0.04/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n008.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1200 0.12/0.33 % DateTime : Wed Jul 14 17:28:00 EDT 2021 0.12/0.34 % CPUTime : 4.47/4.60 ============================== Prover9 =============================== 4.47/4.60 Prover9 (32) version 2009-11A, November 2009. 4.47/4.60 Process 29157 was started by sandbox on n008.cluster.edu, 4.47/4.60 Wed Jul 14 17:28:03 2021 4.47/4.60 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_29003_n008.cluster.edu". 4.47/4.60 ============================== end of head =========================== 4.47/4.60 4.47/4.60 ============================== INPUT ================================= 4.47/4.60 4.47/4.60 % Reading from file /tmp/Prover9_29003_n008.cluster.edu 4.47/4.60 4.47/4.60 set(prolog_style_variables). 4.47/4.60 set(auto2). 4.47/4.60 % set(auto2) -> set(auto). 4.47/4.60 % set(auto) -> set(auto_inference). 4.47/4.60 % set(auto) -> set(auto_setup). 4.47/4.60 % set(auto_setup) -> set(predicate_elim). 4.47/4.60 % set(auto_setup) -> assign(eq_defs, unfold). 4.47/4.60 % set(auto) -> set(auto_limits). 4.47/4.60 % set(auto_limits) -> assign(max_weight, "100.000"). 4.47/4.60 % set(auto_limits) -> assign(sos_limit, 20000). 4.47/4.60 % set(auto) -> set(auto_denials). 4.47/4.60 % set(auto) -> set(auto_process). 4.47/4.60 % set(auto2) -> assign(new_constants, 1). 4.47/4.60 % set(auto2) -> assign(fold_denial_max, 3). 4.47/4.60 % set(auto2) -> assign(max_weight, "200.000"). 4.47/4.60 % set(auto2) -> assign(max_hours, 1). 4.47/4.60 % assign(max_hours, 1) -> assign(max_seconds, 3600). 4.47/4.60 % set(auto2) -> assign(max_seconds, 0). 4.47/4.60 % set(auto2) -> assign(max_minutes, 5). 4.47/4.60 % assign(max_minutes, 5) -> assign(max_seconds, 300). 4.47/4.60 % set(auto2) -> set(sort_initial_sos). 4.47/4.60 % set(auto2) -> assign(sos_limit, -1). 4.47/4.60 % set(auto2) -> assign(lrs_ticks, 3000). 4.47/4.60 % set(auto2) -> assign(max_megs, 400). 4.47/4.60 % set(auto2) -> assign(stats, some). 4.47/4.60 % set(auto2) -> clear(echo_input). 4.47/4.60 % set(auto2) -> set(quiet). 4.47/4.60 % set(auto2) -> clear(print_initial_clauses). 4.47/4.60 % set(auto2) -> clear(print_given). 4.47/4.60 assign(lrs_ticks,-1). 4.47/4.60 assign(sos_limit,10000). 4.47/4.60 assign(order,kbo). 4.47/4.60 set(lex_order_vars). 4.47/4.60 clear(print_given). 4.47/4.60 4.47/4.60 % formulas(sos). % not echoed (3643 formulas) 4.47/4.60 4.47/4.60 ============================== end of input ========================== 4.47/4.60 4.47/4.60 % From the command line: assign(max_seconds, 1200). 4.47/4.60 4.47/4.60 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 4.47/4.60 4.47/4.60 % Formulas that are not ordinary clauses: 4.47/4.60 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 3 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 4 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 5 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 6 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 8 (all A all B -((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,C) & r2_hidden(D,B))))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 9 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(C,D) & r2_hidden(D,A))))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 10 (all A exists B ((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 11 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (D = F <-> E = G))) & (all D -((all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 13 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 14 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 15 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 16 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 17 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 19 (all A all B all C ((all D (r2_hidden(D,C) <-> D = B | D = A)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 21 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 23 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 24 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 25 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 26 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 27 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 29 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (r2_hidden(A,f1_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 30 (all A all B all C -(r1_xboole_0(A,B) & r2_hidden(C,k2_xboole_0(A,B)) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 31 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 32 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 33 (all A all B (r1_xboole_0(A,B) <-> k1_xboole_0 = k3_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 34 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 35 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 36 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 37 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 38 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 39 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 41 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 42 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 43 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 44 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 45 (all A all B (r2_xboole_0(A,B) <-> r1_tarski(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 46 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 47 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 48 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 49 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 50 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 51 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 52 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> -r2_hidden(D,B) & r2_hidden(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 53 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 54 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 55 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 56 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))) <-> k2_xboole_0(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 57 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 58 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 59 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 60 (all A all B all C (-(r2_hidden(A,C) <-> r2_hidden(A,B)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 61 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 65 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 66 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 67 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 68 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 69 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 70 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 71 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 72 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 73 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 74 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 75 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> k1_xboole_0 = A)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 76 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 77 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 78 (all A all B all C all D (r1_xboole_0(C,D) & r1_xboole_0(B,D) & r1_xboole_0(A,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 79 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 80 (all A all B k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 81 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 82 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 83 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 84 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k4_xboole_0(B,A))) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 85 (all A all B all C all D (r1_xboole_0(B,D) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 86 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) & r1_tarski(A,C) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 87 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 88 (all A all B k3_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B))) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 89 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 90 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 91 (all A all B k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B)) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 92 (all A (-(-r1_xboole_0(A,A) & A = k1_xboole_0) & -(A != k1_xboole_0 & r1_xboole_0(A,A)))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 93 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 94 (all A all B all C k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),C)) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 95 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 96 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 97 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 98 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.60 99 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 100 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 101 (all A all B k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 102 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> A = B)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 103 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 104 (all A all B all C (-(-(r1_xboole_0(A,C) & r1_xboole_0(A,B)) & r1_xboole_0(A,k2_xboole_0(B,C))) & -(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,B) & r1_xboole_0(A,C)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 105 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 106 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 107 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 108 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 109 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 110 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 111 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 112 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 113 (all A all B -(r2_xboole_0(A,B) & k4_xboole_0(B,A) = k1_xboole_0)) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 114 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 115 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 116 (all A all B all C k3_xboole_0(k5_xboole_0(A,C),B) = k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 117 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 118 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k2_xboole_0(A,B))) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 119 (all A all B k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 120 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 121 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 122 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 123 (all A all B all C (k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 124 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 125 (all A all B all C all D (r1_xboole_0(C,A) & r1_xboole_0(D,B) & k2_xboole_0(C,D) = k2_xboole_0(A,B) -> C = B)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 126 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 127 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 128 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 129 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 130 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 131 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 132 (all A all B all C (r2_xboole_0(B,C) & r1_tarski(A,B) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 133 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 134 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 135 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 136 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 137 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 138 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 139 (all A all B k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 140 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 141 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 142 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 143 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 144 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 145 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 146 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 147 (all A all B (-v1_xboole_0(B) -> -(r1_tarski(B,A) & r1_xboole_0(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 148 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,A) & r1_xboole_0(A,B) & r1_tarski(C,B)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 149 (all A all B -(-r1_xboole_0(A,B) & r1_xboole_0(k3_xboole_0(A,B),B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 150 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 151 (all A all B all C (r2_xboole_0(A,B) & r1_tarski(B,C) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 152 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 153 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 154 (all A all B A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 155 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 156 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 157 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 158 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 159 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 160 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 161 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 162 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 163 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 164 (all A all B A = k3_xboole_0(A,k2_xboole_0(A,B))) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 165 (all A all B (-(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 166 (all A all B k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 167 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 168 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 169 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 170 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 171 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 172 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 173 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k4_xboole_0(A,C),B)) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 174 (all A all B all C k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 175 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 176 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 177 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C))) = k4_xboole_0(k5_xboole_0(A,B),C)) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 178 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 179 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 180 (all A all B all C ((all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 181 (all A all B all C k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A)) = k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 182 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 183 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> A = k1_xboole_0 | k1_xboole_0 = B | B = D & C = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 184 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 185 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 | k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 186 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 187 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 188 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 189 (all A all B all C all D k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) = k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 190 (all A all B -((all C -(B != C & r2_hidden(C,A))) & k1_xboole_0 != A & A != k1_tarski(B))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 191 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 192 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 193 (all A all B (A = k1_tarski(B) | k1_xboole_0 = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 194 (all A all B (A = k1_xboole_0 | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 195 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 196 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 197 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) -> r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)))) # label(t107_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 198 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 199 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 200 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 201 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 202 (all A all B (k2_zfmisc_1(B,B) = k2_zfmisc_1(A,A) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 203 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 204 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 205 (all A all B all C -(k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 206 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 207 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 208 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 209 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 210 (all A all B all C -(-r2_hidden(A,B) & -r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 211 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 212 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 213 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 214 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 215 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 216 (all A all B all C all D k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 217 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> D = C | r1_xboole_0(C,D))) -> k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_xboole_0(A,B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 218 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 219 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 220 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 221 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 222 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 223 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_xboole_0 & A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 224 (all A all B k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 225 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 226 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 227 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 228 (all A all B all C -(B != C & B != k1_xboole_0 & k1_xboole_0 != C & k1_tarski(A) = k2_xboole_0(B,C))) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 229 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t95_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 230 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(B,C)) & r2_hidden(A,k2_zfmisc_1(D,E)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 231 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 232 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 233 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 234 (all A all B (A != B -> k2_tarski(A,B) = k5_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 235 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 236 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 237 (all A all B all C -(-r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 238 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 239 (all A all B r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t84_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 240 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <-> r2_hidden(A,C) & B = D)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 241 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(A,C) & r1_tarski(B,D) | k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 242 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(C,B))) -> r1_tarski(k3_tarski(A),B))) # label(t94_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 243 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 244 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 245 (all A all B all C all D all E -((all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))) & r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 246 (all A all B all C all D -(C != A & A != D & k2_tarski(C,D) = k2_tarski(A,B))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 247 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 248 (all A all B (r1_tarski(k2_xboole_0(k1_tarski(A),B),B) -> r2_hidden(A,B))) # label(t45_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 249 (all A all B all C -(-(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_tarski(A) = B & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 250 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 251 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 252 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 253 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E C != k4_tarski(D,E)))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 254 (all A all B all C (k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) & k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 255 (all A all B all C k1_xboole_0 != k2_xboole_0(k2_tarski(A,B),C)) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 256 (all A all B (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(B,k1_tarski(A)))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 257 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 258 (all A all B r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B))))) # label(t105_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 259 (all A all B (-r2_hidden(A,B) -> r1_xboole_0(k1_tarski(A),B))) # label(t56_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 260 (all A all B all C (k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k4_xboole_0(A,B),C))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 261 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 262 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 263 (all A all B ((all C (r2_hidden(C,A) -> r1_xboole_0(C,B))) -> r1_xboole_0(k3_tarski(A),B))) # label(t98_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 264 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 265 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 266 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k2_tarski(B,C) != A & A != k1_tarski(C) & A != k1_tarski(B) & k1_xboole_0 != A))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 267 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 268 (all A all B all C (r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) -> r2_hidden(A,C))) # label(t47_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 269 (all A all B r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t97_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 270 (all A all B (k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) -> k1_xboole_0 = B | A = B | k1_xboole_0 = A)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 271 (all A all B all C all D (D = B & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 272 (all A all B all C (k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) & k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) = k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 273 (all A all B all C all D (r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F (r2_hidden(k4_tarski(E,F),A) -> r2_hidden(k4_tarski(E,F),D))) -> r1_tarski(A,D))) # label(t109_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 274 (all A all B (r1_tarski(A,k2_zfmisc_1(B,A)) | r1_tarski(A,k2_zfmisc_1(A,B)) -> k1_xboole_0 = A)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 275 (all A all B all C (-r2_hidden(B,C) & -r2_hidden(A,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 276 (all A all B all C -(r2_hidden(A,C) & r1_xboole_0(k2_tarski(A,B),C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 277 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 278 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 279 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 280 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 281 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 282 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 283 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 284 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 285 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 286 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0 <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 287 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 288 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 289 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 290 (all A all B all C -(r2_hidden(B,C) & B != A & k1_tarski(A) = k3_xboole_0(k2_tarski(A,B),C))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 291 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 292 (all A all B all C all D k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 293 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 294 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 295 (all A all B -(k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)) & A != k1_xboole_0 & A != k1_tarski(B))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 296 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 297 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> B = k2_xboole_0(k2_tarski(A,C),B))) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 298 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B)))) # label(t81_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 299 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 300 (all A all B all C (r1_tarski(A,B) -> r2_hidden(C,A) | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 301 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 302 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 303 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 304 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 305 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k1_tarski(C) = k2_tarski(A,B))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 306 (all A all B (B != A -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 307 (all A all B (-r2_hidden(A,B) -> k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 308 (all A exists B ((all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 309 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 310 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 311 (all A all B all C ((B = A | r2_hidden(B,C)) & -r2_hidden(A,C) <-> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 312 (all A all B all C (k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 313 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 314 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B)))) # label(t86_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 315 (all A all B k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 316 (all A all B -(r2_hidden(A,B) & r1_xboole_0(k1_tarski(A),B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 317 (all A k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 318 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A) & k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 319 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> A = C & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 320 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 321 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 322 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 323 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 324 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 325 (all A all B all C (k2_zfmisc_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 326 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 327 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 328 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 329 (all A all B (k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 330 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 331 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 332 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 333 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 334 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 335 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 336 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 337 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 338 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 339 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 340 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 341 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 342 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 343 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 344 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 345 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 346 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)))))) # label(t41_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 347 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.61 348 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) | r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 349 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,k3_subset_1(A,C)) <-> r1_tarski(B,C)))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 350 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 351 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 352 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 353 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 354 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 355 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 356 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 357 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 358 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 359 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 360 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 361 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))))))) # label(t42_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 362 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & -r2_hidden(E,D) <-> r2_hidden(E,B)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 363 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 364 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> r1_xboole_0(B,k3_subset_1(A,B)))) # label(t26_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 365 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 366 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 367 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B))))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.47/4.62 368 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> A = B))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 369 (all A all B (r2_hidden(A,B) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)))) # label(t63_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 370 (all A all B ((v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))) & (-v1_xboole_0(A) -> (m1_subset_1(B,A) <-> r2_hidden(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 371 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 372 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 373 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 374 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k5_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 375 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 376 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,D) <-> r2_hidden(E,C))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 377 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 378 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 379 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> -r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 380 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 