fof(t2_topreal2,theorem,( v6_compts_1(k2_topreal1,k15_euclid(2)) ), inference(mizar_proof,[status(thm)],[t34_topreal1,t36_topreal1,d5_tops_2,t36_topreal1,d5_tops_2,t11_heine,t27_topmetr,d5_tops_2,t23_compts_1,t12_compts_1,d5_tops_2,t23_compts_1,t12_compts_1,t19_compts_1]), [file(topreal2,t2_topreal2),interesting(1.00)]). fof(l21_topreal2,theorem,( r2_hidden(k23_euclid(0,0),a_0_0_topreal2) ), inference(mizar_proof,[status(thm)],[l4_topreal2]), [file(topreal2,l21_topreal2),interesting(0.84)]). fof(l22_topreal2,theorem,( r2_hidden(k23_euclid(1,1),a_0_0_topreal2) ), inference(mizar_proof,[status(thm)],[l4_topreal2]), [file(topreal2,l22_topreal2),interesting(0.84)]). fof(l1_topreal2,theorem,( ! [A,B] : ( ~ r2_hidden(A,B) => k3_xboole_0(k1_tarski(A),B) = k1_xboole_0 ) ), inference(mizar_proof,[status(thm)],[t56_zfmisc_1,d7_xboole_0]), [file(topreal2,l1_topreal2),interesting(0.80)]). fof(l8_topreal2,theorem,( ~ r2_hidden(k23_euclid(0,1),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t9_topreal1]), [file(topreal2,l8_topreal2),interesting(0.74)]). fof(l7_topreal2,theorem,( ~ r2_hidden(k23_euclid(0,1),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t10_topreal1]), [file(topreal2,l7_topreal2),interesting(0.74)]). fof(l5_topreal2,theorem,( ~ r2_hidden(k23_euclid(0,0),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t9_topreal1]), [file(topreal2,l5_topreal2),interesting(0.74)]). fof(l6_topreal2,theorem,( ~ r2_hidden(k23_euclid(0,0),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t10_topreal1]), [file(topreal2,l6_topreal2),interesting(0.74)]). fof(l12_topreal2,theorem,( ~ r2_hidden(k23_euclid(1,1),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t10_topreal1]), [file(topreal2,l12_topreal2),interesting(0.74)]). fof(l10_topreal2,theorem,( ~ r2_hidden(k23_euclid(1,0),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t10_topreal1]), [file(topreal2,l10_topreal2),interesting(0.74)]). fof(l11_topreal2,theorem,( ~ r2_hidden(k23_euclid(1,1),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t9_topreal1]), [file(topreal2,l11_topreal2),interesting(0.74)]). fof(l9_topreal2,theorem,( ~ r2_hidden(k23_euclid(1,0),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1))) ), inference(mizar_proof,[status(thm)],[l4_topreal2,t9_topreal1]), [file(topreal2,l9_topreal2),interesting(0.74)]). fof(l13_topreal2,theorem,( r2_hidden(k23_euclid(0,0),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l13_topreal2),interesting(0.71)]). fof(l15_topreal2,theorem,( r2_hidden(k23_euclid(0,1),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l15_topreal2),interesting(0.71)]). fof(l14_topreal2,theorem,( r2_hidden(k23_euclid(0,0),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l14_topreal2),interesting(0.71)]). fof(l16_topreal2,theorem,( r2_hidden(k23_euclid(0,1),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l16_topreal2),interesting(0.71)]). fof(l19_topreal2,theorem,( r2_hidden(k23_euclid(1,1),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l19_topreal2),interesting(0.71)]). fof(l20_topreal2,theorem,( r2_hidden(k23_euclid(1,1),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l20_topreal2),interesting(0.71)]). fof(l17_topreal2,theorem,( r2_hidden(k23_euclid(1,0),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l17_topreal2),interesting(0.71)]). fof(l18_topreal2,theorem,( r2_hidden(k23_euclid(1,0),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) ), inference(mizar_proof,[status(thm)],[t6_topreal1]), [file(topreal2,l18_topreal2),interesting(0.71)]). fof(l35_topreal2,theorem,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( v3_struct_0(A) & k2_relat_1(C) = k2_pre_topc(B) ) => v3_struct_0(B) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_xboole_0,d5_funct_1,d1_funct_2,d1_struct_0]), [file(topreal2,l35_topreal2),interesting(0.60)]). fof(t4_topreal2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( v1_topreal2(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r2_hidden(B,A) & r2_hidden(C,A) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_topreal2,d5_tops_2,d10_pre_topc,t56_euclid,t51_tops_2,d10_pre_topc,t20_topreal1,d5_funct_1,d9_pre_topc,d5_tops_2,d5_tops_2,d8_funct_1,d5_funct_1]), [file(topreal2,t4_topreal2),interesting(0.60)]). fof(t6_topreal2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal2(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [E] : ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & B != C & r2_hidden(B,A) & r2_hidden(C,A) & r1_topreal1(k15_euclid(2),B,C,D) & r1_topreal1(k15_euclid(2),B,C,E) & A = k4_subset_1(u1_struct_0(k15_euclid(2)),D,E) & k5_subset_1(u1_struct_0(k15_euclid(2)),D,E) = k2_struct_0(k15_euclid(2),B,C) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[t5_topreal2,t5_topreal2,l32_topreal2]), [file(topreal2,t6_topreal2),interesting(0.59)]). fof(t1_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r2_hidden(A,k2_topreal1) & r2_hidden(B,k2_topreal1) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_topreal1(k15_euclid(2),A,B,C) & r1_topreal1(k15_euclid(2),A,B,D) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),C,D) & k5_subset_1(u1_struct_0(k15_euclid(2)),C,D) = k2_struct_0(k15_euclid(2),A,B) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d4_topreal1,d2_xboole_0,l23_topreal2,l24_topreal2,l25_topreal2,l26_topreal2,d2_xboole_0]), [file(topreal2,t1_topreal2),interesting(0.58)]). fof(l36_topreal2,theorem,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( v3_struct_0(B) & k1_relat_1(C) = k2_pre_topc(A) ) => v3_struct_0(A) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_xboole_0,d5_funct_1,t12_relset_1,d1_struct_0]), [file(topreal2,l36_topreal2),interesting(0.57)]). fof(l37_topreal2,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_tops_2(C,A,B) ) => ( v3_struct_0(A) <=> v3_struct_0(B) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d5_tops_2,l35_topreal2,l36_topreal2]), [file(topreal2,l37_topreal2),interesting(0.56)]). fof(l2_topreal2,theorem,( k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0)),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) = k1_xboole_0 ), inference(mizar_proof,[status(thm)],[t25_topreal1,d7_xboole_0]), [file(topreal2,l2_topreal2),interesting(0.49)]). fof(l3_topreal2,theorem,( k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1)),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) = k1_xboole_0 ), inference(mizar_proof,[status(thm)],[t26_topreal1,d7_xboole_0]), [file(topreal2,l3_topreal2),interesting(0.49)]). fof(l4_topreal2,theorem, ( k21_euclid(k23_euclid(0,0)) = 0 & k22_euclid(k23_euclid(0,0)) = 0 & k21_euclid(k23_euclid(0,1)) = 0 & k22_euclid(k23_euclid(0,1)) = 1 & k21_euclid(k23_euclid(1,0)) = 1 & k22_euclid(k23_euclid(1,0)) = 0 & k21_euclid(k23_euclid(1,1)) = 1 & k22_euclid(k23_euclid(1,1)) = 1 ), inference(mizar_proof,[status(thm)],[t56_euclid]), [file(topreal2,l4_topreal2),interesting(0.46)]). fof(t5_topreal2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal2(A) <=> ( ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & B != C & r2_hidden(B,A) & r2_hidden(C,A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_topreal1(k15_euclid(2),B,C,D) & r1_topreal1(k15_euclid(2),B,C,E) & A = k4_subset_1(u1_struct_0(k15_euclid(2)),D,E) & k5_subset_1(u1_struct_0(k15_euclid(2)),D,E) = k2_struct_0(k15_euclid(2),B,C) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d1_topreal2,t4_topreal2,d5_tops_2,d5_tops_2,d5_tops_2,d4_tops_2,t54_funct_1,t62_funct_1,t55_funct_1,d10_pre_topc,d10_pre_topc,d5_funct_1,d9_pre_topc,t51_tops_2,d8_funct_1,d1_funct_2,d10_pre_topc,d5_funct_1,t1_topreal2,t7_xboole_1,d9_pre_topc,t144_relat_1,t1_xboole_1,t152_relat_1,t148_relat_1,d10_pre_topc,t90_relat_1,t21_xboole_1,d10_pre_topc,d1_funct_2,t11_relset_1,d10_pre_topc,t7_xboole_1,t4_topmetr,t84_funct_1,t146_funct_1,t152_funct_1,d10_xboole_0,t43_pre_topc,t28_xboole_1,t26_xboole_1,t139_funct_1,t137_funct_1,d10_pre_topc,t16_xboole_1,d10_pre_topc,t168_relat_1,t43_pre_topc,d12_pre_topc,t43_pre_topc,d12_pre_topc,d2_topreal1,t11_heine,t27_topmetr,d5_tops_2,t23_compts_1,t3_topmetr,t26_compts_1,d2_tarski,t17_xboole_1,d3_xboole_0,t57_funct_1,t71_funct_1,d2_tarski,t17_xboole_1,d3_xboole_0,t57_funct_1,t71_funct_1,t3_topreal2,t148_relat_1,d10_pre_topc,t90_relat_1,t21_xboole_1,d10_pre_topc,d1_funct_2,t11_relset_1,d10_pre_topc,t7_xboole_1,t4_topmetr,t84_funct_1,t43_pre_topc,t28_xboole_1,t26_xboole_1,t139_funct_1,t137_funct_1,d10_pre_topc,t16_xboole_1,d10_pre_topc,t168_relat_1,t43_pre_topc,d12_pre_topc,t43_pre_topc,d12_pre_topc,d2_topreal1,d5_tops_2,t23_compts_1,t3_topmetr,t26_compts_1,d2_tarski,t17_xboole_1,d3_xboole_0,t57_funct_1,t71_funct_1,d2_tarski,t17_xboole_1,d3_xboole_0,t57_funct_1,t71_funct_1,t3_topreal2,t146_relat_1,t153_relat_1,t121_funct_1,t41_enumset1,t153_relat_1,t117_funct_1,t117_funct_1,t41_enumset1,l32_topreal2]), [file(topreal2,t5_topreal2),interesting(0.45)]). fof(l32_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(A,C) & r2_hidden(B,C) & r1_topreal1(k15_euclid(2),A,B,D) & r1_topreal1(k15_euclid(2),A,B,E) & C = k4_subset_1(u1_struct_0(k15_euclid(2)),D,E) & k5_subset_1(u1_struct_0(k15_euclid(2)),D,E) = k2_struct_0(k15_euclid(2),A,B) ) => ( A = B | v1_topreal2(C) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d2_topreal1,d2_topreal1,t30_topreal1,t31_topreal1,d2_topreal1,t31_topreal1,d2_topreal1,d10_pre_topc,t7_xboole_1,t12_relset_1,d1_funct_2,t1_xboole_1,d1_funct_2,t11_relset_1,t4_topmetr,d5_tops_2,t7_topmetr,d10_pre_topc,t7_xboole_1,t12_relset_1,d1_funct_2,t1_xboole_1,d1_funct_2,t11_relset_1,t4_topmetr,d5_tops_2,t7_topmetr,d10_topreal1,t29_topreal1,d10_pre_topc,l21_topreal2,l22_topreal2,t20_topreal1,d10_pre_topc,t11_heine,t27_topmetr,d5_tops_2,t23_compts_1,t3_topmetr,d5_tops_2,t58_tops_2,d5_tops_2,d4_tops_2,d4_tops_2,t83_borsuk_1,d1_funct_2,t15_rcomp_1,t15_rcomp_1,d5_funct_1,t54_funct_1,t54_funct_1,t54_funct_1,t54_funct_1,t21_funct_1,t54_funct_1,d5_funct_1,t54_funct_1,t54_funct_1,t21_funct_1,t22_funct_1,t54_funct_1,t54_funct_1,t22_funct_1,t15_rcomp_1,t15_rcomp_1,d5_funct_1,t54_funct_1,t54_funct_1,t21_funct_1,t54_funct_1,t54_funct_1,t21_funct_1,t22_funct_1,t54_funct_1,t54_funct_1,t22_funct_1,t7_xboole_1,t4_topmetr,t5_topmetr2,t2_topreal2,t12_compts_1,t3_topmetr,d5_tops_2,t62_funct_1,t46_funct_1,d5_tops_2,t62_funct_1,t46_funct_1,t55_funct_1,t55_funct_1,t46_relat_1,d3_tarski,d12_funct_1,d1_funct_2,d2_tarski,d5_funct_1,d1_funct_2,t47_relat_1,d5_tops_2,t47_relat_1,d5_tops_2,d10_pre_topc,t3_topmetr2,d1_funct_2,d4_xboole_0,d5_funct_1,d3_xboole_0,t21_funct_1,t21_funct_1,t21_funct_1,t22_funct_1,t54_funct_1,d8_funct_1,d8_funct_1,t21_funct_1,t22_funct_1,d5_funct_1,d8_funct_1,d8_funct_1,d4_xboole_0,t21_funct_1,t22_funct_1,d5_funct_1,d8_funct_1,d8_funct_1,t21_funct_1,t22_funct_1,d5_funct_1,d8_funct_1,d8_funct_1,d4_xboole_0,d2_tarski,t2_topmetr2,d1_topreal2,t26_compts_1]), [file(topreal2,l32_topreal2),interesting(0.27)]). fof(l23_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r2_hidden(B,k2_topreal1) & r2_hidden(A,k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_topreal1(k15_euclid(2),A,B,C) & r1_topreal1(k15_euclid(2),A,B,D) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),C,D) & k5_subset_1(u1_struct_0(k15_euclid(2)),C,D) = k2_struct_0(k15_euclid(2),A,B) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d4_topreal1,d2_xboole_0,t19_topreal1,l13_topreal2,t12_topreal1,l15_topreal2,t12_topreal1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t6_topreal1,l14_topreal2,d3_xboole_0,t37_zfmisc_1,t23_topreal1,t26_xboole_1,d10_xboole_0,t26_xboole_1,t3_xboole_1,t6_topreal1,l16_topreal2,d3_xboole_0,t37_zfmisc_1,t21_topreal1,t26_xboole_1,t19_topreal1,t12_topreal1,t57_euclid,l15_topreal2,t12_topreal1,t23_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t37_zfmisc_1,t39_zfmisc_1,t26_xboole_1,d3_tarski,t56_euclid,d3_xboole_0,t10_topreal1,t2_xreal_1,t6_topreal1,l16_topreal2,d3_xboole_0,t37_zfmisc_1,t21_topreal1,t26_xboole_1,t21_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t13_topreal1,t12_topreal1,t26_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t15_topreal1,l4_topreal2,t18_topreal1,t22_topreal1,l2_topreal2,t24_topreal1,t23_xboole_1,t16_topreal1,t23_xboole_1,t23_xboole_1,l3_topreal2,t3_xboole_1,d10_xboole_0,t16_topreal1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t39_zfmisc_1,t17_topreal1,d4_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l3_topreal2,t3_xboole_1,t4_xboole_1,t4_xboole_1,t23_topreal1,t26_xboole_1,t6_topreal1,l14_topreal2,d3_xboole_0,t39_zfmisc_1,l4_topreal2,d3_xboole_0,t10_topreal1,t1_xreal_1,l4_topreal2,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t21_topreal1,t26_xboole_1,l4_topreal2,d3_xboole_0,t10_topreal1,t1_xreal_1,t57_euclid,t56_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t6_topreal1,l16_topreal2,d3_xboole_0,t39_zfmisc_1,t41_enumset1,t23_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t37_zfmisc_1,l13_topreal2,t12_topreal1,t26_xboole_1,d3_tarski,t56_euclid,d3_xboole_0,t10_topreal1,t2_xreal_1,t6_topreal1,l14_topreal2,d3_xboole_0,t37_zfmisc_1,t23_topreal1,t26_xboole_1,t21_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t13_topreal1,t26_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,t15_topreal1,l4_topreal2,t18_topreal1,t22_topreal1,l2_topreal2,t24_topreal1,t23_xboole_1,t17_topreal1,t23_xboole_1,t23_xboole_1,t39_zfmisc_1,d10_xboole_0,t17_topreal1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l3_topreal2,t3_xboole_1,t39_zfmisc_1,d10_xboole_0,t16_topreal1,d4_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,d10_xboole_0,l3_topreal2,t3_xboole_1,d10_xboole_0,t4_xboole_1,t4_xboole_1,t23_topreal1,t26_xboole_1,t6_topreal1,l14_topreal2,d3_xboole_0,t39_zfmisc_1,l4_topreal2,d3_xboole_0,t10_topreal1,t1_xreal_1,l4_topreal2,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t21_topreal1,t26_xboole_1,l4_topreal2,d3_xboole_0,t10_topreal1,t1_xreal_1,t57_euclid,t56_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t6_topreal1,l16_topreal2,d3_xboole_0,t39_zfmisc_1,t41_enumset1,d5_real_1,t19_topreal1,t6_topreal1,l15_topreal2,l16_topreal2,t12_topreal1,d3_xboole_0,t21_topreal1,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t22_topreal1,l19_topreal2,t12_topreal1,t26_xboole_1,l2_topreal2,t3_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t27_xboole_1,t23_xboole_1,t24_topreal1,t39_zfmisc_1,t16_topreal1,t21_topreal1,t27_xboole_1,t39_zfmisc_1,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t57_euclid,t23_xboole_1,t23_xboole_1,t37_zfmisc_1,d10_xboole_0,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,l16_topreal2,t12_topreal1,t14_topreal1,t14_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l4_topreal2,t9_topreal1,t7_topreal1,l1_topreal2,t24_topreal1,t24_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,l4_topreal2,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t21_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l8_topreal2,t21_topreal1,t27_xboole_1,t6_topreal1,l16_topreal2,d3_xboole_0,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t7_topreal1,l1_topreal2,l7_topreal2,t6_topreal1,t27_xboole_1,l15_topreal2,t21_topreal1,d3_xboole_0,t39_zfmisc_1,t4_xboole_1,t41_enumset1,l4_topreal2,t10_topreal1,t7_topreal1,l1_topreal2,t41_enumset1,t23_topreal1,t23_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t21_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t19_topreal1,t6_topreal1,l13_topreal2,l14_topreal2,t12_topreal1,d3_xboole_0,t23_topreal1,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t24_topreal1,l17_topreal2,t12_topreal1,t26_xboole_1,l2_topreal2,t3_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t27_xboole_1,t23_xboole_1,t22_topreal1,t39_