (assume @p38 (forall @t105 (= (_ @t49 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @t104)) (_ @t49 (_ (_ tptp.app_2E2 @t78) @t101))))) % 0.40/0.70 (assume @p39 (forall @t109 (= (_ @t36 (_ tptp.i_mono_2Etyop_2Emin_2Ebool @t108)) (_ @t36 (_ (_ tptp.app_2E2 @t80) @t107))))) % 0.40/0.70 (assume @p40 (forall @t111 (= (_ @t57 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @t110)) (_ @t57 (_ (_ tptp.app_2E2 @t82) @t107))))) % 0.40/0.70 (assume @p41 (forall @t114 (= (_ @t64 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @t113)) (_ @t64 (_ (_ tptp.app_2E2 @t84) (_ @t71 (_ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @t112))))))) % 0.40/0.70 (assume @p42 (forall @t118 (= (_ @t69 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @t117)) (_ @t69 (_ (_ tptp.app_2E2 @t88) @t116))))) % 0.40/0.70 (assume @p43 (forall @t120 (= (_ @t71 (_ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @t119)) (_ @t71 (_ (_ tptp.app_2E2 @t90) @t116))))) % 0.40/0.70 (assume @p44 (= (_ @t67 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29 tptp.mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal)) (_ @t67 tptp.c_2Epair_2E_2C_2E0))) % 0.40/0.70 (assume @p45 (forall (@list @t92 @t115) (= (_ @t71 (_ tptp.i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 (_ (_ tptp.mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @t92) @t115))) (_ @t71 (_ (_ tptp.c_2Epair_2E_2C_2E2 @t93) @t116))))) % 0.40/0.70 (assume @p46 (= (_ @t59 (_ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal)) (_ @t59 tptp.c_2Epred__set_2ESUBSET_2E0))) % 0.40/0.70 (assume @p47 (forall (@list @t85 @t106) (= (_ @t36 (_ tptp.i_mono_2Etyop_2Emin_2Ebool (_ (_ tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t85) @t106))) (_ @t36 (_ (_ tptp.c_2Epred__set_2ESUBSET_2E2 @t86) @t107))))) % 0.40/0.70 (assume @p48 (forall @t103 (= @t102 @t102))) % 0.40/0.70 (assume @p49 (forall @t105 (= @t104 @t104))) % 0.40/0.70 (assume @p50 (forall @t109 (= @t108 @t108))) % 0.40/0.70 (assume @p51 (forall @t111 (= @t110 @t110))) % 0.40/0.70 (assume @p52 (forall @t114 (= @t113 @t113))) % 0.40/0.70 (assume @p53 (forall @t118 (= @t117 @t117))) % 0.40/0.70 (assume @p54 (forall @t120 (= @t119 @t119))) % 0.40/0.70 (assume @p55 tptp.mono_2Ec_2Ebool_2ET) % 0.40/0.70 (assume @p56 (forall (@list @t122 @t121) (=> (=> @t122 @t121) (=> (=> @t121 @t122) (= @t122 @t121))))) % 0.40/0.70 (assume @p57 (forall @t126 (=> @t125 @t124))) % 0.40/0.70 (assume @p58 (forall @t126 (=> @t124 @t125))) % 0.40/0.70 (assume @p59 (forall @t126 (and (= (=> tptp.mono_2Ec_2Ebool_2ET @t123) @t123) (= (=> @t123 tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2ET) (= (=> tptp.mono_2Ec_2Ebool_2EF @t123) tptp.mono_2Ec_2Ebool_2ET) (= (=> @t123 @t123) tptp.mono_2Ec_2Ebool_2ET) (= @t125 @t124)))) % 0.40/0.70 (assume @p60 (and @t127 (= (not tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2EF) (= (not tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2ET))) % 0.40/0.70 (assume @p61 (forall (@list @t3 @t16 @t18) (= (= @t17 @t128) (= @t128 @t17)))) % 0.40/0.70 (assume @p62 (forall @t126 (and (= (= tptp.mono_2Ec_2Ebool_2ET @t123) @t123) (= (= @t123 tptp.mono_2Ec_2Ebool_2ET) @t123) (= (= tptp.mono_2Ec_2Ebool_2EF @t123) @t124) (= (= @t123 tptp.mono_2Ec_2Ebool_2EF) @t124)))) % 0.40/0.70 (assume @p63 (forall (@list @t3 @t129) (= (not (forall @t43 (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ @t130 @t38))))) (exists @t15 (not (_ tptp.j_mono_2Etyop_2Emin_2Ebool (_ @t36 (_ @t130 @t12)))))))) % 0.40/0.70 (assume @p64 (forall (@list @t133 @t132 @t131) (= @t134 @t134))) % 0.40/0.70 (assume @p65 (forall @t136 (= @t135 (or @t132 @t133)))) % 0.40/0.70 (assume @p66 (forall @t136 (and (= (not (and @t133 @t132)) (or @t138 @t137)) (= (not @t135) (and @t138 @t137))))) % 0.40/0.70 (assume @p67 @t146) % 0.40/0.70 (assume @p68 @t154) % 0.40/0.70 (assume @p69 @t156) % 0.40/0.70 (assume @p70 @t127) % 0.40/0.70 (assume @p71 (forall @t158 (=> @t133 @t157))) % 0.40/0.70 (assume @p72 (forall @t162 (= (=> (not (or @t161 @t159)) tptp.mono_2Ec_2Ebool_2EF) (=> (=> @t161 tptp.mono_2Ec_2Ebool_2EF) @t160)))) % 0.40/0.70 (assume @p73 (forall @t162 (= (=> (not (or (not @t161) @t159)) tptp.mono_2Ec_2Ebool_2EF) (=> @t161 @t160)))) % 0.40/0.70 (assume @p74 (forall @t158 (=> @t157 (=> (=> @t133 tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2EF)))) % 0.40/0.70 (assume @p75 (forall @t169 (= (= @t163 (= @t165 @t167)) (and (or @t163 @t165 @t167) (or @t163 @t168 @t166) (or @t165 @t168 @t164) (or @t167 @t166 @t164))))) % 0.40/0.70 (assume @p76 (forall @t169 (= (= @t163 (and @t165 @t167)) (and (or @t163 @t166 @t168) (or @t165 @t164) (or @t167 @t164))))) % 0.40/0.70 (assume @p77 (forall @t169 (= (= @t163 (or @t165 @t167)) (and (or @t163 @t166) @t170 (or @t165 @t167 @t164))))) % 0.40/0.70 (assume @p78 (forall @t169 (= (= @t163 (=> @t165 @t167)) (and (or @t163 @t165) @t170 (or @t166 @t167 @t164))))) % 0.40/0.70 (assume @p79 (forall (@list @t172 @t171) (= (= @t171 @t173) (and (or @t171 @t172) (or @t173 (not @t171)))))) % 0.40/0.70 (assume @p80 @t176) % 0.40/0.70 (assume @p81 true) % 0.40/0.70 (step @p82 :rule refl :args (@t177)) % 0.40/0.70 (step @p83 :rule refl :args (@t148)) % 0.40/0.70 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t148 @t177))) % 0.40/0.70 (step @p85 :rule symm :premises (@p84)) % 0.40/0.70 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.40/0.70 (step @p87 :rule refl :args (@t178)) % 0.40/0.70 (step @p88 :rule refl :args (@t150)) % 0.40/0.70 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t150 @t178))) % 0.40/0.70 (step @p90 :rule symm :premises (@p89)) % 0.40/0.70 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.40/0.70 (step @p92 :rule cong :premises (@p91) :args (@t179)) % 0.40/0.70 (step @p93 :rule refl :args (@t180)) % 0.40/0.70 (step @p94 :rule refl :args (@t151)) % 0.40/0.70 (step @p95 :rule cong :premises (@p94 @p93) :args ((= @t151 @t180))) % 0.40/0.70 (step @p96 :rule symm :premises (@p95)) % 0.40/0.70 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.40/0.70 (step @p98 :rule cong :premises (@p97) :args (@t181)) % 0.40/0.70 (step @p99 :rule nary_cong :premises (@p98 @p92 @p86) :args (@t182)) % 0.40/0.70 (step @p100 :rule cong :premises (@p99) :args ((forall @t153 @t182))) % 0.40/0.70 (step @p101 :rule aci_norm :args ((= (or (or @t181 @t179) @t148) @t182))) % 0.40/0.70 (step @p102 :rule bool-and-de-morgan :args (@t151 @t150 true)) % 0.40/0.70 (step @p103 :rule nary_cong :premises (@p102 @p83) :args ((or (not @t152) @t148))) % 0.40/0.70 (step @p104 :rule trans :premises (@p103 @p101)) % 0.40/0.70 (step @p105 :rule bool-impl-elim :args (@t152 @t148)) % 0.40/0.70 (step @p106 :rule trans :premises (@p105 @p104)) % 0.40/0.70 (step @p107 :rule cong :premises (@p106) :args (@t154)) % 0.40/0.70 (step @p108 :rule trans :premises (@p107 @p100)) % 0.40/0.70 (step @p109 :rule eq_resolve :premises (@p68 @p108)) % 0.40/0.70 (step @p110 :rule refl :args ((tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t142))) % 0.40/0.70 (step @p111 :rule refl :args (@t183)) % 0.40/0.70 (step @p112 :rule refl :args (tptp.mono_2Ec_2Ereal__topology_2Ecball)) % 0.40/0.70 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.40/0.70 (step @p114 :rule cong :premises (@p113) :args (@t185)) % 0.40/0.70 (step @p115 :rule trans :premises (@p114 @p110)) % 0.40/0.70 (step @p116 :rule refl :args (tptp.mono_2Ec_2Ereal__topology_2Ebounded__def)) % 0.40/0.70 (step @p117 :rule ho_cong :premises (@p116 @p113)) % 0.40/0.70 (step @p118 :rule cong :premises (@p117 @p115) :args ((= (_ tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t184) @t185))) % 0.40/0.70 (step @p119 :rule symm :premises (@p118)) % 0.40/0.70 (step @p120 :rule refl :args (@t155)) % 0.40/0.70 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.40/0.70 (step @p122 :rule refl :args (@t141)) % 0.40/0.70 (step @p123 :rule cong :premises (@p122 @p111) :args ((= @t141 @t183))) % 0.40/0.70 (step @p124 :rule symm :premises (@p123)) % 0.40/0.70 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.40/0.70 (step @p126 :rule ho_cong :premises (@p112 @p125)) % 0.40/0.70 (step @p127 :rule ho_cong :premises (@p116 @p126)) % 0.40/0.70 (step @p128 :rule trans :premises (@p127 @p121)) % 0.40/0.70 (step @p129 :rule cong :premises (@p128) :args (@t156)) % 0.40/0.70 (step @p130 :rule eq_resolve :premises (@p69 @p129)) % 0.40/0.70 (step @p131 :rule instantiate :premises (@p130) :args (@t191)) % 0.40/0.70 (step @p132 :rule refl :args ((tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t143 @t142))) % 0.40/0.70 (step @p133 :rule refl :args (tptp.mono_2Ec_2Ereal__topology_2Eball)) % 0.40/0.70 (step @p134 :rule ho_cong :premises (@p133 @p111)) % 0.40/0.70 (step @p135 :rule cong :premises (@p134 @p113) :args (@t192)) % 0.40/0.70 (step @p136 :rule trans :premises (@p135 @p132)) % 0.40/0.70 (step @p137 :rule refl :args (tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal)) % 0.40/0.70 (step @p138 :rule ho_cong :premises (@p137 @p134)) % 0.40/0.70 (step @p139 :rule ho_cong :premises (@p138 @p113)) % 0.40/0.70 (step @p140 :rule cong :premises (@p139 @p136) :args ((= (_ (_ tptp.mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @t186) @t184) @t192))) % 0.40/0.70 (step @p141 :rule symm :premises (@p140)) % 0.40/0.70 (step @p142 :rule refl :args (@t144)) % 0.40/0.70 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.40/0.70 (step @p144 :rule ho_cong :premises (@p133 @p125)) % 0.40/0.70 (step @p145 :rule ho_cong :premises (@p137 @p144)) % 0.40/0.70 (step @p146 :rule ho_cong :premises (@p145 @p126)) % 0.40/0.70 (step @p147 :rule trans :premises (@p146 @p143)) % 0.40/0.70 (step @p148 :rule cong :premises (@p147) :args (@t146)) % 0.40/0.70 (step @p149 :rule eq_resolve :premises (@p67 @p148)) % 0.40/0.70 (step @p150 :rule instantiate :premises (@p149) :args (@t191)) % 0.40/0.70 (step @p151 :rule refl :args ((tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t143))) % 0.40/0.70 (step @p152 :rule cong :premises (@p134) :args (@t187)) % 0.40/0.70 (step @p153 :rule trans :premises (@p152 @p151)) % 0.40/0.70 (step @p154 :rule ho_cong :premises (@p116 @p134)) % 0.40/0.70 (step @p155 :rule cong :premises (@p154 @p153) :args ((= (_ tptp.mono_2Ec_2Ereal__topology_2Ebounded__def @t186) @t187))) % 0.40/0.70 (step @p156 :rule symm :premises (@p155)) % 0.40/0.70 (step @p157 :rule refl :args (@t174)) % 0.40/0.70 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 0.40/0.70 (step @p159 :rule ho_cong :premises (@p116 @p144)) % 0.40/0.70 (step @p160 :rule trans :premises (@p159 @p158)) % 0.40/0.70 (step @p161 :rule cong :premises (@p160) :args (@t175)) % 0.40/0.70 (step @p162 :rule cong :premises (@p161) :args (@t176)) % 0.40/0.70 (step @p163 :rule eq_resolve :premises (@p80 @p162)) % 0.40/0.70 (step @p164 :rule skolemize :premises (@p163)) % 0.40/0.70 (step @p165 :rule cnf_or_pos :args (@t201)) % 0.40/0.70 (step @p166 :rule reordering :premises (@p165) :args ((or @t195 @t198 @t200 @t202))) % 0.40/0.70 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p150 @p131) :args (@t202 (@list true false false) (@list @t195 @t197 @t199))) % 0.40/0.70 (assume-push @p174 @t203) % 0.40/0.70 (step @p169 :rule instantiate :premises (@p109) :args ((@list @t194 @t196))) % 0.40/0.70 (step-pop @p175 :rule scope :premises (@p169)) % 0.40/0.70 (step @p170 :rule process_scope :premises (@p175) :args (@t201)) % 0.40/0.70 (step @p172 :rule implies_elim :premises (@p170)) % 0.40/0.70 (step @p173 false :rule chain_m_resolution :premises (@p172 @p167 @p109) :args (false (@list true false) (@list @t201 @t203))) % 0.40/0.70 ) % 0.40/0.70 % SZS output end Proof % 0.40/0.70 % cvc5 exiting %------------------------------------------------------------------------------