381 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 382 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 383 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 385 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 386 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 387 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 388 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 389 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 390 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 391 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 392 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 393 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (A != k1_xboole_0 -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 394 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 395 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,C) & r2_hidden(B,k3_subset_1(A,C))))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 396 (exists A ((all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))) & m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 397 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 398 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 399 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k2_subset_1(A)))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 400 (all A (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 401 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 402 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) -> r2_subset_1(B,A)))) # label(symmetry_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 403 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 404 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 405 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 406 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 407 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 408 (exists A ((all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 409 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 410 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 411 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 412 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 413 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 414 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 415 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (k1_xboole_0 != A -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 416 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 417 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 418 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 419 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 420 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 421 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 422 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 423 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 424 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 425 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 426 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 427 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 428 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 429 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 430 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 431 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 432 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 433 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 434 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 435 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> k3_subset_1(A,C) = B))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 436 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 437 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 438 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 439 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 440 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),C) -> r1_tarski(k3_subset_1(A,C),B)))))) # label(t36_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 441 (all A all B (r1_tarski(A,B) <-> m1_subset_1(A,k1_zfmisc_1(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 442 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 443 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 444 (all A all B all C -(m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 445 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 446 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 447 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 448 (all A all B (v1_relat_1(B) -> r1_tarski(k7_relat_1(B,A),B))) # label(t88_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 449 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 450 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 451 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 452 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 453 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 454 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) = k7_relat_1(B,A))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 455 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k1_xboole_0 = k10_relat_1(B,A)))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 456 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 457 (all A all B (v1_relat_1(B) -> r1_tarski(k8_relat_1(A,B),B))) # label(t117_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 458 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 459 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 460 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 461 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 462 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B))))) # label(t104_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 463 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 464 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 465 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))))) # label(t155_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 466 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))))))) # label(t15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 467 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t178_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 468 (all A (v1_relat_1(A) -> (all 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)))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 469 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) <-> (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 470 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)))))) # label(t92_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 471 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 472 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(A,C) & r2_hidden(k4_tarski(A,B),D)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 473 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)))))) # label(t44_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 474 (all A all B (v1_relat_1(B) -> (r1_tarski(A,B) -> v1_relat_1(A)))) # label(t3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 475 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 476 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 477 (all A all B (v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 478 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 479 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 480 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 481 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 482 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 483 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 484 (all A (k2_relat_1(k6_relat_1(A)) = A & k1_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 485 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 486 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 487 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C))))) # label(t131_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 488 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 489 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))) = k7_relat_1(A,k1_relat_1(B)))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 490 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 491 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 492 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))))) # label(t147_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 493 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 494 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B)))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 495 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 496 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 497 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 498 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A))))))) # label(t179_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 499 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 500 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 501 (all A (v1_relat_1(A) -> (v2_relat_1(A) <-> -r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(d9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 502 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 503 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))))))) # label(t34_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 504 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 505 (all A (v1_relat_1(A) -> k2_relat_1(A) = k9_relat_1(A,k1_relat_1(A)))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 506 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C))))))) # label(t132_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 507 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t89_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 508 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 509 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 510 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 511 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 512 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 513 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 514 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 515 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 516 (all A all B all C (v1_relat_1(C) -> k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 517 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t118_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 518 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 519 (all A all B (v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k4_tarski(C,C),B))) -> r1_tarski(k6_relat_1(A),B)))) # label(t73_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 520 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 521 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A))) # label(t87_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 522 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 523 (all A all B (v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)))) # label(t10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 524 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 525 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 526 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (C = k5_relat_1(A,B) <-> (all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 527 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 528 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 529 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 530 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 531 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 532 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)))) # label(t161_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 533 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 534 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 535 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 536 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t157_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 537 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 538 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 539 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 540 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 541 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 542 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(k5_relat_1(A,B),C))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 543 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 544 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 545 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 546 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,C) = k7_relat_1(A,C) & k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 547 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 548 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k2_relat_1(B))) & r2_hidden(A,k1_relat_1(B))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 549 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)))))) # label(t45_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 550 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))))) # label(t163_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 551 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 552 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (k8_relat_1(A,B) = C <-> (all D all E (r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 553 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 554 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 555 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 556 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.62 557 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 558 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 559 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 560 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k1_relat_1(k4_relat_1(A)) = k2_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 561 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k5_relat_1(B,D) = k6_relat_1(A) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 562 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 563 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))))))) # label(t28_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 564 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k7_relat_1(B,A)))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 565 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 566 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k1_xboole_0 = k9_relat_1(B,A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 567 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 568 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 569 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 570 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 571 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> k2_relat_1(E) = k2_tarski(B,D) & k1_relat_1(E) = k2_tarski(A,C)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 572 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 573 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 574 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 575 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 576 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 577 (all A all B all C (v1_relat_1(C) -> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t176_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 578 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 579 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_relat_1(A)) = A)) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 580 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k1_relat_1(B))) & r2_hidden(A,k2_relat_1(B))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 581 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A))))))) # label(t105_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 582 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 583 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t48_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 584 (all A (v1_relat_1(A) <-> (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 585 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))))))))) # label(t52_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 586 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 587 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 588 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 589 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 590 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 591 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k7_relat_1(C,B)) = k7_relat_1(k8_relat_1(A,C),B))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 592 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 593 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 594 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 595 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 596 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(C,A) & C = D <-> r2_hidden(k4_tarski(C,D),B))) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 597 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 598 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 599 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 600 (all A all B (v1_relat_1(B) -> k5_relat_1(k6_relat_1(A),B) = k7_relat_1(B,A))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 601 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> B = k2_relat_1(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 602 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C))) <-> r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C)))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 603 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))))) # label(t183_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 604 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 605 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 606 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 607 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 608 (exists A (v1_relat_1(A) & (all B all C (p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1) & r2_hidden(B,f1_s1_relat_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 609 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 610 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 611 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(A),k3_relat_1(A)) & r1_tarski(k2_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 612 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 613 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 614 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)))))) # label(t93_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 615 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 616 (all A (v1_relat_1(A) -> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 617 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 618 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 619 (all A (v1_relat_1(A) -> A = k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 620 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 621 (all A all B all C all D v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 622 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)))) # label(t144_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 623 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 624 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 625 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 626 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 627 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 628 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 629 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 630 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 631 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k1_xboole_0 = k5_relat_1(A,B)))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 632 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))))))))) # label(t53_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 633 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 634 (all A (v1_relat_1(A) -> k3_relat_1(k4_relat_1(A)) = k3_relat_1(A))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 635 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 636 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 637 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 638 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 639 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 640 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))))) # label(t177_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 641 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(E,D),A))) <-> r2_hidden(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 642 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 643 (all A (v1_relat_1(A) -> (all 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)))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 644 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))))))))) # label(t49_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 645 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k7_relat_1(B,A) = k1_xboole_0))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 646 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t99_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 647 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t27_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 648 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 649 (all A (v1_xboole_0(A) -> v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 650 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 651 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 652 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 653 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)))))) # label(t121_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 654 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 655 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k8_relat_1(A,B)))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 656 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 657 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 658 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A))) # label(t116_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 659 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t154_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 660 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 661 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 662 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 663 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 664 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 665 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 666 (all A all B (v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(t9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 667 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 668 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 669 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 != A))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 670 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))))) # label(t170_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 671 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 672 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 673 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 674 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 675 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 676 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 677 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> k5_relat_1(A,B) = C))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 678 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 679 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 680 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 681 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(C,A) = k5_relat_1(B,A) & k1_relat_1(C) = k1_relat_1(B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> B = C)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 682 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & k1_funct_1(A,E) = D)))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 683 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 684 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 685 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 686 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 687 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (D = k1_funct_1(A,C) <-> k1_funct_1(B,D) = C))) & k1_relat_1(B) = k2_relat_1(A) & k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 688 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 689 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 690 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> k1_funct_1(A,B) = C)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 691 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 692 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 693 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 694 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 695 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_1(A)) & v1_relat_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 696 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 697 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k9_relat_1(k8_relat_1(A,C),B) = k3_xboole_0(A,k9_relat_1(C,B)))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 698 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 699 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 700 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 701 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 702 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 703 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 704 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 705 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 706 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 707 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 708 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 709 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 710 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 711 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 712 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 713 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 714 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))) = k3_xboole_0(k9_relat_1(C,A),B))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 715 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 716 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & k2_relat_1(A) = k1_relat_1(B) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 717 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 718 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 719 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 720 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 721 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -((all B -p1_s2_funct_1(A,B)) & r2_hidden(A,f1_s2_funct_1))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 722 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 723 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 724 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,A) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 725 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 726 (all A all B all 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)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 727 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 728 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) & k1_relat_1(C) = A -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 729 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 730 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 731 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 732 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 733 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 734 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 735 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 736 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 737 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 738 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 739 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 740 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k1_relat_1(A) = k2_relat_1(B) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 741 (all A all B -(-(A = k1_xboole_0 & B != k1_xboole_0) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -(k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 742 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all 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))))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 743 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) & r2_hidden(C,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 744 (all A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A) -> v1_funct_1(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 745 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 746 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 747 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 748 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 749 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 750 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 751 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 752 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 753 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) & k1_relat_1(B) = k1_relat_1(C) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 754 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 755 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k10_relat_1(B,k1_tarski(A)) != k1_xboole_0))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 756 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A & k1_relat_1(C) = A -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 757 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 758 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D ((r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k2_relat_1(A) = k1_relat_1(B) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 759 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 760 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 761 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 762 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 763 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 764 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.63 765 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(D) = A & k1_relat_1(C) = A & k2_relat_1(B) = A -> C = D))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 766 (all A all B all 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)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 767 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 768 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 769 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 770 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 771 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 772 (all A (A != k1_xboole_0 -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = A & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 773 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 774 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 775 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 776 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 777 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 778 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 779 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 780 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 781 