zfmisc_1,t16_topreal1,t23_topreal1,t27_xboole_1,t39_zfmisc_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t10_topreal1,t57_euclid,t57_euclid,t23_xboole_1,t23_xboole_1,t37_zfmisc_1,d10_xboole_0,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,l14_topreal2,t12_topreal1,t14_topreal1,t14_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l4_topreal2,t9_topreal1,t56_zfmisc_1,t7_topreal1,d7_xboole_0,t22_topreal1,t22_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,l4_topreal2,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t23_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l5_topreal2,t23_topreal1,t27_xboole_1,t6_topreal1,l14_topreal2,d3_xboole_0,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t7_topreal1,l4_topreal2,t10_topreal1,l1_topreal2,t41_enumset1,t21_topreal1,t7_topreal1,l1_topreal2,l6_topreal2,t26_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t23_topreal1,t39_zfmisc_1,t4_xboole_1,t41_enumset1,t21_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t41_enumset1,t19_topreal1,l18_topreal2,t6_topreal1,t12_topreal1,t22_topreal1,d3_xboole_0,t27_xboole_1,t39_zfmisc_1,l4_topreal2,t18_topreal1,l18_topreal2,t12_topreal1,t27_xboole_1,l3_topreal2,t3_xboole_1,t23_xboole_1,d10_xboole_0,t17_topreal1,t4_xboole_1,l20_topreal2,t12_topreal1,t6_topreal1,t27_xboole_1,l19_topreal2,t24_topreal1,d3_xboole_0,t39_zfmisc_1,l4_topreal2,t18_topreal1,t27_xboole_1,l3_topreal2,t3_xboole_1,t23_xboole_1,d10_xboole_0,t17_topreal1,t4_xboole_1,t11_topreal1,d4_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t11_topreal1,t4_xboole_1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_xboole_0,l4_topreal2,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d3_tarski,d10_xboole_0,t27_xboole_1,l3_topreal2,t3_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_xboole_0,l4_topreal2,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d3_tarski,l18_topreal2,t12_topreal1,t27_xboole_1,l3_topreal2,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l2_topreal2,t23_xboole_1,d10_xboole_0,t23_xboole_1,t7_topreal1,l1_topreal2,l12_topreal2,t24_topreal1,t7_topreal1,l1_topreal2,l10_topreal2,t22_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t22_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t27_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l7_topreal2,t41_enumset1,t21_topreal1,t27_xboole_1,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t21_topreal1,t27_xboole_1,d3_xboole_0,t56_euclid,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t7_topreal1,l1_topreal2,l6_topreal2,t41_enumset1,t23_topreal1,d2_xboole_0]), [file(topreal2,l23_topreal2),interesting(0.22)]). fof(l24_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r2_hidden(B,k2_topreal1) & r2_hidden(A,k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_topreal1(k15_euclid(2),A,B,C) & r1_topreal1(k15_euclid(2),A,B,D) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),C,D) & k5_subset_1(u1_struct_0(k15_euclid(2)),C,D) = k2_struct_0(k15_euclid(2),A,B) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d4_topreal1,d2_xboole_0,t19_topreal1,l16_topreal2,t12_topreal1,l19_topreal2,t12_topreal1,t26_xboole_1,l2_topreal2,t3_xboole_1,t6_topreal1,l15_topreal2,d3_xboole_0,t26_xboole_1,t26_xboole_1,l2_topreal2,t3_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t24_topreal1,t26_xboole_1,t19_topreal1,t6_topreal1,l15_topreal2,l16_topreal2,t12_topreal1,d3_xboole_0,t27_xboole_1,t21_topreal1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t22_topreal1,l13_topreal2,t6_topreal1,t12_topreal1,l14_topreal2,t23_topreal1,d3_xboole_0,t26_xboole_1,t27_xboole_1,l3_topreal2,t3_xboole_1,l15_topreal2,t12_topreal1,t23_xboole_1,t39_zfmisc_1,t16_topreal1,t27_xboole_1,t21_topreal1,t39_zfmisc_1,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t57_euclid,t23_xboole_1,t23_xboole_1,t37_zfmisc_1,t39_zfmisc_1,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,t14_topreal1,t14_topreal1,l3_topreal2,t27_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t7_topreal1,l1_topreal2,l8_topreal2,t21_topreal1,t27_xboole_1,t6_topreal1,l16_topreal2,d3_xboole_0,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t7_topreal1,l4_topreal2,t9_topreal1,l1_topreal2,t24_topreal1,t4_xboole_1,t24_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t21_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t27_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t23_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t7_topreal1,l4_topreal2,t10_topreal1,l1_topreal2,t41_enumset1,t23_topreal1,t7_topreal1,l1_topreal2,l7_topreal2,t27_xboole_1,t6_topreal1,l15_topreal2,d3_xboole_0,t21_topreal1,t39_zfmisc_1,t4_xboole_1,t41_enumset1,t19_topreal1,t57_euclid,l19_topreal2,t12_topreal1,l16_topreal2,t12_topreal1,t12_topreal1,t15_topreal1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t2_xreal_1,t24_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t26_xboole_1,t6_topreal1,l15_topreal2,d3_xboole_0,t23_xboole_1,t23_xboole_1,t23_xboole_1,t21_topreal1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t23_topreal1,t23_xboole_1,l3_topreal2,t22_topreal1,t16_topreal1,t26_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t24_topreal1,t39_zfmisc_1,t21_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t37_zfmisc_1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t16_topreal1,t17_topreal1,t4_xboole_1,t4_xboole_1,t13_topreal1,t4_xboole_1,d4_topreal1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t6_topreal1,l15_topreal2,d3_xboole_0,t21_topreal1,t39_zfmisc_1,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t24_topreal1,t26_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t39_zfmisc_1,t41_enumset1,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t15_topreal1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t2_xreal_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t24_topreal1,t26_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t23_xboole_1,t23_xboole_1,t23_xboole_1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t22_topreal1,t23_xboole_1,l3_topreal2,t23_topreal1,t16_topreal1,t21_topreal1,t26_xboole_1,t6_topreal1,l15_topreal2,d3_xboole_0,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t16_topreal1,t17_topreal1,t4_xboole_1,t4_xboole_1,t13_topreal1,d4_topreal1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t6_topreal1,l15_topreal2,d3_xboole_0,t21_topreal1,t39_zfmisc_1,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t24_topreal1,t26_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t39_zfmisc_1,t41_enumset1,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,d5_real_1,t19_topreal1,l17_topreal2,t6_topreal1,t12_topreal1,l18_topreal2,d3_xboole_0,t27_xboole_1,t22_topreal1,t39_zfmisc_1,l4_topreal2,t18_topreal1,l17_topreal2,t12_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t39_zfmisc_1,t17_topreal1,t4_xboole_1,l14_topreal2,t6_topreal1,t12_topreal1,l13_topreal2,t23_topreal1,d3_xboole_0,t27_xboole_1,t39_zfmisc_1,l4_topreal2,t18_topreal1,l14_topreal2,t12_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t21_topreal1,t39_zfmisc_1,t17_topreal1,t4_xboole_1,t11_topreal1,t11_topreal1,d4_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t1_xboole_1,l2_topreal2,t3_xboole_1,t14_topreal1,t14_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l3_topreal2,t23_xboole_1,t23_xboole_1,t7_topreal1,l1_topreal2,l8_topreal2,t21_topreal1,t7_topreal1,l1_topreal2,l11_topreal2,t24_topreal1,t4_xboole_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l5_topreal2,t41_enumset1,t23_topreal1,t7_topreal1,l1_topreal2,l9_topreal2,t22_topreal1,t4_xboole_1,t41_enumset1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t1_xreal_1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t41_enumset1,t19_topreal1,t6_topreal1,l19_topreal2,l20_topreal2,t12_topreal1,d3_xboole_0,t24_topreal1,