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) <-> (all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 782 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 783 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 784 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) <-> k8_relat_1(A,C) = B))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 785 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 786 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 787 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 788 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 789 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 790 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 791 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k2_relat_1(A) & A = k5_relat_1(A,B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 792 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 793 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 794 (all A all 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)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 795 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 796 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 797 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_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)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 798 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 799 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 800 (all A all B (r2_hidden(B,A) -> B = k1_funct_1(k6_relat_1(A),B))) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 801 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 802 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 803 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 804 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 805 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 806 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 807 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 808 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 809 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 810 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 811 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 812 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 813 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 814 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 815 (all A all B all C (v1_relat_1(C) -> k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 816 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 817 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 818 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> f2_s3_funct_1(B) = k1_funct_1(A,B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 819 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(C)) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(k5_relat_1(B,C),k9_relat_1(C,A)))))))) # label(t160_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 820 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 821 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 822 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 823 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 824 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 825 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 826 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 827 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 828 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 829 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 830 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 831 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 832 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 833 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 834 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 835 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 836 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 837 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 838 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & r1_tarski(A,k1_relat_1(C)) & v2_funct_1(C) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 839 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C ((exists D (r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D))) <-> r2_hidden(C,B))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 840 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 841 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 842 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 843 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 844 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 845 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 846 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 847 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 848 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A)))))) # label(t146_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 849 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 850 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 851 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 852 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 853 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 854 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 855 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 856 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 857 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 858 (all A all B (v1_relat_1(B) -> ((all C -(k10_relat_1(B,k1_tarski(C)) = k1_xboole_0 & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 859 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 860 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(C = k1_funct_1(B,D) & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 861 (all A all B all C (v1_relat_1(C) -> r1_tarski(k3_xboole_0(A,k10_relat_1(C,B)),k10_relat_1(C,k3_xboole_0(k9_relat_1(C,A),B))))) # label(t151_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 862 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 863 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 864 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 865 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 866 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 867 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 868 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 869 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 870 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 871 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r1_tarski(k5_relat_1(A,A),A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 872 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 873 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v5_relat_2(k4_relat_1(A))))) # label(t36_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 874 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 875 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k2_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 876 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(A) -> v2_relat_2(k4_xboole_0(A,B))))))) # label(t33_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 877 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 878 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 879 (all A (v1_relat_1(A) -> (v4_relat_2(A) -> v4_relat_2(k4_relat_1(A))))) # label(t40_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 880 (all A (v1_relat_1(A) -> (r2_relat_2(A,k3_relat_1(A)) <-> v2_relat_2(A)))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 881 (all A (v1_relat_1(A) -> (r1_relat_2(A,k3_relat_1(A)) <-> v1_relat_2(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 882 (all A (v1_relat_1(A) -> (r4_relat_2(A,k3_relat_1(A)) <-> v4_relat_2(A)))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 883 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k1_relat_1(k4_relat_1(A)) = k1_relat_1(A)))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 884 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r8_relat_2(A,k3_relat_1(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 885 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v6_relat_2(A) & v1_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 886 (all A (v1_relat_1(A) -> (r1_xboole_0(k6_relat_1(k3_relat_1(A)),A) <-> v2_relat_2(A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 887 (all A (v1_relat_1(A) -> (v8_relat_2(A) -> v8_relat_2(k4_relat_1(A))))) # label(t42_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 888 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) <-> (all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 889 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 890 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 891 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 892 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 893 (all A (v1_relat_1(A) -> (v5_relat_2(A) <-> r5_relat_2(A,k3_relat_1(A))))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 894 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 895 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> v1_relat_2(k4_relat_1(A))))) # label(t27_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 896 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 897 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 898 (all A (v1_relat_1(A) -> (v3_relat_2(A) -> v3_relat_2(k4_relat_1(A))))) # label(t34_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 899 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 900 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 901 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) -> v5_relat_2(k4_xboole_0(A,B))))))) # label(t38_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 902 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 903 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 904 (all A (v1_relat_1(A) -> (A = k4_relat_1(A) <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 905 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,C),A) & r2_hidden(C,B))) <-> r2_relat_2(A,B))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 906 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 907 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 908 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 909 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(B) & v2_relat_2(A) -> v2_relat_2(k2_xboole_0(A,B)) & v2_relat_2(k3_xboole_0(A,B))))))) # label(t32_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 910 (all A (v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 911 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 912 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k3_xboole_0(A,B)) & v4_relat_2(k4_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 913 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 914 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 915 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r6_relat_2(A,k3_relat_1(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 916 (all A all B (v1_relat_1(B) -> (r4_relat_2(B,A) <-> r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 917 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 918 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 919 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 920 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 921 (all A (v1_relat_1(A) -> (v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 922 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 923 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A)))))) # label(t45_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 924 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v4_relat_2(A) & v2_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 925 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 926 (all A (v1_relat_1(A) -> (all B (r7_relat_2(A,B) <-> (all C all D -(-r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 927 (all A (v1_relat_1(A) -> (r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A))) <-> v4_relat_2(A)))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 928 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 929 (all A (v1_relat_1(A) -> (r1_tarski(k6_relat_1(k3_relat_1(A)),A) <-> v1_relat_2(A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 930 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> r7_relat_2(A,k3_relat_1(A))))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 931 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 932 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) & v5_relat_2(B) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 933 (all A all B (v1_relat_1(B) -> (r5_relat_2(B,A) -> r4_relat_2(k2_xboole_0(B,k6_relat_1(A)),A)))) # label(t20_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 934 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_ordinal1(A,B) <-> r1_tarski(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 935 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 936 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 937 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 938 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 939 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 940 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) <-> v5_ordinal1(A)))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 941 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 942 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 943 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> A = B | r2_hidden(A,B))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 944 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 945 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 946 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D))))))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 947 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 948 (all A exists B ((all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))) & -r2_hidden(B,A) & v3_ordinal1(B))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 949 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B) & r1_tarski(B,A))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 950 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r1_ordinal1(k1_ordinal1(A),B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 951 (all A all B all C all D -(r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 952 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 953 (all A all B (m1_ordinal1(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 954 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 955 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 956 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 957 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A (v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 958 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 959 (all A all B (m1_ordinal1(B,A) -> (all C (v3_ordinal1(C) -> m1_ordinal1(k2_ordinal1(B,C),A))))) # label(t48_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 960 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 961 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 962 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 963 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 964 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 965 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 966 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v1_relat_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 967 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 968 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k3_tarski(A)))) # label(t35_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 969 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 970 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 971 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 972 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 973 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 974 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 975 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 976 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 977 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 978 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A)))) <-> v4_ordinal1(A)))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 979 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_xboole_0(A,B) -> r2_hidden(A,B)))))) # label(t21_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 980 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 981 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 982 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 983 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 984 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 985 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 986 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 987 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 988 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 989 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 990 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 991 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 992 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,B) | r2_hidden(B,A))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 993 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(C,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 994 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 995 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 996 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 997 (all A all B all C -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 998 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 999 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(C,D))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 1000 (all A (v3_ordinal1(A) -> -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)) & -((exists B (v3_ordinal1(B) & k1_ordinal1(B) = A)) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 1001 (all A all B (r1_tarski(A,B) -> (all C (m1_ordinal1(C,A) -> m1_ordinal1(C,B))))) # label(t47_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 1002 (all A -((all B (v3_ordinal1(B) -> -r1_tarski(A,B))) & (all B (r2_hidden(B,A) -> v3_ordinal1(B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.64 1003 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1004 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,f1_s4_ordinal1) & C = k2_ordinal1(A,B) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1005 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1006 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1007 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1008 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1009 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1010 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1011 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s2_ordinal1(B)))) -> p1_s2_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> p1_s2_ordinal1(A))) # label(s2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1012 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & B = k2_ordinal1(f3_s3_ordinal1,A) -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1013 (all A (A = k3_tarski(A) <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1014 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1015 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & B = f3_s5_ordinal1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f2_s5_ordinal1(A) = k1_funct_1(f1_s5_ordinal1,A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1016 (all A all B all C (m1_relset_1(C,A,B) -> m2_relset_1(k6_relset_1(A,B,C),B,A))) # label(dt_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1017 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k11_relset_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1018 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1019 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1020 (all A all B all C all D (m2_relset_1(D,B,C) -> (r1_tarski(A,D) -> m2_relset_1(A,B,C)))) # label(t4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1021 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1022 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1023 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1024 (all A all B all C (m2_relset_1(C,A,B) -> (k5_relset_1(A,B,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C))))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1025 (all A all B all C (m1_relset_1(C,A,B) <-> m2_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1026 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(A,B) -> m2_relset_1(D,B,C)))) # label(t15_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1027 (all A all B all C all D (m2_relset_1(D,A,C) -> m2_relset_1(k8_relset_1(A,C,D,B),B,C))) # label(t33_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1028 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A)))) # label(t10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1029 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1030 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1031 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k4_xboole_0(C,D) = k3_relset_1(A,B,C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1032 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(k2_relat_1(D),B) -> m2_relset_1(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1033 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(k1_relat_1(D),B) -> m2_relset_1(D,B,C)))) # label(t13_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1034 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1035 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1036 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> C = k1_xboole_0))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1037 (all A all B all C (m1_relset_1(C,A,B) -> C = k6_relset_1(A,B,k6_relset_1(A,B,C)))) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1038 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1039 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1040 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1041 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1042 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(A,B) -> m2_relset_1(D,C,B)))) # label(t16_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1043 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1044 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(E,D),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1045 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1046 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1047 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1048 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1049 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)))) # label(t19_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1050 (all A all B all C (m1_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k1_relat_1(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1051 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1052 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k5_relset_1(B,A,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C))))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1053 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1054 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> k8_relset_1(B,A,D,C) = D))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1055 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1056 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1057 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_xboole_0(C,D) = k2_relset_1(A,B,C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1058 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1059 (all A all B all C (m1_relset_1(C,A,B) <-> r1_tarski(C,k2_zfmisc_1(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1060 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & B = k5_relat_1(B,k6_relat_1(A)))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1061 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1062 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1063 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C)))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1064 (all A all B all C all D (m1_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(dt_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1065 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1066 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1067 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1068 (all A all B all C all D (m2_relset_1(D,C,A) -> m2_relset_1(k9_relset_1(C,A,B,D),C,B))) # label(t35_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1069 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1070 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1071 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1072 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1073 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1074 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k5_relset_1(A,B,D)) & r1_tarski(C,k4_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1075 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1076 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k11_relset_1(A,B,C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1077 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1078 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1079 (all A all B all C all D (m1_relset_1(C,A,B) -> m2_relset_1(k8_relset_1(A,B,C,D),A,B))) # label(dt_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1080 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1081 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> m2_relset_1(B,A,k2_relat_1(B))))) # label(t9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1082 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1083 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1084 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1085 (all A all B all C all D (m1_relset_1(D,A,B) -> k8_relat_1(C,D) = k9_relset_1(A,B,C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1086 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1087 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1088 (exists A (m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1) & (all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (p1_s2_relset_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))))))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1089 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1090 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> r1_tarski(B,k5_relset_1(B,A,C)) & B = k4_relset_1(B,A,C)))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1091 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1092 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1093 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k2_relset_1(A,B,C,D),A,B))) # label(dt_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1094 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1095 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1096 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1097 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1098 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1099 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1100 (all A all B all C all D (m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k8_relset_1(A,B,C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1101 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1102 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1103 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1104 (all A all B all C (m2_relset_1(C,B,A) -> k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) & k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1105 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1106 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1107 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1108 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1109 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1110 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1111 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1112 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1113 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(B,C) & r1_tarski(A,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1114 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1115 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(C,A),k4_partfun1(C,B)))) # label(t127_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1116 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1117 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1118 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1119 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1120 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1121 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1122 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1123 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1124 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1125 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1126 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1127 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1128 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1129 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1130 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1131 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1132 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1133 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1134 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1135 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1136 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1137 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1138 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1139 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1140 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1141 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1142 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1143 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1144 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1145 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1146 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1147 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1148 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1149 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1150 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1151 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1152 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1153 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A)))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1154 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1155 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1156 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_partfun1 & (all B (r2_hidden(B,f1_s1_partfun1) -> (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)) & (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1157 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1158 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1159 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1160 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1161 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1162 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1163 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1164 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1165 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1166 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1167 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1168 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1169 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1170 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1171 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1172 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1173 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1174 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))) & (all B (p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1175 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1176 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1177 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1178 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1179 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1180 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1181 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1182 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1183 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1184 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1185 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1186 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1187 (all A exists B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B) & v1_relat_2(B) & v1_relat_1(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1188 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1189 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1190 (all A (v8_relat_2(A) & v3_relat_2(A) & v1_relat_1(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1191 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1192 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1193 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_funct_1(C) & C = k2_xboole_0(A,B) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1194 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1195 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1196 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1197 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1198 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1199 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1200 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1201 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)) & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1202 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1203 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1204 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1205 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1206 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1207 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1208 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1209 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1210 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.65 1211 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1212 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1213 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1214 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> A = k1_xboole_0)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1215 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1216 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1217 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1218 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1219 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1220 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1221 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1222 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1223 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1224 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1225 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1226 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1227 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1228 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1229 (all A (m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1230 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k2_partfun1(A,B,C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1231 (all A all B all C (C = k4_partfun1(A,B) <-> (all D ((exists E (v1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1232 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1233 (all A all B all C all D all E all F (r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1234 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1235 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1236 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1237 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1238 (all A (v1_relat_1(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1239 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1240 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1241 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1242 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1243 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1244 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1245 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (v1_relat_1(C) & v1_funct_1(C) -> C != k2_xboole_0(A,B))) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1246 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k9_relat_1(D,A))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1247 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1248 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1249 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1250 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1251 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1252 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1253 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1254 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1255 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1256 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1257 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1258 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1259 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1260 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1261 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1262 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1263 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> C = D)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & (all B all C (r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1264 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1265 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1266 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) <-> k1_tarski(C) = k5_partfun1(A,B,C)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1267 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1268 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1269 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1270 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_relat_1(D) = k1_tarski(A) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1271 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1272 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1273 (all A all B r1_tarski(k4_partfun1(k1_xboole_0,A),k4_partfun1(B,A))) # label(t126_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1274 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1275 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1276 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) <-> r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1277 (all A all B all C (m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1278 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1279 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1280 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1281 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1282 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1283 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1284 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1285 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1286 (all A all B exists C (v1_funct_1(C) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1287 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1288 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1289 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1290 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1291 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1292 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1293 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1294 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1295 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1296 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1297 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1298 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(C,k6_relat_1(B)) = C)) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1299 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> B = C)) & (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1300 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1301 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1302 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & E = F)) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1303 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1304 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1305 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1306 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1307 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1308 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1309 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1310 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1311 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1312 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1313 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)))) # label(t125_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1314 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1315 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1316 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1317 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1318 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1319 (all A all B all C (v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1320 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(C) & k2_relat_1(B) = A -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1321 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1322 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1323 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1324 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1325 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1326 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1327 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_2(C,A,A) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1328 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1329 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1330 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1331 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1332 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1333 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(A != k1_xboole_0 & B != k1_xboole_0 & -((all D all E (v1_funct_1(E) & m2_relset_1(E,D,A) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> E = F))))) <-> v2_funct_1(C))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1334 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1335 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1336 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1337 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1338 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1339 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1340 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1341 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1342 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_1(B) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1343 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1344 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1345 (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1346 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1347 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1348 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (f3_s10_funct_2 != B -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1349 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1350 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1351 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> B = k1_xboole_0 | v2_funct_1(C) & k2_relat_1(D) = A))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1352 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1353 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)))) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1354 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1355 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1356 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1357 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1358 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1359 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1360 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1361 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)) & k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.66 1362 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1363 (all A all B all C (m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1364 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1365 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1366 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (all E k1_tarski(E) != B) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1367 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1368 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1369 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1370 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_1(A))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1371 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1372 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1373 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1374 (all A -((all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_1(A))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1375 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1376 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1377 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1378 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1379 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1380 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1381 (all A all B all C ((all D ((exists E (E = D & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k1_funct_2(A,B))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1382 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1383 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1384 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1385 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> k1_xboole_0 != A & B = k1_xboole_0 | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1386 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1387 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1388 (all A all B all C (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1389 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | B = k1_xboole_0 & k1_xboole_0 != A | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1390 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1391 (all A all B (-v1_xboole_0(B) -> -v1_xboole_0(k1_funct_2(A,B)))) # label(fc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1392 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1393 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1394 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,B,C) & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1395 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1396 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1397 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> B = C))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1398 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1399 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1400 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1401 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1402 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1403 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1404 (all A all B all C (m1_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1405 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1406 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1407 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1408 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> A != k1_xboole_0 & k1_xboole_0 = B | v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1409 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1410 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1411 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1412 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1413 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1414 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1415 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1416 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1417 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1418 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1419 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1420 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1421 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) & B = k2_relat_1(C) -> k1_xboole_0 = B | D = k2_funct_1(C) | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1422 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1423 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1424 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1425 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> ((all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1426 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f4_s11_funct_2 != B & f3_s11_funct_2 != B))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2)) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1427 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 != A & B = k1_xboole_0 | D = C))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1428 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1429 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1430 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1431 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1432 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1433 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1434 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1435 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1436 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1437 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1438 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1439 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v2_funct_1(C) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1440 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D))))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1441 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1442 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1443 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -((all F -(k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.55/4.67 1444 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k1_xboole_0 = B | k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C)))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1445 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1446 (all A all B all 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)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1447 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C)) & B = k2_relat_1(D) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1448 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1449 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1450 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1451 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> D = E)) <-> v2_funct_1(C))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1452 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1453 (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1454 (all A all B all C all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> B = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1455 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1456 (all A all B all C all D (-v1_xboole_0(A) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1457 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) & k2_relat_1(D) = B -> k1_xboole_0 != B & C = k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1458 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1459 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1460 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1461 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1462 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1463 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1464 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A ((all B all C (r2_hidden(C,f2_s5_funct_2) & r2_hidden(B,f1_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_1(A))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1465 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1466 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1467 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1468 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1469 (all A all B all C all D all E all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(D,A) & r2_hidden(E,B) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1470 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1471 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1472 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (-(A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1473 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1474 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B != k1_xboole_0 -> (B = k2_relat_1(C) <-> (all D (k1_xboole_0 != D -> (all E (v1_funct_1(E) & m2_relset_1(E,B,D) & v1_funct_2(E,B,D) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1475 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1476 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,C,B) & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1477 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1478 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1479 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1480 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) & v2_funct_1(D) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | B = k1_xboole_0))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1481 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1482 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1483 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1484 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k5_funct_2(A,B,C) = C -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1485 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1486 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1487 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & k5_partfun1(A,B,D) = k5_partfun1(A,B,C) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1488 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -(D = k1_funct_1(C,E) & r2_hidden(E,A))))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1489 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1490 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1491 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1492 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1493 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1494 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1495 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v1_partfun1(C,A,B) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1496 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1497 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-v2_funct_1(C) & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & B != k1_xboole_0))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1498 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1499 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1500 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1501 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1502 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1503 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1504 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1505 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1506 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1507 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1508 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | B = k1_xboole_0 & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1509 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1510 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1511 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1512 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1513 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1514 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1515 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1516 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | k1_xboole_0 = B))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1517 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1518 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1519 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1520 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_1(k4_funct_2(A,B,C)) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_2(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1521 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1522 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1523 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1524 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1525 (all A all B r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B))) # label(t141_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1526 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1527 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1528 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (m1_subset_1(B,f2_s14_funct_2) & p1_s14_funct_2(A,B))))) -> (exists A (v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1529 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1530 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> B = k1_funct_1(D,C)))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.67 1531 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & (all E all F ((E = k1_funct_1(C,F) & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1532 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1533 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1534 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E)) = k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)))))) <-> r7_binop_1(A,B,C)))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1535 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_xboole_0(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1536 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1537 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1538 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> k1_binop_1(B,C,C) = C))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1539 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C) & D = k1_binop_1(B,C,D)))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1540 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F))))))))))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1541 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1542 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1543 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1544 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F))))))))))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1545 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,B,D,C) = k2_binop_1(A,A,A,B,C,D)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1546 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1547 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)))))))))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1548 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1549 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F)))))))) <-> r4_binop_1(A,B,C)))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1550 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = k1_binop_1(B,D,C))))) <-> v1_binop_1(B,A)))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1551 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r4_binop_1(A,B,C) & r5_binop_1(A,B,C) <-> r6_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1552 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k1_binop_1(D,E,F) = k2_binop_1(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1553 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C))))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1554 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1555 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1556 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,B,D))) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1557 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1558 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1559 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1560 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1561 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1562 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,C,C)))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1563 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1564 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r3_binop_1(A,B,C) <-> r2_binop_1(A,B,C) & r1_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1565 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A))) -> (all C (m1_subset_1(C,A) -> (k3_binop_1(A,B) = C <-> r3_binop_1(A,C,B))))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1566 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1567 (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & (all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_1(A))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1568 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1569 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> k1_binop_1(C,D,B) = D)) <-> r2_binop_1(A,B,C)))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1570 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_funct_1(B,k1_binop_1(C,D,E)) = k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E)))))) <-> r7_binop_1(A,B,C)))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1571 (all A all B all C all D all E all F (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1572 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(C,B,D) = D))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1573 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r5_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1574 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1575 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,B,C,E,F,G) = k2_binop_1(A,B,C,D,F,G))))) -> E = D))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1576 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1577 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (m1_subset_1(C,f1_s1_binop_1) & p1_s1_binop_1(A,B,C))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & (all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & v1_funct_1(A))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1578 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1579 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1580 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1581 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1582 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F))))))))))))) # label(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1583 