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t23_topreal1,l18_topreal2,t12_topreal1,t26_xboole_1,l3_topreal2,t3_xboole_1,t6_topreal1,l17_topreal2,t22_topreal1,d3_xboole_0,t27_xboole_1,t23_xboole_1,t39_zfmisc_1,t16_topreal1,t24_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t23_xboole_1,t23_xboole_1,t21_topreal1,t39_zfmisc_1,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,l20_topreal2,t12_topreal1,t14_topreal1,t14_topreal1,t27_xboole_1,l3_topreal2,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l4_topreal2,t10_topreal1,t7_topreal1,l1_topreal2,t22_topreal1,t7_topreal1,l1_topreal2,l12_topreal2,t24_topreal1,t27_xboole_1,t6_topreal1,l20_topreal2,d3_xboole_0,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t24_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l4_topreal2,t9_topreal1,l1_topreal2,t41_enumset1,t21_topreal1,t7_topreal1,l1_topreal2,l11_topreal2,t27_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t24_topreal1,t39_zfmisc_1,t4_xboole_1,t41_enumset1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t41_enumset1,d2_xboole_0]), [file(topreal2,l24_topreal2),interesting(0.22)]). fof(l26_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r2_hidden(B,k2_topreal1) & r2_hidden(A,k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_topreal1(k15_euclid(2),A,B,C) & r1_topreal1(k15_euclid(2),A,B,D) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),C,D) & k5_subset_1(u1_struct_0(k15_euclid(2)),C,D) = k2_struct_0(k15_euclid(2),A,B) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d4_topreal1,d2_xboole_0,t19_topreal1,l20_topreal2,t12_topreal1,l18_topreal2,t12_topreal1,t26_xboole_1,t6_topreal1,l17_topreal2,d3_xboole_0,t26_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t19_topreal1,l15_topreal2,t12_topreal1,l13_topreal2,t12_topreal1,t6_topreal1,l16_topreal2,d3_xboole_0,t26_xboole_1,t21_topreal1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t27_xboole_1,l3_topreal2,t3_xboole_1,t23_xboole_1,t24_topreal1,t39_zfmisc_1,t17_topreal1,t4_xboole_1,t6_topreal1,t26_xboole_1,l14_topreal2,t23_topreal1,d3_xboole_0,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t27_xboole_1,l3_topreal2,t3_xboole_1,t23_xboole_1,t22_topreal1,t39_zfmisc_1,t17_topreal1,t4_xboole_1,t11_topreal1,t11_topreal1,d4_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t14_topreal1,t26_topreal1,d7_xboole_0,t27_xboole_1,t3_xboole_1,t26_topreal1,d7_xboole_0,t27_xboole_1,t3_xboole_1,t14_topreal1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l2_topreal2,t23_xboole_1,t23_xboole_1,t7_topreal1,l1_topreal2,l10_topreal2,t22_topreal1,t7_topreal1,l1_topreal2,l12_topreal2,t24_topreal1,t4_xboole_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t24_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l6_topreal2,t41_enumset1,t23_topreal1,t7_topreal1,l1_topreal2,l7_topreal2,t21_topreal1,t4_xboole_1,t41_enumset1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t23_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t19_topreal1,l19_topreal2,t12_topreal1,l16_topreal2,t12_topreal1,t6_topreal1,t24_topreal1,d3_xboole_0,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t23_topreal1,t26_xboole_1,l2_topreal2,t3_xboole_1,t6_topreal1,l15_topreal2,t21_topreal1,d3_xboole_0,t27_xboole_1,t23_xboole_1,t39_zfmisc_1,t16_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t23_xboole_1,t23_xboole_1,t22_topreal1,t39_zfmisc_1,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,t14_topreal1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t14_topreal1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t7_topreal1,l4_topreal2,t10_topreal1,l1_topreal2,t22_topreal1,t4_xboole_1,t7_topreal1,l1_topreal2,l12_topreal2,t6_topreal1,l20_topreal2,d3_xboole_0,t24_topreal1,t27_xboole_1,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t24_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l4_topreal2,t9_topreal1,l1_topreal2,t41_enumset1,t21_topreal1,t27_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t24_topreal1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l11_topreal2,t4_xboole_1,t41_enumset1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t21_topreal1,t39_zfmisc_1,t41_enumset1,t19_topreal1,l17_topreal2,t12_topreal1,l14_topreal2,t12_topreal1,t6_topreal1,t22_topreal1,d3_xboole_0,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t21_topreal1,t26_xboole_1,l2_topreal2,t3_xboole_1,t6_topreal1,l13_topreal2,t23_topreal1,d3_xboole_0,t27_xboole_1,t23_xboole_1,t39_zfmisc_1,t16_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t23_xboole_1,t23_xboole_1,t24_topreal1,t39_zfmisc_1,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,t14_topreal1,t14_topreal1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t7_topreal1,l1_topreal2,l10_topreal2,t22_topreal1,t27_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t7_topreal1,l4_topreal2,t10_topreal1,l1_topreal2,t24_topreal1,t4_xboole_1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t22_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l4_topreal2,t9_topreal1,l1_topreal2,t41_enumset1,t23_topreal1,t27_xboole_1,t6_topreal1,l17_topreal2,d3_xboole_0,t22_topreal1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l9_topreal2,t4_xboole_1,t41_enumset1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t41_enumset1,t19_topreal1,t57_euclid,l20_topreal2,t12_topreal1,l18_topreal2,t12_topreal1,t12_topreal1,t15_topreal1,d3_tarski,t56_euclid,d3_xboole_0,t10_topreal1,t2_xreal_1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t26_xboole_1,t6_topreal1,l17_topreal2,d3_xboole_0,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t22_topreal1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t23_topreal1,t23_xboole_1,l2_topreal2,t21_topreal1,t16_topreal1,t24_topreal1,t26_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t39_zfmisc_1,t22_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t37_zfmisc_1,t39_zfmisc_1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t16_topreal1,t17_topreal1,t4_xboole_1,t4_xboole_1,t13_topreal1,t4_xboole_1,d4_topreal1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t6_topreal1,l17_topreal2,d3_xboole_0,t22_topreal1,t39_zfmisc_1,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t26_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t24_topreal1,t39_zfmisc_1,t41_enumset1,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t41_enumset1,t15_topreal1,d3_tarski,t56_euclid,d3_xboole_0,t10_topreal1,t2_xreal_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t26_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t24_topreal1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t21_topreal1,t23_xboole_1,l2_topreal2,t23_topreal1,t16_topreal1,t22_topreal1,t26_xboole_1,t6_topreal1,l17_topreal2,d3_xboole_0,t39_zfmisc_1,t24_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t39_zfmisc_1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t16_topreal1,t17_topreal1,t4_xboole_1,t4_xboole_1,t13_topreal1,d4_topreal1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t6_topreal1,l19_topreal2,d3_xboole_0,t24_topreal1,t39_zfmisc_1,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t26_xboole_1,t6_topreal1,l17_topreal2,d3_xboole_0,t22_topreal1,t39_zfmisc_1,t41_enumset1,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t41_enumset1,d5_real_1,d2_xboole_0]), [file(topreal2,l26_topreal2),interesting(0.22)]). fof(l25_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r2_hidden(B,k2_topreal1) & r2_hidden(A,k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_topreal1(k15_euclid(2),A,B,C) & r1_topreal1(k15_euclid(2),A,B,D) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),C,D) & k5_subset_1(u1_struct_0(k15_euclid(2)),C,D) = k2_struct_0(k15_euclid(2),A,B) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d4_topreal1,d2_xboole_0,t19_topreal1,l14_topreal2,t12_topreal1,l17_topreal