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,D,B))) <-> r2_binop_1(A,B,C)))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1584 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1585 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E))))))) <-> v2_binop_1(B,A)))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1586 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r6_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)) & k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F)))))))))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1587 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1588 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1589 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1590 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> k7_funcop_1(A,B,C,E,F) = D))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1591 (all A (k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1592 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1593 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1594 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> k3_funcop_1(C,D,E) = k6_funcop_1(A,B,C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1595 (all A all B k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1596 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1597 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1598 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1599 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1600 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> ((all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> k3_funcop_1(C,A,B) = D))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1601 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1602 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1603 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1604 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1605 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> -((all D all E k4_tarski(D,E) != k1_funct_1(A,C)) & k1_funct_1(A,C) != k1_funct_1(B,C)) & (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))))) <-> k1_funcop_1(A) = B))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1606 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1607 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1608 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1609 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1610 (all A k13_funct_3(k6_partfun1(A),k6_partfun1(A)) = k12_funct_3(A)) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1611 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1612 (all A all B (v1_xboole_0(B) -> v2_funct_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1613 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1614 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1615 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C)))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1616 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1617 (all A all B all C (-r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0)) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1618 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1619 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1620 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1621 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) = k4_funcop_1(A,B,C)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1622 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1623 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1624 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1625 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1626 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1627 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1628 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1629 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1630 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1631 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1632 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1633 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1634 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1635 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1636 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1637 (all A all B (v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1638 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1639 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1640 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1641 (all A all B (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1642 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1643 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1644 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> B = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C | C = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1645 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1646 (all A all B all C (r2_hidden(B,A) -> k1_funct_1(k2_funcop_1(A,C),B) = C)) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1647 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(A) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1648 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1649 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1650 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,B) & m2_relset_1(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1651 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) = k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F)))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1652 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & m1_subset_1(D,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1653 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1654 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) & k1_relat_1(A) = k1_xboole_0 -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.68 1655 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1656 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1657 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1658 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1659 (all A all B (-v1_xboole_0(B) -> v1_funct_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1660 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1661 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1662 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1663 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(C) & -v1_xboole_0(B) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1664 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1665 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1666 (all A (v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1667 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1668 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funcop_1(B,A,C,D,E) = k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1669 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1670 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1671 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1672 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1673 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1674 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1675 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1676 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1677 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1678 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1679 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1680 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1681 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1682 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1683 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1684 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1685 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & v1_funct_1(k5_funcop_1(C,E,D)))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1686 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1687 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> v1_funct_1(k3_funcop_1(C,D,E)) & m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1688 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1689 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1690 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1691 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1692 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1693 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1694 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1695 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1696 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1697 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1698 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != k1_xboole_0 & r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1699 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.61/4.69 1700 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1701 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1702 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1703 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1704 (all A all B all C k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1705 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1706 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> A = k1_xboole_0 | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1707 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1708 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1709 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f4_s8_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1710 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0))) <-> f2_s6_ordinal2(A) = B)))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,A) = f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_xboole_0) = f4_s6_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1711 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1712 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1713 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k9_ordinal2(C) = B & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1714 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r2_hidden(C,A)))) -> r1_ordinal1(k7_ordinal2(B),A))))) # label(t28_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1715 (exists A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1716 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1717 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1718 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1719 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s3_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1720 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1721 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1722 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1723 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1724 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_ordinal2(A) <-> (exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1725 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(B),A))))) # label(t22_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1726 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1727 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1728 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.80 1729 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1730 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1731 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1732 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k7_ordinal2(A),k7_ordinal2(B)))) # label(t30_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1733 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1734 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1735 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1736 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1737 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C))) <-> B = f3_s10_ordinal2(A))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1738 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f3_s16_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s16_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_ordinal1(A) = k1_relat_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> k1_funct_1(f1_s16_ordinal2,A) = f3_s16_ordinal2(A)))) & v4_ordinal1(f2_s16_ordinal2) -> f3_s16_ordinal2(f2_s16_ordinal2) = f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1739 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(k6_ordinal2(B),B))))) # label(t25_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1740 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k15_ordinal2(A,k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D))) <-> C = k16_ordinal2(A,B)))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1741 (exists A (v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s2_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1742 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1743 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k16_ordinal2(k4_ordinal2,A) = k4_ordinal2)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1744 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> r1_ordinal1(A,k6_ordinal2(B)) | k2_ordinal2(B) = k1_xboole_0)))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1745 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1746 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1747 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1748 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v4_ordinal1(B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1749 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1750 (all A (A = k5_ordinal2 <-> r2_hidden(k1_xboole_0,A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1751 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,C))))))))) # label(t58_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1752 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1753 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(A,k7_ordinal2(B)))))) # label(t27_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1754 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1755 (all A all B (v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1756 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1757 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k8_ordinal2(C) = B & v1_funct_1(C) & v1_relat_1(C))) <-> B = k11_ordinal2(A)))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1758 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1759 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1760 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1761 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t49_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1762 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1763 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1764 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> A = k1_xboole_0 | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1765 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1766 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1767 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1768 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1769 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,C))))))))) # label(t51_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1770 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1771 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1772 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1773 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1774 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1775 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f4_s15_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s15_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_funct_1(C)))))))) -> (all A (v3_ordinal1(A) -> f2_s15_ordinal2(A,f4_s15_ordinal2(A)) = f4_s15_ordinal2(k1_ordinal1(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1776 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k1_setfam_1(A)))) # label(t17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1777 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & k14_ordinal2(B,C) = A)) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.71/4.81 1778 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> k1_xboole_0 = B | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1779 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1780 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f2_s12_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f6_s12_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & B = k1_ordinal2(C)))))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> A = k1_xboole_0 | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1781 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1782 (all A (v3_ordinal1(A) -> A = k15_ordinal2(k4_ordinal2,A) & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1783 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_ordinal2(A),k3_ordinal2(B)))) # label(t14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1784 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1785 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t50_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1786 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & k1_ordinal1(B) = k1_relat_1(D))) <-> C = k14_ordinal2(A,B)))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1787 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B) <-> k7_ordinal2(A) = B))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1788 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1789 (exists A (v2_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1790 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1791 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1792 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/4.98 1793 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1794 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_ordinal2(A),k2_ordinal2(B)))) # label(t11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1795 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_relat_1(C))) & B != A & (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_ordinal2(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1796 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v5_ordinal1(B) & A = k1_ordinal2(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & v1_ordinal2(B) & v1_funct_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1797 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1798 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1799 (all A k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A))) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1800 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1801 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1802 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s9_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1803 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k14_ordinal2(k1_funct_1(D,E),B) = k1_funct_1(D,k1_ordinal1(E))))) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.00 1804 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1805 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1806 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1807 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1808 f1_s4_ordinal2 = k1_relat_1(f5_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1809 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1810 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1811 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1812 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(C) & v1_relat_1(C))) & A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & B = k1_ordinal2(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1813 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & k1_funct_1(B,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(B) & k1_ordinal2(B) = A & v5_ordinal1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1814 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_funct_1(A,B) = C & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1815 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (D = C & v4_ordinal1(D) & v3_ordinal1(D))))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1816 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1817 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F))))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (A = k1_xboole_0 -> ((exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_xboole_0))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1818 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1819 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(C,A),k15_ordinal2(C,B))))))))) # label(t59_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1820 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1821 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1822 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (k12_ordinal2(A) = B <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1823 (exists A (v1_relat_1(A) & v5_ordinal1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1824 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1825 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1826 (all A all B ((all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))) <-> B = k2_ordinal2(A))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1827 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1828 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (A = B & np__0 = k1_funct_1(B,k13_arytm_3) & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1829 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1830 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1831 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1832 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1833 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1834 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1835 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1836 (exists A (v1_xboole_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1837 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1838 (all A (v1_xreal_0(A) -> (v3_xreal_0(A) <-> -r1_xreal_0(np__0,A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1839 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1840 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1841 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1842 (all A (v1_xreal_0(A) & v2_xreal_0(A) -> -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1843 (exists A (v1_xcmplx_0(A) & -v3_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1844 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1845 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1846 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1847 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1848 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1849 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1850 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1851 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1852 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1853 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1854 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1855 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & v1_xcmplx_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1856 (all A (v1_xreal_0(A) -> (v2_xreal_0(A) <-> -r1_xreal_0(A,np__0)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1857 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1858 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1859 (all A all B (v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1860 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1861 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1862 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1863 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(A) -> v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1864 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1865 (all A (v1_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1866 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) -> -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1867 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) & -v2_xreal_0(A) & -v1_xboole_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1868 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1869 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,A))) # label(reflexivity_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1870 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1871 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1872 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1873 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1874 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1875 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C ((exists D (k4_tarski(np__0,D) = B & r1_arytm_2(D,C) & A = k4_tarski(np__0,C) & m1_subset_1(D,k2_arytm_2))) & m1_subset_1(C,k2_arytm_2))))) & -(-(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) <-> r1_xreal_0(A,B))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & C = A & r1_arytm_2(C,D) & D = B)))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1876 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v3_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1877 (all A all B (-v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1878 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1879 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,B) | r1_xreal_0(B,A))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1880 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1881 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> A = k2_numbers))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1882 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_int_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1883 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1884 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1885 (all A (-v1_xboole_0(A) & v3_membered(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1886 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1887 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1888 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1889 (all A all B (v5_membered(A) -> v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1890 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_tarski(A,B) <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1891 (all A all B (v3_membered(A) & v3_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1892 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1893 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1894 (all A all B (v4_membered(A) & v4_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1895 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1896 (all A ((all B (r2_hidden(B,A) -> v4_membered(B))) -> v4_membered(k3_tarski(A)))) # label(t24_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1897 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1898 (all A all B (v3_membered(B) & r2_hidden(B,A) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1899 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1900 (all A (v1_xreal_0(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1901 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1902 (all A all B (r2_hidden(B,A) & v5_membered(B) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1903 (all A all B (v3_membered(A) -> v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1904 (all A (v1_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1905 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1906 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (v1_int_1(B) & r2_hidden(B,A))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1907 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v1_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1908 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1909 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1910 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1911 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1912 (all A all B (v1_membered(A) & v1_membered(B) -> v1_membered(k5_xboole_0(A,B)))) # label(fc42_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1913 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> k3_numbers = A))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1914 (all A all B all C (v1_int_1(C) & v1_int_1(B) & v1_int_1(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1915 (all A all B all C (v1_xreal_0(C) & v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1916 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1917 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1918 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1919 (all A all B (v4_membered(B) & r2_hidden(B,A) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1920 (all A all B (r2_hidden(B,A) & v1_membered(B) -> v1_membered(k1_setfam_1(A)))) # label(t26_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1921 (exists A ((all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))) & v3_membered(A))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1922 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1923 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1924 (all A ((all B (r2_hidden(B,A) -> v1_membered(B))) -> v1_membered(k3_tarski(A)))) # label(t21_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1925 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1926 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1927 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1928 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1929 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1930 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1931 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1932 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v1_membered(A) & v2_membered(A) & v4_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1933 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1934 (all A all B (v3_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1935 (all A (v1_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1936 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1937 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1938 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1939 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v1_membered(A) & v2_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1940 (exists A ((all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))) & v1_membered(A))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1941 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v2_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1942 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1943 (all A all B (v1_int_1(B) & v1_int_1(A) -> v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1944 (all A all B (v3_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1945 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (B = A <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1946 (all A (v2_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xreal_0(B))))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1947 (all A (v5_membered(A) & -v1_xboole_0(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1948 (all A all B all C (v4_ordinal2(B) & v4_ordinal2(C) & v4_ordinal2(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1949 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1950 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1951 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1952 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v4_ordinal2(B) & v1_int_1(B) & v1_rat_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1953 