2,t12_topreal1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t26_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t26_xboole_1,t14_topreal1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t19_topreal1,l13_topreal2,t12_topreal1,l15_topreal2,t12_topreal1,t6_topreal1,t23_topreal1,d3_xboole_0,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t24_topreal1,t26_xboole_1,l3_topreal2,t3_xboole_1,t6_topreal1,l16_topreal2,d3_xboole_0,t27_xboole_1,t23_xboole_1,t21_topreal1,t39_zfmisc_1,t16_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t10_topreal1,t57_euclid,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t23_xboole_1,t23_xboole_1,t22_topreal1,t39_zfmisc_1,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,t14_topreal1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t14_topreal1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t7_topreal1,l1_topreal2,l5_topreal2,t6_topreal1,t23_topreal1,d3_xboole_0,t26_xboole_1,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t7_topreal1,l4_topreal2,t9_topreal1,l1_topreal2,t22_topreal1,t4_xboole_1,t22_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t23_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t27_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t23_topreal1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l6_topreal2,t4_xboole_1,t41_enumset1,t7_topreal1,l4_topreal2,t10_topreal1,l1_topreal2,t41_enumset1,t21_topreal1,t41_enumset1,t21_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t21_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t41_enumset1,t19_topreal1,l16_topreal2,t12_topreal1,l19_topreal2,t12_topreal1,t6_topreal1,l15_topreal2,t21_topreal1,d3_xboole_0,t26_xboole_1,t39_zfmisc_1,l4_topreal2,t18_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t23_topreal1,t39_zfmisc_1,t17_topreal1,t4_xboole_1,t6_topreal1,t26_xboole_1,l20_topreal2,t24_topreal1,d3_xboole_0,t39_zfmisc_1,l4_topreal2,t18_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t23_xboole_1,t22_topreal1,t39_zfmisc_1,t17_topreal1,t4_xboole_1,t11_topreal1,d4_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t14_topreal1,t27_xboole_1,l2_topreal2,t3_xboole_1,t25_topreal1,d7_xboole_0,t27_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,l3_topreal2,t7_topreal1,l1_topreal2,l5_topreal2,t23_topreal1,t4_xboole_1,t7_topreal1,l1_topreal2,l9_topreal2,t22_topreal1,t22_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t23_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t7_topreal1,l1_topreal2,l8_topreal2,t21_topreal1,t4_xboole_1,t41_enumset1,t7_topreal1,l1_topreal2,l11_topreal2,t41_enumset1,t24_topreal1,t21_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t24_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t19_topreal1,t57_euclid,l17_topreal2,t12_topreal1,l14_topreal2,t12_topreal1,t12_topreal1,t15_topreal1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t2_xreal_1,t22_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t26_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_topreal1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t21_topreal1,t23_xboole_1,l3_topreal2,t24_topreal1,t16_topreal1,t26_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t22_topreal1,t39_zfmisc_1,t23_topreal1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t37_zfmisc_1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t16_topreal1,t17_topreal1,t4_xboole_1,t4_xboole_1,t13_topreal1,d4_topreal1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t23_topreal1,t39_zfmisc_1,t26_xboole_1,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t22_topreal1,t26_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t39_zfmisc_1,t41_enumset1,t22_topreal1,t26_xboole_1,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,t15_topreal1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t2_xreal_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t22_topreal1,t26_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t23_xboole_1,t23_xboole_1,t23_xboole_1,t39_zfmisc_1,l4_topreal2,t15_topreal1,t16_topreal1,t24_topreal1,t23_xboole_1,l3_topreal2,t21_topreal1,t16_topreal1,t23_topreal1,t26_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t16_topreal1,t17_topreal1,t4_xboole_1,t4_xboole_1,t13_topreal1,t4_xboole_1,d4_topreal1,t4_xboole_1,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t6_topreal1,d3_xboole_0,t37_zfmisc_1,d3_tarski,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,t1_xreal_1,t57_euclid,t57_euclid,d1_tarski,d10_xboole_0,t25_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t6_topreal1,l13_topreal2,d3_xboole_0,t23_topreal1,t39_zfmisc_1,t26_xboole_1,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t22_topreal1,t26_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t39_zfmisc_1,t41_enumset1,t22_topreal1,t26_xboole_1,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t41_enumset1,d5_real_1,t19_topreal1,l18_topreal2,t12_topreal1,l20_topreal2,t12_topreal1,t6_topreal1,t22_topreal1,d3_xboole_0,t27_xboole_1,t39_zfmisc_1,t18_topreal1,l4_topreal2,t15_topreal1,t5_topreal1,t21_topreal1,t26_xboole_1,l3_topreal2,t3_xboole_1,t6_topreal1,l19_topreal2,t24_topreal1,d3_xboole_0,t27_xboole_1,t23_xboole_1,t39_zfmisc_1,t16_topreal1,t22_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t23_xboole_1,t23_xboole_1,t23_topreal1,t39_zfmisc_1,t17_topreal1,t11_topreal1,t11_topreal1,t4_xboole_1,t4_xboole_1,t4_xboole_1,t4_xboole_1,d4_topreal1,t4_xboole_1,t14_topreal1,t14_topreal1,t26_topreal1,d7_xboole_0,t26_xboole_1,t3_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t23_xboole_1,t7_topreal1,l4_topreal2,t9_topreal1,l1_topreal2,t23_topreal1,t4_xboole_1,t7_topreal1,l1_topreal2,l9_topreal2,t27_xboole_1,t6_topreal1,d3_xboole_0,t22_topreal1,t39_zfmisc_1,t4_xboole_1,t4_xboole_1,t26_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t9_topreal1,t57_euclid,t37_zfmisc_1,t23_topreal1,t39_zfmisc_1,t27_xboole_1,t56_euclid,d3_xboole_0,t9_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t22_topreal1,t39_zfmisc_1,t22_topreal1,t27_xboole_1,t6_topreal1,l18_topreal2,d3_xboole_0,t39_zfmisc_1,t7_topreal1,l1_topreal2,l10_topreal2,t4_xboole_1,t41_enumset1,t7_topreal1,l4_topreal2,t10_topreal1,l1_topreal2,t41_enumset1,t24_topreal1,t22_topreal1,t27_xboole_1,t56_euclid,d3_xboole_0,l4_topreal2,t10_topreal1,t57_euclid,t37_zfmisc_1,t39_zfmisc_1,t26_xboole_1,t56_euclid,d3_xboole_0,t10_topreal1,l4_topreal2,t1_xreal_1,t57_euclid,t37_zfmisc_1,t24_topreal1,t39_zfmisc_1,t41_enumset1,d2_xboole_0]), [file(topreal2,l25_topreal2),interesting(0.21)]). fof(d5_tops_2,definition,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v3_tops_2(C,A,B) <=> ( k1_relat_1(C) = k2_pre_topc(A) & k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & v5_pre_topc(C,A,B) & v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ), file(tops_2,d5_tops_2), [interesting(0.00)]). fof(d1_xboole_0,definition,( ! [A] : ( A = k1_xboole_0 <=> ! [B] : ~ r2_hidden(B,A) ) ), file(xboole_0,d1_xboole_0), [interesting(0.00)]). fof(d5_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), [interesting(0.00)]). fof(d1_funct_2,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), [interesting(0.00)]). fof(d1_struct_0,definition,( ! [A] : ( l1_struct_0(A) => ( v3_struct_0(A) <=> v1_xboole_0(u1_struct_0(A)) ) ) ), file(struct_0,d1_struct_0), [interesting(0.00)]). fof(t12_relset_1,theorem,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), [interesting(0.00)]). fof(d1_topreal2,definition,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) <=> ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k3_pre_topc(k15_euclid(2),k2_topreal1)),u1_struct_0(k3_pre_topc(k15_euclid(2),A))) & m2_relset_1(B,u1_struct_0(k3_pre_topc(k15_euclid(2),k2_topreal1)),u1_struct_0(k3_pre_topc(k15_euclid(2),A))) & v3_tops_2(B,k3_pre_topc(k15_euclid(2),k2_topreal1),k3_pre_topc(k15_euclid(2),A)) ) ) ) ), file(topreal2,d1_topreal2), [interesting(0.00)]). fof(d10_pre_topc,definition,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_pre_topc(C) & m1_pre_topc(C,A) ) => ( C = k3_pre_topc(A,B) <=> k2_pre_topc(C) = B ) ) ) ) ), file(pre_topc,d10_pre_topc), [interesting(0.00)]). fof(t56_euclid,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k21_euclid(k23_euclid(A,B)) = A & k22_euclid(k23_euclid(A,B)) = B ) ) ) ), file(euclid,t56_euclid), [interesting(0.00)]). fof(t51_tops_2,theorem,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( k1_relat_1(C) = k2_pre_topc(A) & r1_tarski(k2_relat_1(C),k2_pre_topc(B)) ) ) ) ) ), file(tops_2,t51_tops_2), [interesting(0.00)]). fof(t20_topreal1,theorem,( k2_topreal1 = a_0_4_topreal1 ), file(topreal1,t20_topreal1), [interesting(0.00)]). fof(d9_pre_topc,definition,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( m1_pre_topc(B,A) <=> ( r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(C,u1_pre_topc(B)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(D,u1_pre_topc(A)) & C = k3_xboole_0(D,k2_pre_topc(B)) ) ) ) ) ) ) ) ), file(pre_topc,d9_pre_topc), [interesting(0.00)]). fof(d8_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), [interesting(0.00)]). fof(d4_tops_2,definition,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) ) => k2_tops_2(A,B,C) = k2_funct_1(C) ) ) ) ) ), file(tops_2,d4_tops_2), [interesting(0.00)]). fof(t54_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k2_funct_1(A) <=> ( k1_relat_1(B) = k2_relat_1(A) & ! [C,D] : ( ( ( r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C) ) => ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) & ( ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) => ( r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C) ) ) ) ) ) ) ) ) ), file(funct_1,t54_funct_1), [interesting(0.00)]). fof(t62_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => v2_funct_1(k2_funct_1(A)) ) ) ), file(funct_1,t62_funct_1), [interesting(0.00)]). fof(t55_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ), file(funct_1,t55_funct_1), [interesting(0.00)]). fof(d4_topreal1,definition,( k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),k4_subset_1(u1_struct_0(k15_euclid(2)),k1_topreal1(2,k23_euclid(0,0),k23_euclid(0,1)),k1_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))),k4_subset_1(u1_struct_0(k15_euclid(2)),k1_topreal1(2,k23_euclid(1,1),k23_euclid(1,0)),k1_topreal1(2,k23_euclid(1,0),k23_euclid(0,0)))) ), file(topreal1,d4_topreal1), [interesting(0.00)]). fof(d2_xboole_0,definition,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), [interesting(0.00)]). fof(t19_topreal1,theorem, ( k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1)) = a_0_0_topreal1 & k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1)) = a_0_1_topreal1 & k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0)) = a_0_2_topreal1 & k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1)) = a_0_3_topreal1 ), file(topreal1,t19_topreal1), [interesting(0.00)]). fof(t6_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k1_topreal1(A,B,C)) & r2_hidden(C,k1_topreal1(A,B,C)) ) ) ) ) ), file(topreal1,t6_topreal1), [interesting(0.00)]). fof(t12_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(D,k3_topreal1(A,B,C)) & r2_hidden(E,k3_topreal1(A,B,C)) ) => r1_tarski(k3_topreal1(A,D,E),k3_topreal1(A,B,C)) ) ) ) ) ) ) ), file(topreal1,t12_topreal1), [interesting(0.00)]). fof(t26_topreal1,theorem,( r1_subset_1(k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1)),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) ), file(topreal1,t26_topreal1), [interesting(0.00)]). fof(d7_xboole_0,definition,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), [interesting(0.00)]). fof(t26_xboole_1,theorem,( ! [A,B,C] : ( r1_tarski(A,B) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ), file(xboole_1,t26_xboole_1), [interesting(0.00)]). fof(t3_xboole_1,theorem,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), [interesting(0.00)]). fof(d3_xboole_0,definition,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), [interesting(0.00)]). fof(t37_zfmisc_1,theorem,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_1), [interesting(0.00)]). fof(t23_topreal1,theorem,( k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1)),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0))) = k1_struct_0(k15_euclid(2),k23_euclid(0,0)) ), file(topreal1,t23_topreal1), [interesting(0.00)]). fof(d10_xboole_0,definition,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), [interesting(0.00)]). fof(t21_topreal1,theorem,( k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,0),k23_euclid(0,1)),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) = k1_struct_0(k15_euclid(2),k23_euclid(0,1)) ), file(topreal1,t21_topreal1), [interesting(0.00)]). fof(t57_euclid,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => A = k23_euclid(k21_euclid(A),k22_euclid(A)) ) ), file(euclid,t57_euclid), [interesting(0.00)]). fof(t10_topreal1,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xreal_0(k22_euclid(A),k22_euclid(B)) & r2_hidden(C,k3_topreal1(2,A,B)) ) => ( r1_xreal_0(k22_euclid(A),k22_euclid(C)) & r1_xreal_0(k22_euclid(C),k22_euclid(B)) ) ) ) ) ) ), file(topreal1,t10_topreal1), [interesting(0.00)]). fof(t39_zfmisc_1,theorem,( ! [A,B] : ( r1_tarski(A,k1_tarski(B)) <=> ( A = k1_xboole_0 | A = k1_tarski(B) ) ) ), file(zfmisc_1,t39_zfmisc_1), [interesting(0.00)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.00)]). fof(t2_xreal_1,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), [interesting(0.00)]). fof(t1_xreal_1,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & r1_xreal_0(B,A) ) => A = B ) ) ) ), file(xreal_1,t1_xreal_1), [interesting(0.00)]). fof(t13_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(B,k3_topreal1(A,D,E)) & r2_hidden(C,k3_topreal1(A,D,E)) ) => k3_topreal1(A,D,E) = k4_subset_1(u1_struct_0(k15_euclid(A)),k4_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,D,B),k3_topreal1(A,B,C)),k3_topreal1(A,C,E)) ) ) ) ) ) ) ), file(topreal1,t13_topreal1), [interesting(0.00)]). fof(t9_topreal1,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xreal_0(k21_euclid(A),k21_euclid(B)) & r2_hidden(C,k3_topreal1(2,A,B)) ) => ( r1_xreal_0(k21_euclid(A),k21_euclid(C)) & r1_xreal_0(k21_euclid(C),k21_euclid(B)) ) ) ) ) ) ), file(topreal1,t9_topreal1), [interesting(0.00)]). fof(d1_tarski,definition,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), [interesting(0.00)]). fof(t15_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( B != C => r1_topreal1(k15_euclid(A),B,C,k3_topreal1(A,B,C)) ) ) ) ) ), file(topreal1,t15_topreal1), [interesting(0.00)]). fof(t18_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( k5_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,B,C),k3_topreal1(A,C,D)) = k1_struct_0(k15_euclid(A),C) => ( ( B = C & C = D ) | r1_topreal1(k15_euclid(A),B,D,k4_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,B,C),k3_topreal1(A,C,D))) ) ) ) ) ) ) ), file(topreal1,t18_topreal1), [interesting(0.00)]). fof(t22_topreal1,theorem,( k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0)),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) = k1_struct_0(k15_euclid(2),k23_euclid(1,0)) ), file(topreal1,t22_topreal1), [interesting(0.00)]). fof(t25_topreal1,theorem,( r1_subset_1(k3_topreal1(2,k23_euclid(0,0),k23_euclid(1,0)),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1))) ), file(topreal1,t25_topreal1), [interesting(0.00)]). fof(t24_topreal1,theorem,( k5_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,k23_euclid(0,1),k23_euclid(1,1)),k3_topreal1(2,k23_euclid(1,0),k23_euclid(1,1))) = k1_struct_0(k15_euclid(2),k23_euclid(1,1)) ), file(topreal1,t24_topreal1), [interesting(0.00)]). fof(t23_xboole_1,theorem,( ! [A,B,C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ), file(xboole_1,t23_xboole_1), [interesting(0.00)]). fof(t16_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r1_topreal1(k15_euclid(A),C,D,B) & k5_subset_1(u1_struct_0(k15_euclid(A)),B,k3_topreal1(A,D,E)) = k1_struct_0(k15_euclid(A),D) ) => r1_topreal1(k15_euclid(A),C,E,k4_subset_1(u1_struct_0(k15_euclid(A)),B,k3_topreal1(A,D,E))) ) ) ) ) ) ) ), file(topreal1,t16_topreal1), [interesting(0.00)]). fof(t17_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r1_topreal1(k15_euclid(A),D,C,B) & k5_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,E,D),B) = k1_struct_0(k15_euclid(A),D) ) => r1_topreal1(k15_euclid(A),E,C,k4_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,E,D),B)) ) ) ) ) ) ) ), file(topreal1,t17_topreal1), [interesting(0.00)]). fof(t4_xboole_1,theorem,( ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ), file(xboole_1,t4_xboole_1), [interesting(0.00)]). fof(t41_enumset1,theorem,( ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ), file(enumset1,t41_enumset1), [interesting(0.00)]). fof(d5_real_1,definition,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) <=> ~ ( r1_xreal_0(B,A) & B != A ) ) ) ) ), file(real_1,d5_real_1), [interesting(0.00)]). fof(t27_xboole_1,theorem,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ), file(xboole_1,t27_xboole_1), [interesting(0.00)]). fof(t5_topreal1,theorem,( ! [A] : ( ( v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_topreal1(A,D,E,B) & r1_topreal1(A,E,F,C) & k5_subset_1(u1_struct_0(A),B,C) = k1_tarski(E) ) => r1_topreal1(A,D,F,k4_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ) ) ) ), file(topreal1,t5_topreal1), [interesting(0.00)]). fof(t11_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k3_topreal1(A,C,D)) => k3_topreal1(A,C,D) = k4_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,C,B),k3_topreal1(A,B,D)) ) ) ) ) ) ), file(topreal1,t11_topreal1), [interesting(0.00)]). fof(t14_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k3_topreal1(A,C,D)) => k5_subset_1(u1_struct_0(k15_euclid(A)),k3_topreal1(A,C,B),k3_topreal1(A,B,D)) = k1_struct_0(k15_euclid(A),B) ) ) ) ) ) ), file(topreal1,t14_topreal1), [interesting(0.00)]). fof(t7_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k1_topreal1(A,B,B) = k1_struct_0(k15_euclid(A),B) ) ) ), file(topreal1,t7_topreal1), [interesting(0.00)]). fof(t56_zfmisc_1,theorem,( ! [A,B] : ( ~ r2_hidden(A,B) => r1_xboole_0(k1_tarski(A),B) ) ), file(zfmisc_1,t56_zfmisc_1), [interesting(0.00)]). fof(t1_xboole_1,theorem,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), [interesting(0.00)]). fof(t7_xboole_1,theorem,( ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ), file(xboole_1,t7_xboole_1), [interesting(0.00)]). fof(t144_relat_1,theorem,( ! [A,B] : ( v1_relat_1(B) => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ), file(relat_1,t144_relat_1), [interesting(0.00)]). fof(t152_relat_1,theorem,( ! [A,B] : ( v1_relat_1(B) => ~ ( A != k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k9_relat_1(B,A) = k1_xboole_0 ) ) ), file(relat_1,t152_relat_1), [interesting(0.00)]). fof(t148_relat_1,theorem,( ! [A,B] : ( v1_relat_1(B) => k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A) ) ), file(relat_1,t148_relat_1), [interesting(0.00)]). fof(t90_relat_1,theorem,( ! [A,B] : ( v1_relat_1(B) => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ), file(relat_1,t90_relat_1), [interesting(0.00)]). fof(t21_xboole_1,theorem,( ! [A,B] : k3_xboole_0(A,k2_xboole_0(A,B)) = A ), file(xboole_1,t21_xboole_1), [interesting(0.00)]). fof(t11_relset_1,theorem,( ! [A,B,C] : ( v1_relat_1(C) => ( ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) => m2_relset_1(C,A,B) ) ) ), file(relset_1,t11_relset_1), [interesting(0.00)]). fof(t4_topmetr,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_pre_topc(B,C) ) ) ) ) ), file(topmetr,t4_topmetr), [interesting(0.00)]). fof(t84_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => v2_funct_1(k7_relat_1(B,A)) ) ) ), file(funct_1,t84_funct_1), [interesting(0.00)]). fof(t146_funct_1,theorem,( ! [A,B] : ( v1_relat_1(B) => ( r1_tarski(A,k1_relat_1(B)) => r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A))) ) ) ), file(funct_1,t146_funct_1), [interesting(0.00)]). fof(t152_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A) ) ) ), file(funct_1,t152_funct_1), [interesting(0.00)]). fof(t43_pre_topc,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v4_pre_topc(C,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D,A) & k3_xboole_0(D,k2_pre_topc(B)) = C ) ) ) ) ) ), file(pre_topc,t43_pre_topc), [interesting(0.00)]). fof(t28_xboole_1,theorem,( ! [A,B] : ( r1_tarski(A,B) => k3_xboole_0(A,B) = A ) ), file(xboole_1,t28_xboole_1), [interesting(0.00)]). fof(t139_funct_1,theorem,( ! [A,B,C] : ( v1_relat_1(C) => k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)) ) ), file(funct_1,t139_funct_1), [interesting(0.00)]). fof(t137_funct_1,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k10_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) ) ), file(funct_1,t137_funct_1), [interesting(0.00)]). fof(t16_xboole_1,theorem,( ! [A,B,C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) ), file(xboole_1,t16_xboole_1), [interesting(0.00)]). fof(t168_relat_1,theorem,( ! [A,B] : ( v1_relat_1(B) => k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) ) ), file(relat_1,t168_relat_1), [interesting(0.00)]). fof(d12_pre_topc,definition,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v5_pre_topc(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( v4_pre_topc(D,B) => v4_pre_topc(k5_pre_topc(A,B,C,D),A) ) ) ) ) ) ) ), file(pre_topc,d12_pre_topc), [interesting(0.00)]). fof(d2_topreal1,definition,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_topreal1(A,B,C,D) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(A,D))) & m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(A,D))) & v3_tops_2(E,k5_topmetr,k3_pre_topc(A,D)) & k1_funct_1(E,0) = B & k1_funct_1(E,1) = C ) ) ) ) ) ) ), file(topreal1,d2_topreal1), [interesting(0.00)]). fof(t11_heine,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => v2_compts_1(k4_topmetr(A,B)) ) ) ) ), file(heine,t11_heine), [interesting(0.00)]). fof(t27_topmetr,theorem,( k4_topmetr(0,1) = k22_borsuk_1 ), file(topmetr,t27_topmetr), [interesting(0.00)]). fof(t23_compts_1,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( v2_compts_1(A) & v5_pre_topc(C,A,B) & k2_relat_1(C) = k2_pre_topc(B) ) => v2_compts_1(B) ) ) ) ) ), file(compts_1,t23_compts_1), [interesting(0.00)]). fof(t3_topmetr,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ( v3_compts_1(A) => v3_compts_1(B) ) ) ) ), file(topmetr,t3_topmetr), [interesting(0.00)]). fof(t26_compts_1,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( v2_compts_1(A) & v3_compts_1(B) & k1_relat_1(C) = k2_pre_topc(A) & k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & v5_pre_topc(C,A,B) ) => v3_tops_2(C,A,B) ) ) ) ) ), file(compts_1,t26_compts_1), [interesting(0.00)]). fof(d2_tarski,definition,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), [interesting(0.00)]). fof(t17_xboole_1,theorem,( ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ), file(xboole_1,t17_xboole_1), [interesting(0.00)]). fof(t57_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) ) => ( A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) ) ) ) ), file(funct_1,t57_funct_1), [interesting(0.00)]). fof(t71_funct_1,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t71_funct_1), [interesting(0.00)]). fof(t71_tops_2,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) ) => ( ( v3_tops_2(D,A,B) & v3_tops_2(E,B,C) ) => v3_tops_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ), file(tops_2,t71_tops_2), [interesting(0.00)]). fof(t83_borsuk_1,theorem,( u1_struct_0(k22_borsuk_1) = k1_rcomp_1(0,1) ), file(borsuk_1,t83_borsuk_1), [interesting(0.00)]). fof(t15_rcomp_1,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ ( ~ r1_xreal_0(B,A) & k2_rcomp_1(A,B) = k1_xboole_0 ) & ( r1_xreal_0(A,B) => ( r2_hidden(A,k1_rcomp_1(A,B)) & r2_hidden(B,k1_rcomp_1(A,B)) ) ) & r1_tarski(k2_rcomp_1(A,B),k1_rcomp_1(A,B)) ) ) ) ), file(rcomp_1,t15_rcomp_1), [interesting(0.00)]). fof(t23_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), [interesting(0.00)]). fof(t3_topreal2,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k3_pre_topc(k15_euclid(2),C)),u1_struct_0(k3_pre_topc(k15_euclid(2),D))) & m2_relset_1(E,u1_struct_0(k3_pre_topc(k15_euclid(2),C)),u1_struct_0(k3_pre_topc(k15_euclid(2),D))) ) => ( ( v3_tops_2(E,k3_pre_topc(k15_euclid(2),C),k3_pre_topc(k15_euclid(2),D)) & r1_topreal1(k15_euclid(2),A,B,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ( ( F = k1_funct_1(E,A) & G = k1_funct_1(E,B) ) => r1_topreal1(k15_euclid(2),F,G,D) ) ) ) ) ) ) ) ) ) ), inference(mizar_proof,[status(thm)],[d2_topreal1,t71_tops_2,t83_borsuk_1,d1_funct_2,t15_rcomp_1,t23_funct_1,t15_rcomp_1,t23_funct_1,d2_topreal1]), [file(topreal2,t3_topreal2),interesting(0.00)]). fof(t146_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A) ) ), file(relat_1,t146_relat_1), [interesting(0.00)]). fof(t153_relat_1,theorem,( ! [A,B,C] : ( v1_relat_1(C) => k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) ), file(relat_1,t153_relat_1), [interesting(0.00)]). fof(t121_funct_1,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v2_funct_1(C) => k9_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ), file(funct_1,t121_funct_1), [interesting(0.00)]). fof(t117_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k1_relat_1(B)) => k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A)) ) ) ), file(funct_1,t117_funct_1), [interesting(0.00)]). fof(t30_topreal1,theorem,( ? [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) & ? [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v4_topreal1(A) & v4_topreal1(B) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,A),k5_topreal1(2,B)) & k5_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(2,A),k5_topreal1(2,B)) = k2_struct_0(k15_euclid(2),k23_euclid(0,0),k23_euclid(1,1)) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1) = k23_euclid(0,0) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) = k23_euclid(1,1) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,1) = k23_euclid(0,0) & k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B)) = k23_euclid(1,1) ) ) ), file(topreal1,t30_topreal1), [interesting(0.00)]). fof(t31_topreal1,theorem,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => r1_topreal1(k15_euclid(2),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,1),k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)),k5_topreal1(2,A)) ) ) ), file(topreal1,t31_topreal1), [interesting(0.00)]). fof(t7_topmetr,theorem,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) ) => ( ( v5_pre_topc(D,A,C) & m1_pre_topc(C,B) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) ) => ( E = D => v5_pre_topc(E,A,B) ) ) ) ) ) ) ) ), file(topmetr,t7_topmetr), [interesting(0.00)]). fof(d10_topreal1,definition,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) <=> ( v2_funct_1(A) & r1_xreal_0(2,k3_finseq_1(A)) & v2_topreal1(A) & v3_topreal1(A) & v1_topreal1(A) ) ) ) ), file(topreal1,d10_topreal1), [interesting(0.00)]). fof(t29_topreal1,theorem,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ~ ( r1_xreal_0(2,k3_finseq_1(B)) & k5_topreal1(A,B) = k1_xboole_0 ) ) ) ), file(topreal1,t29_topreal1), [interesting(0.00)]). fof(t58_tops_2,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( ~ v3_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) ) => ( ( v5_pre_topc(D,A,C) & v5_pre_topc(E,C,B) ) => v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(B),D,E),A,B) ) ) ) ) ) ) ), file(tops_2,t58_tops_2), [interesting(0.00)]). fof(t21_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) <=> ( r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) ) ) ) ) ), file(funct_1,t21_funct_1), [interesting(0.00)]). fof(t22_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ), file(funct_1,t22_funct_1), [interesting(0.00)]). fof(t5_topmetr2,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_pre_topc(C,B) => ! [D] : ( m1_pre_topc(D,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(G,u1_struct_0(C),u1_struct_0(A)) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(D),u1_struct_0(A)) & m2_relset_1(H,u1_struct_0(D),u1_struct_0(A)) ) => ( ( k2_xboole_0(k2_pre_topc(C),k2_pre_topc(D)) = k2_pre_topc(B) & k3_xboole_0(k2_pre_topc(C),k2_pre_topc(D)) = k2_struct_0(B,E,F) & v2_compts_1(C) & v2_compts_1(D) & v3_compts_1(B) & v5_pre_topc(G,C,A) & v5_pre_topc(H,D,A) & k1_funct_1(G,E) = k1_funct_1(H,E) & k1_funct_1(G,F) = k1_funct_1(H,F) ) => ( v1_funct_1(k1_funct_4(G,H)) & v1_funct_2(k1_funct_4(G,H),u1_struct_0(B),u1_struct_0(A)) & v5_pre_topc(k1_funct_4(G,H),B,A) & m2_relset_1(k1_funct_4(G,H),u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ), file(topmetr2,t5_topmetr2), [interesting(0.00)]). fof(t34_topreal1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [B] : ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v5_topreal1(A) & v5_topreal1(B) & k2_topreal1 = k4_subset_1(u1_struct_0(k15_euclid(2)),A,B) & k5_subset_1(u1_struct_0(k15_euclid(2)),A,B) = k2_struct_0(k15_euclid(2),k23_euclid(0,0),k23_euclid(1,1)) ) ) ), file(topreal1,t34_topreal1), [interesting(0.00)]). fof(t36_topreal1,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( v5_topreal1(A) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(2),A))) & m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(2),A))) ) => ~ v3_tops_2(B,k5_topmetr,k3_pre_topc(k15_euclid(2),A)) ) ) ) ), file(topreal1,t36_topreal1), [interesting(0.00)]). fof(t12_compts_1,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( B = k1_xboole_0 => ( v6_compts_1(B,A) <=> v2_compts_1(k3_pre_topc(A,B)) ) ) & ( v2_pre_topc(A) => ( B = k1_xboole_0 | ( v6_compts_1(B,A) <=> v2_compts_1(k3_pre_topc(A,B)) ) ) ) ) ) ) ), file(compts_1,t12_compts_1), [interesting(0.00)]). fof(t19_compts_1,theorem,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v6_compts_1(B,A) & v6_compts_1(C,A) ) => v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ), file(compts_1,t19_compts_1), [interesting(0.00)]). fof(t46_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(A) & v2_funct_1(B) ) => v2_funct_1(k5_relat_1(A,B)) ) ) ) ), file(funct_1,t46_funct_1), [interesting(0.00)]). fof(t46_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), [interesting(0.00)]). fof(d12_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k9_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & D = k1_funct_1(A,E) ) ) ) ) ), file(funct_1,d12_funct_1), [interesting(0.00)]). fof(t47_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k1_relat_1(A),k2_relat_1(B)) => k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) ) ) ) ), file(relat_1,t47_relat_1), [interesting(0.00)]). fof(t3_topmetr2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k9_relat_1(A,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))),k2_relat_1(B)) => k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k1_funct_4(A,B)) ) ) ) ), file(topmetr2,t3_topmetr2), [interesting(0.00)]). fof(d4_xboole_0,definition,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), [interesting(0.00)]). fof(t2_topmetr2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(A) & v2_funct_1(B) & ! [C,D] : ~ ( r2_hidden(C,k1_relat_1(B)) & r2_hidden(D,k4_xboole_0(k1_relat_1(A),k1_relat_1(B))) & k1_funct_1(B,C) = k1_funct_1(A,D) ) ) => v2_funct_1(k1_funct_4(A,B)) ) ) ) ), file(topmetr2,t2_topmetr2), [interesting(0.00)]).