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1954 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1955 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xcmplx_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1956 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1957 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1958 (all A all B (v2_membered(A) & v2_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1959 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1960 (all A all B all C (v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1961 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1962 (all A (v2_membered(A) -> ((all B (v1_xreal_0(B) -> r2_hidden(B,A))) -> A = k1_numbers))) # label(t12_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1963 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1964 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v1_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1965 (all A all B (v3_membered(B) & v3_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1966 (all A ((all B (r2_hidden(B,A) -> v2_membered(B))) -> v2_membered(k3_tarski(A)))) # label(t22_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1967 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1968 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_xreal_0(B))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1969 (exists A ((all B (v1_int_1(B) -> (p1_s4_membered(B) <-> r2_hidden(B,A)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1970 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1971 (all A all B all C (v1_xcmplx_0(C) & v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1972 (all A (v1_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1973 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1974 (exists A (-v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v5_membered(A) & v4_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1975 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (A = B <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1976 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1977 (all A all B (v4_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1978 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1979 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1980 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> A = k4_numbers))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1981 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_rat_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1982 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1983 (all A (v4_ordinal2(A) -> v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1984 (all A ((all B (r2_hidden(B,A) -> v3_membered(B))) -> v3_membered(k3_tarski(A)))) # label(t23_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1985 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1986 (exists A (v2_membered(A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1987 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1988 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d6_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1989 (all A (v5_membered(A) -> ((all B (v4_ordinal2(B) -> r2_hidden(B,A))) -> k5_numbers = A))) # label(t15_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1990 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1991 (all A all B (r2_hidden(B,A) & v2_membered(B) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1992 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1993 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1994 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1995 (all A ((all B (r2_hidden(B,A) -> v5_membered(B))) -> v5_membered(k3_tarski(A)))) # label(t25_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1996 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1997 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1998 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k6_partfun1(A) = k4_eqrel_1(A,k6_partfun1(A),B))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 1999 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> m2_relset_1(k3_eqrel_1(A,B,C),A,A))) # label(dt_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2000 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> ((exists C k6_eqrel_1(A,B,C) = A) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2001 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = A -> (B = k1_xboole_0 <-> m1_eqrel_1(B,A))) & (k1_xboole_0 != A -> (m1_eqrel_1(B,A) <-> k5_setfam_1(A,B) = A & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & -r1_xboole_0(C,D) & D != C)))))))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2002 (all A (v3_relat_2(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2003 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> -(B = k1_xboole_0 & (exists C r2_hidden(C,A))))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2004 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2005 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & -v1_xboole_0(A) -> v1_setfam_1(k7_eqrel_1(A,B)) & -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2006 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2007 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2008 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2009 (all A all B all C all D all E (v1_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v3_relat_2(E) -> (r2_hidden(B,k6_eqrel_1(A,E,C)) & r2_hidden(D,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2010 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2011 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2012 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_1(k1_eqrel_1(A)))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2013 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v3_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2014 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2015 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2016 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2017 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v3_relat_2(B) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2018 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,B,C) = k2_eqrel_1(A,C,B))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2019 (all A all B (m1_eqrel_1(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2020 (all A all B (m1_eqrel_1(B,A) -> (exists C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & B = k7_eqrel_1(A,C) & v8_relat_2(C) & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2021 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_eqrel_1(A,B,B) = B)) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2022 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2023 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) -> (k3_eqrel_1(A,B,C) = D -> (all E -(k6_eqrel_1(A,B,E) != k6_eqrel_1(A,D,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & r2_hidden(E,A)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2024 (all A all B (m2_relset_1(B,A,A) -> k2_eqrel_1(A,k1_eqrel_1(A),B) = B)) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2025 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2026 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2027 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2028 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2029 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) -> v3_relat_2(k4_eqrel_1(A,B,C)) & v8_relat_2(k4_eqrel_1(A,B,C)) & v1_partfun1(k4_eqrel_1(A,B,C),A,A) & m2_relset_1(k4_eqrel_1(A,B,C),A,A))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2030 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2031 (all A (v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v1_partfun1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2032 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2033 (all A all B (m2_relset_1(B,A,A) -> (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) <-> v1_relat_2(B) & A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2034 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2035 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v1_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) <-> r2_hidden(B,k6_eqrel_1(A,D,C))))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2036 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2037 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2038 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k8_eqrel_1(A,B) = k7_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2039 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B)))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.04 2040 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> -(C != k1_eqrel_1(A) & k1_eqrel_1(A) != B & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2041 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2042 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2043 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2044 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,C,B) = k3_eqrel_1(A,B,C))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2045 (all A all B all C (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2046 (all A (r1_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2047 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2048 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A)))) -> ((all C (r2_hidden(C,B) -> v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A))) -> v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) | B = k1_xboole_0))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2049 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2050 (all A all B all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2051 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2052 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C -(r2_hidden(C,A) & (all D -r2_hidden(C,k6_eqrel_1(A,B,D))))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2053 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (k5_eqrel_1(A,B,C) = D <-> r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v3_relat_2(E) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E))))))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2054 (all A all B (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2055 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2056 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v3_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2057 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k4_eqrel_1(A,C,B) = k4_eqrel_1(A,B,C))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2058 (all A all B (r2_hidden(B,A) -> k1_tarski(B) = k6_eqrel_1(A,k6_partfun1(A),B))) # label(t33_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2059 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -(r2_hidden(A,k7_eqrel_1(B,C)) & (all D (m1_subset_1(D,B) -> k6_eqrel_1(B,C,D) != A))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2060 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D -(r2_hidden(C,A) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & r2_hidden(D,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2061 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_eqrel_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,A) & k6_eqrel_1(A,B,E) = D)))))))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2062 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)) = B)))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2063 (all A all B all C (v1_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2064 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2065 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B all C (p1_s1_eqrel_1(B,C) & p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(A,C))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) -> (exists A ((all B all C (r2_hidden(B,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) <-> r2_hidden(k4_tarski(B,C),A))) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A) & v3_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2066 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C k10_relset_1(A,A,B,k1_tarski(C)) = k6_eqrel_1(A,B,C)))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2067 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (A = k1_xboole_0 -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2068 (all A all B (r2_hidden(B,A) -> k6_eqrel_1(A,k1_eqrel_1(A),B) = A)) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2069 (all A all B (m2_relset_1(B,A,A) -> (exists C ((all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2070 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,B) = B)) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2071 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2072 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2073 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2074 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) & v8_relat_2(D) -> (all E (v8_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_relat_1(F) & v1_funct_1(F) & r1_xreal_0(np__1,k3_finseq_1(F)) & k1_funct_1(F,np__1) = A & k1_funct_1(F,k3_finseq_1(F)) = C & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))) & v1_finseq_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2075 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> m2_relset_1(k2_eqrel_1(A,B,C),A,A))) # label(dt_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2076 (all A all B all C all D all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2077 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (all C (m1_struct_0(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2078 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_struct_0(C,A,B) -> m1_subset_1(C,u1_struct_0(A)))))) # label(dt_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2079 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2080 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> C = A & B = D)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2081 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2082 (all A all B (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2083 (all A (v1_struct_0(g1_struct_0(A)) & l1_struct_0(g1_struct_0(A)))) # label(dt_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2084 (all A all B (g1_struct_0(B) = g1_struct_0(A) -> A = B)) # label(free_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2085 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2086 (all A (l2_struct_0(A) -> m1_subset_1(u2_struct_0(A),u1_struct_0(A)))) # label(dt_u2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2087 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2088 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2089 (all A all B (m1_subset_1(B,A) -> v2_struct_0(g2_struct_0(A,B)) & l2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2090 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2091 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2092 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2093 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2094 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2095 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_struct_0(A,C,B) = k2_struct_0(A,B,C))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2096 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> k1_tarski(B) = k1_struct_0(A,B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2097 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2098 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2099 (exists A (v2_struct_0(A) & l2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2100 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> g1_struct_0(u1_struct_0(A)) = A))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2101 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2102 (all A (l2_struct_0(A) -> (v2_struct_0(A) -> A = g2_struct_0(u1_struct_0(A),u2_struct_0(A))))) # label(abstractness_v2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2103 (all A (l1_struct_0(A) -> (v3_struct_0(A) <-> v1_xboole_0(u1_struct_0(A))))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2104 (all A (l1_struct_0(A) -> m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2105 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2106 (all A (l1_pre_topc(A) -> (v1_pre_topc(A) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = A))) # label(abstractness_v1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2107 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2108 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2109 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)))))))) # label(t50_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2110 (exists A (v2_pre_topc(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2111 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2112 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) <-> k2_pre_topc(A) = k5_setfam_1(u1_struct_0(A),B)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2113 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B))) & (k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & v2_pre_topc(A) -> v3_pre_topc(B,A)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2114 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B))) & B != k1_pre_topc(A)))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2115 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> l1_pre_topc(B))))) # label(dt_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2116 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B))))) # label(cc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.90/5.05 2117 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) = k6_pre_topc(B,D)))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2118 (all A (l1_struct_0(A) -> k1_xboole_0 = k1_pre_topc(A))) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2119 (all A (l1_struct_0(A) -> (all B (r1_tarski(B,k2_pre_topc(A)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t16_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2120 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & l1_struct_0(A) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2121 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))))) # label(t39_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2122 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2123 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2124 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2125 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k6_pre_topc(A,B) = B) & (k6_pre_topc(A,B) = B & v2_pre_topc(A) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2126 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(A,B) = g1_pre_topc(C,D) -> B = D & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2127 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2128 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2129 (all A (l1_struct_0(A) -> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2130 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2131 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2132 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k6_pre_topc(A,B)))))) # label(t48_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2133 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2134 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2135 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2136 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k3_subset_1(u1_struct_0(A),B))))) # label(t17_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2137 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) -> r2_hidden(C,D))))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2138 (all A all B all C all D (l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2139 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2140 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all 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)) & v1_funct_1(C) -> (v5_pre_topc(C,A,B) <-> (all 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))))))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2141 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2142 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2143 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2144 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = B)))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2145 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t44_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2146 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2147 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2148 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2149 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2150 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> r2_hidden(B,u1_pre_topc(A))))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2151 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2152 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2153 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2154 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2155 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2156 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2157 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2158 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2159 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) & r2_hidden(C,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & r2_hidden(u1_struct_0(A),u1_pre_topc(A))))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2160 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2161 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2162 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2163 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2164 (all A (l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2165 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t51_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2166 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2167 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (m1_pre_topc(B,A) <-> r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(C,u1_pre_topc(B)) <-> (exists D (C = k3_xboole_0(D,k2_pre_topc(B)) & r2_hidden(D,u1_pre_topc(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))))))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2168 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_pre_topc(k3_pre_topc(A,B),A) & v1_pre_topc(k3_pre_topc(A,B)))) # label(dt_k3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2169 (all A (l1_pre_topc(A) -> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_u1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2170 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2171 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2172 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (r2_hidden(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_xboole_0(B,E) & r2_hidden(D,E)))) <-> r2_hidden(D,C)))) <-> C = k6_pre_topc(A,B)))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2173 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2174 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2175 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2176 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v4_pre_topc(D,A) & r1_tarski(B,D)))))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2177 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2178 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A)))) & -v3_struct_0(A) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2179 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> r2_hidden(k1_xboole_0,u1_pre_topc(A)))) # label(t5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2180 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2181 (all A (l1_struct_0(A) -> v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2182 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2183 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A) <-> v4_pre_topc(B,A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2184 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k2_pre_topc(A)))))) # label(t14_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2185 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t15_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2186 (all A (l1_struct_0(A) -> k3_subset_1(u1_struct_0(A),k1_pre_topc(A)) = k2_pre_topc(A))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2187 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2188 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2189 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & -v3_struct_0(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2190 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2191 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2192 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t49_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2193 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2194 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k2_pre_topc(A)))))) # label(t13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2195 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k2_pre_topc(A) != B & k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & -(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) != k1_xboole_0 & B = k2_pre_topc(A)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2196 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2197 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2198 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (B = k2_pre_topc(C) <-> C = k3_pre_topc(A,B)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2199 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (v4_pre_topc(D,A) & C = k3_xboole_0(D,k2_pre_topc(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2200 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2201 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2202 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v3_tops_1(B,A)))))) # label(cc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2203 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)))))) # label(t73_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2204 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> r1_tarski(B,k2_tops_1(A,B))))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2205 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2206 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> k2_pre_topc(A) = k1_tops_1(A,k2_pre_topc(A)))) # label(t43_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2207 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v1_tops_1(C,A) & v3_pre_topc(C,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2208 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v3_pre_topc(B,A) -> r1_tarski(B,k1_tops_1(A,C))))))))) # label(t56_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2209 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> r1_tarski(k2_tops_1(A,B),B)))))) # label(t69_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2210 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2211 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2212 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) <-> r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) & r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2213 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))))) # label(t51_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2214 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A))) # label(t22_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2215 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(t92_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2216 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)) = k2_tops_1(A,B))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2217 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2218 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t71_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2219 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)))))))))) # label(t40_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2220 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> B = k1_xboole_0))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2221 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2222 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v2_tops_1(B,A) & v3_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2223 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v4_pre_topc(B,A) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2224 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> k2_tops_1(A,k1_tops_1(A,B)) = k2_tops_1(A,B)))))) # label(t102_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2225 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2226 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2227 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_xboole_0(B) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v4_membered(B) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2228 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2229 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) <-> r1_tarski(B,C)))))))) # label(t20_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2230 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2231 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t45_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2232 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) & v5_tops_1(C,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2233 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2234 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> D = k1_tops_1(B,D)) & (C = k1_tops_1(A,C) -> v3_pre_topc(C,A)))))))))) # label(t55_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2235 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k6_pre_topc(A,B)),k2_tops_1(A,B)))))) # label(t72_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2236 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2237 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)) = k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2238 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2239 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2240 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))))))))) # label(t41_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2241 (all A (l1_pre_topc(A) -> (exists B (v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v4_membered(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2242 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2243 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2244 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2245 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2246 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2247 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t95_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2248 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k6_pre_topc(A,k1_tops_1(A,B)) <-> v5_tops_1(B,A)))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2249 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2250 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2251 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2252 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) <-> v4_pre_topc(B,A)))))) # label(t29_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2253 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t103_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2254 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(k6_pre_topc(A,B),A) <-> v3_tops_1(B,A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2255 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k6_pre_topc(A,B) = k2_pre_topc(A)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2256 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2257 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,B),B))))) # label(t44_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2258 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2259 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2260 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != k1_xboole_0 & r1_xboole_0(B,C) & v3_pre_topc(C,A))))))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2261 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & r1_tarski(B,C) -> v1_tops_1(C,A)))))))) # label(t79_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2262 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2263 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k6_pre_topc(A,B)) = k6_pre_topc(A,B))))) # label(t26_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2264 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2265 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2266 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2267 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2268 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B)) <-> v4_pre_topc(B,A)))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2269 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t70_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2270 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v3_pre_topc(B,A) & v4_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2271 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t74_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2272 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v2_tops_1(B,A)))))) # label(cc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2273 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2274 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v4_tops_1(k1_tops_1(A,B),A) & v4_tops_1(k6_pre_topc(A,B),A)))))) # label(t111_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2275 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k2_tops_1(A,B))))) # label(t62_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2276 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A) & v4_pre_topc(k1_pre_topc(A),A) & v2_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2277 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) & v4_tops_1(D,B) -> v6_tops_1(D,B)) & (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2278 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v4_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v5_membered(B) & v3_membered(B) & v2_membered(B) & v1_xboole_0(B)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2279 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(C,A) & v6_tops_1(B,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2280 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)) = k6_pre_topc(A,C))))))))) # label(t81_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2281 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))) = k2_tops_1(A,k2_tops_1(A,B)))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2282 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C (r2_hidden(C,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(D,B) & r2_hidden(C,D) & v3_pre_topc(D,A)))))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2283 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2284 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2285 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(cc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2286 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2287 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(C,A) & v2_tops_1(C,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2288 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,B) <-> v3_pre_topc(B,A)))))) # label(t76_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2289 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r1_tarski(D,C) & v3_pre_topc(D,A)))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2290 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))))))))) # label(t32_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2291 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0))))) # label(t110_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2292 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k2_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t68_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2293 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,B) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2294 (all A (l1_pre_topc(A) -> k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t27_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2295 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2296 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v1_xboole_0(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2297 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2298 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (k2_tops_1(A,B) = B <-> v3_tops_1(B,A))))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2299 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A))) # label(t53_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2300 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_pre_topc(B,A) -> (v5_tops_1(B,A) <-> v6_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2301 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t66_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2302 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) = k1_tops_1(A,B))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2303 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t48_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2304 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2305 (all A all B (l1_pre_topc(A) & v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A))) # label(fc11_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2306 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2307 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2308 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2309 (all A all B (v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v2_membered(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v1_membered(k1_tops_1(A,B)) & v1_xboole_0(k1_tops_1(A,B)))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2310 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2311 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2312 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_tops_1(A,k6_pre_topc(A,B)) <-> v6_tops_1(B,A)))))) # label(d8_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2313 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)))))) # label(t63_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2314 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v6_tops_1(B,A)))))) # label(t101_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2315 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t96_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2316 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_tops_1(C,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2317 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))) = k6_pre_topc(A,k1_tops_1(A,B)))))) # label(t58_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2318 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_xboole_0(B,D) & D != k1_xboole_0 & r1_tarski(D,C)))) & v3_pre_topc(C,A)))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2319 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2320 (all A (l1_struct_0(A) -> k3_subset_1(u1_struct_0(A),k2_pre_topc(A)) = k1_pre_topc(A))) # label(t8_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2321 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2322 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(B,A) -> v3_tops_1(B,A)))))) # label(t93_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2323 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))))))))) # label(t49_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2324 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(A),B) -> C = B))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2325 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> k2_tops_1(A,B) = k2_tops_1(A,k6_pre_topc(A,B)) & k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,k6_pre_topc(A,B))))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2326 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k2_tops_1(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,D) & v3_pre_topc(D,A) -> -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D) & -r1_xboole_0(B,D))))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2327 (all A all B (l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2328 (all A (l1_pre_topc(A) -> k1_tops_1(A,k1_pre_topc(A)) = k1_pre_topc(A))) # label(t47_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2329 (all A (l1_pre_topc(A) -> v1_membered(k1_tops_1(A,k1_pre_topc(A))) & v3_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2330 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2331 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2332 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2333 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v5_tops_1(C,A) -> v4_pre_topc(C,A) & v4_tops_1(C,A)) & (v4_tops_1(D,B) & v4_pre_topc(D,B) -> v5_tops_1(D,B)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2334 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t50_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2335 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2336 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t91_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2337 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2338 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2339 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2340 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2341 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t67_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2342 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v3_pre_topc(C,A) -> C = k1_xboole_0))) <-> v2_tops_1(B,A)))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2343 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_tops_1(A,B) = k1_xboole_0 <-> v2_tops_1(B,A)))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2344 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A))))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2345 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k6_pre_topc(A,k5_pre_topc(A,B,C,D)),k5_pre_topc(A,B,C,k6_pre_topc(B,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t56_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2346 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all 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)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(k4_pre_topc(A,B,C,D),B) <-> v4_pre_topc(D,A)))) & v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) & k1_relat_1(C) = k2_pre_topc(A) <-> v3_tops_2(C,A,B)))))))) # label(t72_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2347 $T # label(t30_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2348 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_pre_topc(A,B,C,k6_pre_topc(A,D)),k6_pre_topc(B,k4_pre_topc(A,B,C,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t57_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2349 $T # label(t9_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2350 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),D)) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,C),k5_setfam_1(u1_struct_0(k3_pre_topc(A,C)),k1_tops_2(A,C,D)))))))))))) # label(t42_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2351 $T # label(t69_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2352 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) & v1_tops_2(B,A) -> v1_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t20_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2353 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(C) -> v1_finset_1(k1_tops_2(A,B,C))))))))) # label(t46_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2354 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k7_setfam_1(A,B) = k1_xboole_0 & k1_xboole_0 != B) & -(B = k1_xboole_0 & k7_setfam_1(A,B) != k1_xboole_0))) # label(t10_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2355 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all 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) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> v3_pre_topc(k5_pre_topc(A,B,C,D),A))))))))))) # label(t55_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2356 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(C,D) -> r1_tarski(k1_tops_2(A,B,C),k1_tops_2(A,B,D))))))))))) # label(t40_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2357 $T # label(t14_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2358 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v4_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (D = B -> v4_pre_topc(D,C))))))))))) # label(t34_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2359 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) & r1_tarski(B,C) -> v1_tops_2(B,A)))))))) # label(t18_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2360 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all 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_tops_2(k2_tops_2(A,B,C),B,A)))))))) # label(t70_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2361 $T # label(t61_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2362 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all 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)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(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)))))))))))) # label(t71_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2363 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all 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_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k5_relat_1(k2_tops_2(A,B,C),C) = k6_relat_1(k2_relat_1(C)) & k5_relat_1(C,k2_tops_2(A,B,C)) = k6_relat_1(k1_relat_1(C))))))))) # label(t65_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2364 (all A all B all C (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> m1_subset_1(k1_tops_2(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))))) # label(dt_k1_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2365 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> v2_funct_1(k2_tops_2(A,B,C))))))))) # label(t63_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2366 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) -> v1_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t47_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2367 $T # label(t37_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2368 $T # label(t8_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2369 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all 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) <-> k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k5_pre_topc(A,B,C,k6_pre_topc(B,D)) = k6_pre_topc(A,k5_pre_topc(A,B,C,D)))) & k2_pre_topc(A) = k1_relat_1(C)))))))) # label(t73_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2370 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v1_finset_1(B) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t28_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2371 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & k1_xboole_0 = B))))) # label(t5_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2372 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B))))) # label(t11_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2373 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v3_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (B = D -> v3_pre_topc(D,C))))))))))) # label(t33_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2374 $T # label(t7_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2375 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> k5_pre_topc(B,A,k2_tops_2(A,B,C),D) = k4_pre_topc(A,B,C,D)))))))))) # label(t67_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2376 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all 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)) & v1_funct_1(C) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k2_tops_2(B,A,k2_tops_2(A,B,C)) = C))))))) # label(t64_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2377 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t29_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2378 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) -> v2_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t48_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2379 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) -> k2_tops_2(A,B,C) = k2_funct_1(C)))))))) # label(d4_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2380 $T # label(t39_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2381 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C)))))))))) # label(t38_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2382 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v2_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (D = B -> v2_tops_2(D,C))))))))))) # label(t36_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2383 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k3_subset_1(A,k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t12_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2384 (all A (l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v5_pre_topc(C,A,B) & v1_tops_2(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (E = k9_relat_1(k3_funct_3(C),D) -> v1_tops_2(E,A))))))))))))) # label(t59_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2385 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (E = k2_pre_topc(B) -> k1_tops_2(A,E,D) = C))) & v1_tops_2(D,A)))) & v1_tops_2(C,B)))))))) # label(t49_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2386 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v2_tops_2(C,A) -> v2_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t23_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2387 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t31_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2388 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t25_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2389 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A))))))))) # label(d2_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2390 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A) <-> v2_tops_2(B,A)))))) # label(t16_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2391 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all 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_pre_topc(B) = k2_relat_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(B,k4_pre_topc(A,B,C,D)) = k4_pre_topc(A,B,C,k6_pre_topc(A,D)))) & v2_funct_1(C) & k2_pre_topc(A) = k1_relat_1(C) <-> v3_tops_2(C,A,B)))))))) # label(t74_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2392 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),C)),k5_setfam_1(u1_struct_0(A),k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))))))))) # label(t6_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2393 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),C)) -> k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)) = B))))))) # label(t43_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2394 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_tops_2(C,A,B) <-> k2_pre_topc(B) = k2_relat_1(C) & v5_pre_topc(k2_tops_2(A,B,C),B,A) & v5_pre_topc(C,A,B) & v2_funct_1(C) & k1_relat_1(C) = k2_pre_topc(A)))))))) # label(d5_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2395 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t3_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2396 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (k1_relat_1(D) = k2_pre_topc(A) & k2_pre_topc(B) = k1_relat_1(E) & v2_funct_1(E) & k2_relat_1(E) = k2_pre_topc(C) & v2_funct_1(D) & k2_pre_topc(B) = k2_relat_1(D) -> k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),k2_tops_2(B,C,E),k2_tops_2(A,B,D)) = k2_tops_2(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))))))))))))) # label(t66_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2397 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r2_hidden(B,D) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k1_tops_2(A,C,D))))))))))) # label(t41_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2398 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C))) -> r1_tarski(B,k5_setfam_1(u1_struct_0(A),C))))))))) # label(t45_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2399 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) & v1_finset_1(B) -> v3_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t27_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2400 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all 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)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(k9_relat_1(k3_funct_3(C),D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t54_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2401 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (-v3_struct_0(C) & l1_pre_topc(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B)) -> (v5_pre_topc(E,C,B) & v5_pre_topc(D,A,C) -> v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(B),D,E),A,B)))))))))))) # label(t58_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2402 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v1_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (B = D -> v1_tops_2(D,C))))))))))) # label(t35_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2403 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all 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)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k4_pre_topc(B,A,k2_tops_2(A,B,C),D) = k5_pre_topc(A,B,C,D)))))))))) # label(t68_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2404 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t22_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2405 (all A all B all C (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(k2_tops_2(A,B,C)))) # label(dt_k2_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2406 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)),k5_setfam_1(u1_struct_0(A),C)))))))) # label(t44_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2407 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v5_pre_topc(C,A,B) & v2_tops_2(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k9_relat_1(k3_funct_3(C),D) = E -> v2_tops_2(E,A))))))))))))) # label(t60_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2408 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))) -> (k1_tops_2(A,B,C) = D <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> ((exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(F,C) & E = k5_subset_1(u1_struct_0(A),F,B))) <-> r2_hidden(E,D))))))))))))) # label(d3_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2409 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t21_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2410 $T # label(t15_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2411 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t24_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2412 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (k2_pre_topc(B) = k2_relat_1(C) & v2_funct_1(C) -> k2_pre_topc(A) = k2_relat_1(k2_tops_2(A,B,C)) & k2_pre_topc(B) = k1_relat_1(k2_tops_2(A,B,C))))))))) # label(t62_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2413 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,k2_pre_topc(B)) & v3_pre_topc(D,A))) <-> v3_pre_topc(C,B)))))))) # label(t32_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2414 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all 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_pre_topc(A) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),k2_pre_topc(B)))))))) # label(t51_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2415 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(B,k1_zfmisc_1(k2_pre_topc(A))))))) # label(t1_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2416 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v2_tops_2(C,A) -> v2_tops_2(B,A)))))))) # label(t19_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2417 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v3_pre_topc(C,A)))) <-> v1_tops_2(B,A)))))) # label(d1_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2418 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (exists D (v1_funct_1(D) & (all E (r2_hidden(E,C) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (F = E -> k5_subset_1(u1_struct_0(A),F,B) = k1_funct_1(D,E)))))) & k1_tops_2(A,B,C) = k2_relat_1(D) & C = k1_relat_1(D) & v1_relat_1(D))))))))) # label(t50_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2419 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all 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_pre_topc(A) = k5_pre_topc(A,B,C,k2_pre_topc(B)))))))) # label(t52_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2420 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v3_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t26_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2421 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(k7_setfam_1(u1_struct_0(A),B),A) <-> v1_tops_2(B,A)))))) # label(t17_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2422 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(k7_setfam_1(u1_struct_0(A),B)) <-> v1_finset_1(B)))))) # label(t13_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2423 $T # label(t4_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2424 $T # label(t53_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2425 $T # label(t2_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2426 (all A (l1_metric_1(A) -> (v3_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v7_metric_1(A)))) # label(d8_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2427 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v5_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E)))))))))))) # label(d6_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2428 (exists A (v1_metric_1(A) & v7_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v6_metric_1(A) & -v3_struct_0(A) & l1_metric_1(A))) # label(rc3_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2429 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (all C all D (g1_metric_1(C,D) = g1_metric_1(A,B) -> C = A & B = D)))) # label(free_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2430 (exists A l1_metric_1(A)) # label(existence_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2431 (all A all B all C (v8_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k4_metric_1(A,B,C),k1_numbers))) # label(dt_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2432 (all A (l1_metric_1(A) -> (v1_metric_1(A) -> g1_metric_1(u1_struct_0(A),u1_metric_1(A)) = A))) # label(abstractness_v1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2433 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,k11_metric_1(B,C,A)) <-> k2_metric_1(B,C,D) = A & -v3_struct_0(B)))))))))) # label(t14_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2434 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k9_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t15_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2435 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (B = k5_metric_1(A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> np__0 = k1_metric_1(A,A,B,C,C) & (C != D -> np__1 = k1_metric_1(A,A,B,C,D))))))))) # label(d11_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2436 (all A all B all C all D (m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & -v3_struct_0(C) & v1_xreal_0(B) -> (r2_hidden(A,a_3_0_metric_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(C)) & A = E & -r1_xreal_0(B,k2_metric_1(C,D,E))))))) # label(fraenkel_a_3_0_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2437 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k2_metric_1(A,B,C),k1_numbers))) # label(dt_k2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2438 (all A (v1_xreal_0(A) -> (all B (-v3_struct_0(B) & l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k9_metric_1(B,C,A) = a_3_0_metric_1(A,B,C))))))) # label(t18_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2439 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> a_3_1_metric_1(A,B,C) = k10_metric_1(B,C,A))))))) # label(t19_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2440 (all A (l1_metric_1(A) -> (v8_metric_1(A) <-> v4_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d9_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2441 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k10_metric_1(B,C,A) = k4_subset_1(u1_struct_0(B),k11_metric_1(B,C,A),k9_metric_1(B,C,A)))))))) # label(t17_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2442 (all A all B all C all D (m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & -v3_struct_0(C) & v1_xreal_0(B) -> (r2_hidden(A,a_3_2_metric_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(C)) & k2_metric_1(C,D,E) = B & E = A))))) # label(fraenkel_a_3_2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2443 (all A all B all C (l1_metric_1(A) & v1_xreal_0(C) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k10_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k10_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2444 (all A (l1_metric_1(A) -> (v6_metric_1(A) <-> v2_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d7_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2445 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v3_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_metric_1(A,A,B,C,D) = np__0 -> D = C)))))))) # label(d4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2446 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) -> m1_subset_1(k9_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k9_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2447 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_metric_1(u1_struct_0(A),u1_struct_0(A),u1_metric_1(A),B,C) = k2_metric_1(A,B,C))))))) # label(d1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2448 (all A all B all C all D all E (m1_subset_1(E,B) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & v1_funct_1(C) -> m1_subset_1(k1_metric_1(A,B,C,D,E),k1_numbers))) # label(dt_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2449 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> k1_metric_1(A,A,B,C,C) = np__0)) <-> v2_metric_1(B,A)))) # label(d3_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2450 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) -> m1_subset_1(k11_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k11_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2451 (all A g1_metric_1(A,k5_metric_1(A)) = k6_metric_1(A)) # label(d12_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2452 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k11_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t16_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2453 (all A (v6_metric_1(k6_metric_1(A)) & v7_metric_1(k6_metric_1(A)) & v9_metric_1(k6_metric_1(A)) & v8_metric_1(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(fc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2454 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,A) = k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B))))) # label(t10_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2455 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> r1_xreal_0(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B),k3_real_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,C),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,C,B))))))))) # label(t11_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2456 (all A (l1_metric_1(A) -> (v5_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v9_metric_1(A)))) # label(d10_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2457 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r1_xreal_0(k2_metric_1(B,C,D),A) & -v3_struct_0(B) <-> r2_hidden(D,k10_metric_1(B,C,A))))))))))) # label(t13_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2458 (exists A (l1_metric_1(A) & v1_metric_1(A))) # label(rc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2459 (all A (-v1_xboole_0(A) -> -v3_struct_0(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(fc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2460 (all A all B all C (v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_metric_1(A,B,C) = k4_metric_1(A,C,B))) # label(commutativity_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2461 $T # label(t7_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2462 (all A (v1_metric_1(k6_metric_1(A)) & l1_metric_1(k6_metric_1(A)))) # label(dt_k6_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2463 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = np__0 <-> A = B))))) # label(t9_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2464 (all A all B all C all D all E (v1_funct_1(C) & m1_subset_1(E,B) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) -> k1_binop_1(C,D,E) = k1_metric_1(A,B,C,D,E))) # label(redefinition_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2465 (all A all B all C all D (l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) & -v3_struct_0(C) & v1_xreal_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & r1_xreal_0(k2_metric_1(C,D,E),B) & A = E)) <-> r2_hidden(A,a_3_1_metric_1(B,C,D))))) # label(fraenkel_a_3_1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2466 $T # label(t8_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2467 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,B,C) = k2_metric_1(A,C,B))))) <-> v8_metric_1(A)))) # label(t3_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2468 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_struct_0(A) -> (v1_xboole_0(D) <-> D = k9_metric_1(A,B,C))) & (-v3_struct_0(A) -> ((exists E (-v3_struct_0(E) & l1_metric_1(E) & (exists F (B = F & a_3_0_metric_1(C,E,F) = D & A = E & m1_subset_1(F,u1_struct_0(E)))))) <-> D = k9_metric_1(A,B,C))))))))))) # label(d15_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2469 (all A (l1_metric_1(A) -> v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_1(u1_metric_1(A)))) # label(dt_u1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2470 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k18_complex1(k5_real_1(B,C)) = k1_metric_1(k1_numbers,k1_numbers,A,B,C))))) <-> k7_metric_1 = A))) # label(d13_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2471 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_struct_0(A) -> (k10_metric_1(A,B,C) = D <-> v1_xboole_0(D))) & (-v3_struct_0(A) -> (D = k10_metric_1(A,B,C) <-> (exists E (-v3_struct_0(E) & (exists F (m1_subset_1(F,u1_struct_0(E)) & A = E & F = B & a_3_1_metric_1(C,E,F) = D)) & l1_metric_1(E))))))))))))) # label(d16_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2472 (all A (l1_metric_1(A) -> (v7_metric_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_metric_1(A,B,C) = np__0 -> C = B)))))))) # label(t2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2473 (all A (v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_xreal_0(np__0,k4_metric_1(A,B,C)))))))) # label(t5_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2474 (exists A (-v3_struct_0(A) & v1_metric_1(A) & l1_metric_1(A))) # label(rc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2475 (all A (l1_metric_1(A) -> (v6_metric_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> np__0 = k2_metric_1(A,B,B)))))) # label(t1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2476 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (-v3_struct_0(B) & -r1_xreal_0(A,k2_metric_1(B,C,D)) <-> r2_hidden(D,k9_metric_1(B,C,A))))))))))) # label(t12_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2477 (all A all B all C (v8_metric_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) -> k2_metric_1(A,B,C) = k4_metric_1(A,B,C))) # label(redefinition_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2478 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> l1_metric_1(g1_metric_1(A,B)) & v1_metric_1(g1_metric_1(A,B)))) # label(dt_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2479 (all A (v1_funct_1(k5_metric_1(A)) & m2_relset_1(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers))) # label(dt_k5_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2480 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (v4_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_metric_1(A,A,B,D,C) = k1_metric_1(A,A,B,C,D)))))))) # label(d5_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2481 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) -> ((exists E (-v3_struct_0(E) & l1_metric_1(E) & (exists F (F = B & D = a_3_2_metric_1(C,E,F) & E = A & m1_subset_1(F,u1_struct_0(E)))))) <-> k11_metric_1(A,B,C) = D)) & (v3_struct_0(A) -> (v1_xboole_0(D) <-> k11_metric_1(A,B,C) = D)))))))))) # label(d17_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2482 (all A (l1_metric_1(A) -> (v9_metric_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D)))))))))))) # label(t4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2483 (all A (l1_metric_1(A) -> l1_struct_0(A))) # label(dt_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2484 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> a_3_2_metric_1(A,B,C) = k11_metric_1(B,C,A))))))) # label(t20_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2485 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k2_metric_1(A,B,C) = np__0 -> C = B) & r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))) & k2_metric_1(A,B,C) = k2_metric_1(A,C,B) & (C = B -> k2_metric_1(A,B,C) = np__0))))))) -> v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) & v7_metric_1(A) & v6_metric_1(A)))) # label(t6_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2486 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v3_pre_topc(B,A) -> v2_connsp_2(B,A))))))) # label(t23_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2487 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists C m2_connsp_2(C,A,B)))) # label(existence_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2488 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r3_connsp_1(A,B) & r1_tarski(B,C) -> r4_connsp_1(A,C,B)))))))) # label(t13_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2489 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) & -v3_struct_0(A) -> (all C (m1_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2490 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v3_pre_topc(B,A) -> m1_connsp_2(B,A,C)))))))) # label(t5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2491 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = C -> r1_tarski(k1_connsp_1(B,D),k1_connsp_1(A,C))))))))))) # label(t14_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2492 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (v3_pre_topc(C,A) & r2_hidden(B,C) -> r2_connsp_2(A,C,B))))))))) # label(t22_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2493 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> r1_connsp_2(A,B))) <-> v1_connsp_2(A)))) # label(d4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2494 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) & m1_connsp_2(D,A,B) <-> m1_connsp_2(k5_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2495 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v1_connsp_2(k3_pre_topc(A,B)) <-> v2_connsp_2(B,A)))))) # label(d6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2496 $T # label(t18_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2497 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(k1_xboole_0 = C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v3_pre_topc(D,A) & v4_pre_topc(D,A) & r2_hidden(B,D))))))))))) # label(t28_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2498 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> -((all D (m1_subset_1(D,u1_struct_0(k3_pre_topc(A,C))) -> -(B = D & r2_hidden(B,k1_tops_1(k3_pre_topc(A,C),k1_connsp_1(k3_pre_topc(A,C),D)))))) & r2_hidden(B,C) & v3_pre_topc(C,A)))) <-> r1_connsp_2(A,B)))))) # label(t20_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2499 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v5_compts_1(A) & v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_xboole_0 & v4_pre_topc(B,A) & v4_pre_topc(C,A) & v2_connsp_1(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_connsp_1(D,A) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(C,E) & r1_xboole_0(D,E) & r1_tarski(B,D) & v2_connsp_1(E,A)))))) & v2_connsp_1(B,A) & r1_xboole_0(B,C) & C != k1_xboole_0)))))))) # label(t27_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2500 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_connsp_1(A,B) -> v3_pre_topc(B,A))))))) # label(t21_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2501 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_connsp_2(A,B,C) <-> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(D = B & (all E (m1_subset_1(E,u1_struct_0(k3_pre_topc(A,D))) -> -(r1_connsp_2(k3_pre_topc(A,D),E) & E = C))))))))))))) # label(d5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2502 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> m1_subset_1(k1_connsp_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2503 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(C,A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -(m1_connsp_2(D,A,B) & v3_pre_topc(D,A) & r1_tarski(D,C))))))))))) # label(t7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2504 $T # label(t29_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2505 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r2_hidden(B,D) & r1_tarski(D,C))) <-> m1_connsp_2(C,A,B)))))))) # label(t8_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2506 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m2_connsp_2(C,A,B) <-> r1_tarski(B,k1_tops_1(A,C))))))))) # label(d2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2507 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v1_connsp_2(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r4_connsp_1(A,B,C) -> v3_pre_topc(C,A))))))))) # label(t24_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2508 $T # label(t16_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2509 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) <-> m2_connsp_2(C,A,k1_struct_0(A,B))))))))) # label(t10_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2510 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) <-> r2_hidden(B,k1_tops_1(A,C))))))))) # label(d1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2511 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> (all C (m2_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2512 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_connsp_2(B,A,C) -> r2_hidden(C,B)))))))) # label(t6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2513 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (v3_pre_topc(B,A) & E = D & C = F & m1_connsp_2(D,k3_pre_topc(A,B),C) -> m1_connsp_2(E,A,F)))))))))))))) # label(t11_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2514 $T # label(t17_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2515 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & r1_tarski(C,k1_connsp_2(A,B)) & r2_hidden(B,C) & v4_pre_topc(C,A) -> C = k1_connsp_2(A,B)))))))) # label(t31_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2516 $T # label(t15_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2517 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> (exists C m1_connsp_2(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2518 $T # label(t2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2519 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v4_pre_topc(k1_connsp_2(A,B),A))))) # label(t32_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2520 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (C = k6_setfam_1(u1_struct_0(A),D) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(E,A) & v4_pre_topc(E,A) & r2_hidden(B,E) <-> r2_hidden(E,D)))) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) <-> k1_connsp_2(A,B) = C))))))) # label(d7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2521 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) & r2_hidden(B,D) & r4_connsp_1(A,C,D) -> m1_connsp_2(D,A,B)))))) <-> r1_connsp_2(A,B)))))) # label(t19_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2522 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_connsp_1(D,A) & r1_tarski(D,C) & m1_connsp_2(D,A,B)))) & m1_connsp_2(C,A,B)))) <-> r1_connsp_2(A,B)))))) # label(d3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2523 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = C & E = D & m1_connsp_2(E,A,F) -> m1_connsp_2(D,k3_pre_topc(A,B),C)))))))))))))) # label(t12_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2524 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,B) & m1_connsp_2(D,A,C)))) & r2_hidden(C,B)))) <-> v3_pre_topc(B,A)))))) # label(t9_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2525 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (m1_connsp_2(C,A,B) & m1_connsp_2(D,A,B) -> m1_connsp_2(k4_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2526 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != B & k2_pre_topc(A) != C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_tarski(B,D) & r1_tarski(k6_pre_topc(A,D),C)))) & v3_pre_topc(C,A) & v4_pre_topc(B,A) & r1_tarski(B,C)))))) <-> v5_compts_1(A)))) # label(t26_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2527 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_connsp_1(A,B),k1_connsp_2(A,B)))))) # label(t33_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2528 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) & -v1_xboole_0(C) -> -(v2_connsp_1(C,k3_pre_topc(A,B)) & v3_pre_topc(C,k3_pre_topc(A,B)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & C = k5_subset_1(u1_struct_0(A),B,D) & v2_connsp_1(D,A)))))))))))) # label(t25_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2529 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k1_connsp_2(A,B)))))) # label(t30_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2530 $T # label(t1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2531 (all A (l1_metric_1(A) -> m1_subset_1(k4_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2532 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> ((exists B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & r1_pcomps_1(u1_struct_0(A),B) & u1_pre_topc(A) = k4_pcomps_1(k6_pcomps_1(u1_struct_0(A),B)) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers))) <-> v3_pcomps_1(A)))) # label(d9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2533 (exists A (l1_pre_topc(A) & v2_pre_topc(A) & v3_compts_1(A) & v1_pre_topc(A) & -v3_struct_0(A))) # label(rc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2534 (all A v2_compts_1(k2_pcomps_1(k1_tarski(A)))) # label(t9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2535 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & r2_hidden(D,B)))))))))) # label(t5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2536 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) -> r1_tarski(k3_pcomps_1(A,B),k3_pcomps_1(A,C))))))))) # label(t17_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2537 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B)) = k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))))))) # label(t19_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2538 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> v1_pcomps_1(B,A)))))) # label(t13_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2539 (all A (v9_metric_1(A) & l1_metric_1(A) & v8_metric_1(A) & v7_metric_1(A) & v6_metric_1(A) & -v3_struct_0(A) -> v3_compts_1(k5_pcomps_1(A)))) # label(t38_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2540 (all A u1_struct_0(k2_pcomps_1(A)) = A) # label(t8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2541 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r1_tarski(k9_metric_1(A,B,C),u1_struct_0(A)) & -r1_xreal_0(C,np__0) & m1_subset_1(C,k1_numbers))))))) # label(t29_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2542 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_pcomps_1(A) & v3_compts_1(A) -> v5_compts_1(A)))) # label(t28_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2543 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(a_3_1_pcomps_1(A,B,C),B))))))) # label(t11_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2544 (all A (l1_metric_1(A) -> v2_pre_topc(k5_pcomps_1(A)) & v1_pre_topc(k5_pcomps_1(A)))) # label(fc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2545 (all A (l1_metric_1(A) -> v2_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))) & l1_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))))) # label(t37_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2546 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & v2_pre_topc(B) -> ((exists E (A = E & r2_hidden(E,C) & -r1_xboole_0(E,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_1_pcomps_1(B,C,D))))) # label(fraenkel_a_3_1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2547 (exists A (v2_pre_topc(A) & v3_pcomps_1(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2548 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) -> v2_pcomps_1(A)))) # label(t25_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2549 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_xreal_0(D) -> -((all E (m1_subset_1(E,k1_numbers) -> -(r1_tarski(k9_metric_1(A,B,E),k9_metric_1(A,C,D)) & -r1_xreal_0(E,np__0)))) & r2_hidden(B,k9_metric_1(A,C,D)) & v9_metric_1(A)))))))))) # label(t30_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2550 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & k6_pre_topc(A,E) = D & r2_hidden(E,B))) <-> r2_hidden(D,C)))) <-> C = k3_pcomps_1(A,B)))))))) # label(d3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2551 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (B = k4_pcomps_1(A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_numbers) -> -(r1_tarski(k9_metric_1(A,D,E),C) & -r1_xreal_0(E,np__0)))) & r2_hidden(D,C)))) <-> r2_hidden(C,B))))))))) # label(d5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2552 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != B & k1_xboole_0 = k6_pre_topc(A,B)) & -(k6_pre_topc(A,B) != k1_xboole_0 & B = k1_xboole_0))))) # label(t2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2553 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k4_pcomps_1(A)) & r2_hidden(C,k4_pcomps_1(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k4_pcomps_1(A))))))))) # label(t35_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2554 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(v9_metric_1(A) & (all G (m1_subset_1(G,k1_numbers) -> -(r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,E,B)) & r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,F,C))))) & r2_hidden(D,k5_subset_1(u1_struct_0(A),k9_metric_1(A,E,B),k9_metric_1(A,F,C)))))))))))))))) # label(t31_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2555 (all A (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(A,f2_s1_pcomps_1) -> r2_hidden(f4_s1_pcomps_1(A),f3_s1_pcomps_1)))) -> (exists A (v1_funct_2(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(B,f2_s1_pcomps_1) -> k1_funct_1(A,B) = f4_s1_pcomps_1(B)))) & m2_relset_1(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & v1_funct_1(A))) # label(s1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2556 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (C = k1_tarski(B) -> k3_pcomps_1(A,C) = k1_tarski(k6_pre_topc(A,B))))))))) # label(t16_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2557 (all A (l1_metric_1(A) -> l1_pre_topc(k5_pcomps_1(A)))) # label(dt_k5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2558 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r2_hidden(C,D) & v1_finset_1(a_3_0_pcomps_1(A,B,D)) & v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(d2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2559 (all A m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A)))) # label(dt_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2560 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_compts_1(A) -> v4_pre_topc(k1_struct_0(A,B),A)))))) # label(t10_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2561 (all A k1_zfmisc_1(A) = k1_pcomps_1(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2562 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_pcomps_1(A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(C,E) & r1_xboole_0(D,E) & r1_tarski(B,D) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_tarski(B,E) & r1_xboole_0(E,F) & r2_hidden(D,F) & v3_pre_topc(F,A)))))) & r2_hidden(D,C)))) & r1_xboole_0(B,C) & v4_pre_topc(C,A) & v4_pre_topc(B,A)))))))) # label(t26_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2563 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> k3_pcomps_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)) = k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C)))))))) # label(t18_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2564 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B)) = k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))))))) # label(t23_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2565 (all A (l1_metric_1(A) -> k5_pcomps_1(A) = g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A)))) # label(d6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2566 (all A g1_pre_topc(A,k1_pcomps_1(A)) = k2_pcomps_1(A)) # label(d1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2567 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v1_pcomps_1(B,A) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t24_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2568 (all A (-v1_xboole_0(A) -> -v3_struct_0(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)) & v2_pre_topc(k2_pcomps_1(A)))) # label(fc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2569 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> m1_subset_1(k3_pcomps_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2570 $T # label(t3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2571 $T # label(t4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2572 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (B = k1_xboole_0 -> k3_pcomps_1(A,B) = k1_xboole_0))))) # label(t15_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2573 (all A (l1_metric_1(A) -> r2_hidden(u1_struct_0(A),k4_pcomps_1(A)))) # label(t34_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2574 (all A (l1_pre_topc(A) -> (v2_pcomps_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & v1_tops_2(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_tops_2(C,A) & r1_setfam_1(C,B) & v1_pcomps_1(C,A) & r1_pre_topc(A,C)))))))))) # label(d4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2575 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t22_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2576 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_setfam_1(B,k3_pcomps_1(A,B)))))) # label(t20_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2577 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (v9_metric_1(A) -> r2_hidden(k9_metric_1(A,B,C),k4_pcomps_1(A))))))))) # label(t33_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2578 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> v1_pcomps_1(k3_pcomps_1(A,B),A)))))) # label(t21_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2579 (all A all B all C all D (l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> ((exists E (E = A & r2_hidden(E,C) & -r1_xboole_0(E,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_0_pcomps_1(B,C,D))))) # label(fraenkel_a_3_0_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2580 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (r1_pcomps_1(A,B) <-> v6_metric_1(g1_metric_1(A,B)) & v8_metric_1(g1_metric_1(A,B)) & v9_metric_1(g1_metric_1(A,B)) & l1_metric_1(g1_metric_1(A,B)) & v7_metric_1(g1_metric_1(A,B))))) # label(t39_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2581 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v1_pcomps_1(C,A) -> v1_pcomps_1(B,A)))))))) # label(t12_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2582 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> v2_tops_2(k3_pcomps_1(A,B),A))))) # label(t14_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2583 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v3_compts_1(A) & v2_pcomps_1(A) -> v4_compts_1(A)))) # label(t27_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2584 (all A all B (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> v6_metric_1(k6_pcomps_1(A,B)) & v9_metric_1(k6_pcomps_1(A,B)) & l1_metric_1(k6_pcomps_1(A,B)) & v8_metric_1(k6_pcomps_1(A,B)) & v7_metric_1(k6_pcomps_1(A,B)) & v1_metric_1(k6_pcomps_1(A,B)) & -v3_struct_0(k6_pcomps_1(A,B)))) # label(dt_k6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2585 $T # label(t6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2586 (exists A (v2_pcomps_1(A) & v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2587 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (r1_pcomps_1(A,B) -> k6_pcomps_1(A,B) = g1_metric_1(A,B)))))) # label(d8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2588 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_metric_1(A,A,B,C,D) = np__0 -> D = C) & r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E))) & k1_metric_1(A,A,B,C,D) = k1_metric_1(A,A,B,D,C) & (D = C -> k1_metric_1(A,A,B,C,D) = np__0))))))) <-> r1_pcomps_1(A,B)))) # label(d7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2589 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k4_pcomps_1(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),k4_pcomps_1(A))))))) # label(t36_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2590 (all A l1_pre_topc(k2_pcomps_1(A))) # label(dt_k2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2591 $T # label(t32_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2592 (all A (l1_metric_1(A) & -v3_struct_0(A) -> v2_pre_topc(k5_pcomps_1(A)) & v1_pre_topc(k5_pcomps_1(A)) & -v3_struct_0(k5_pcomps_1(A)))) # label(fc4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2593 (all A u1_pre_topc(k2_pcomps_1(A)) = k1_pcomps_1(A)) # label(t7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2594 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) -> r1_tarski(k9_metric_1(A,B,C),k9_metric_1(A,B,D))))))))))) # label(t1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2595 (all A (v2_pre_topc(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)))) # label(fc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2596 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (r1_borsuk_1(A,B) <-> (exists 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_borsuk_1(C,A,B) & v5_pre_topc(C,A,B)))))))) # label(d20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2597 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -((all F (v1_funct_2(F,B,C) & m2_relset_1(F,B,C) & v1_funct_1(F) -> E != k7_funct_2(A,B,C,D,F))) & (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k8_funct_2(A,B,D,G) = k8_funct_2(A,B,D,F) -> k8_funct_2(A,C,E,F) = k8_funct_2(A,C,E,G))))))))))))))))) # label(t19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2598 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)) = C))))))) # label(t54_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2599 (all A all B all C all D all E all F (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m2_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & m1_subset_1(D,u1_struct_0(B)) & v2_pre_topc(B) & v2_pre_topc(A) -> m2_connsp_2(k10_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,k1_struct_0(B,D))))) # label(dt_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2600 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D))))))))) # label(t71_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2601 (all A all B all C all D all E all F (l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & m1_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & l1_pre_topc(B) & v2_pre_topc(A) & -v3_struct_0(A) -> k2_zfmisc_1(E,F) = k9_borsuk_1(A,B,C,D,E,F))) # label(redefinition_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2602 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v6_compts_1(k1_struct_0(A,B),A))))) # label(t41_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2603 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,C) -> k3_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k6_domain_1(k2_zfmisc_1(B,C),k1_domain_1(B,C,E,F))) = k12_mcart_1(A,C,k3_funct_2(A,B,D,k6_domain_1(B,E)),k6_domain_1(C,F)))))))))))))) # label(t24_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2604 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)) = k1_tops_1(k6_borsuk_1(A,B),C))))))) # label(t55_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2605 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_connsp_2(D,A,C) -> (r1_tarski(B,C) -> m2_connsp_2(D,A,B)))))))))) # label(t39_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2606 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r2_hidden(C,D) -> k8_funct_2(A,B,k2_borsuk_1(A,B),C) = D))))))))) # label(t29_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2607 (all A (l1_struct_0(A) -> m1_eqrel_1(k15_borsuk_1(A),u1_struct_0(A)))) # label(dt_k15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2608 (all A all B all C r1_tarski(k9_relat_1(k2_funcop_1(A,B),C),k1_tarski(B))) # label(t6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2609 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k7_borsuk_1(A,B,k1_tops_1(A,C),k1_tops_1(B,D)) = k1_tops_1(k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)))))))))) # label(t47_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2610 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> (exists F (m1_subset_1(F,k1_zfmisc_1(A)) & (exists G (m1_subset_1(G,k1_zfmisc_1(B)) & k12_mcart_1(A,B,F,G) = E)))) & r1_tarski(E,C))) -> r1_tarski(k2_zfmisc_1(k1_setfam_1(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k3_tarski(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2611 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v4_pre_topc(C,A))))))))) # label(d14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2612 $T # label(d4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2613 (all A all B all C all D (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))))) # label(dt_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2614 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_compts_1(A,C,D) & (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(E,C) & r1_compts_1(A,E,D) & (all F -(r1_xboole_0(F,D) & r2_hidden(F,E))))))))))))))) # label(t63_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2615 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((exists C (v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(k22_borsuk_1)) -> k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,E)) = D))) & r2_hidden(k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k24_borsuk_1)),u1_struct_0(B)) & k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k23_borsuk_1)) = D)) & v5_pre_topc(C,k6_borsuk_1(A,k22_borsuk_1),A) & v1_funct_1(C))) <-> r2_borsuk_1(A,B)))))) # label(d21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2616 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> r1_tarski(C,k18_borsuk_1(A,B,C)))))))) # label(t73_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2617 (all A all B (-v1_xboole_0(A) & m1_eqrel_1(B,A) & -v1_xboole_0(B) -> v1_funct_1(k2_borsuk_1(A,B)) & m2_relset_1(k2_borsuk_1(A,B),A,B) & v1_funct_2(k2_borsuk_1(A,B),A,B))) # label(dt_k2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2618 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & (exists G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) & k7_borsuk_1(A,B,F,G) = E)))))) -> r1_tarski(k7_borsuk_1(A,B,k5_setfam_1(u1_struct_0(A),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),D)),k6_setfam_1(u1_struct_0(B),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),D))),C)))))))))) # label(t56_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2619 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> k3_funct_2(A,B,k2_borsuk_1(A,B),k6_domain_1(B,C)) = C)))))) # label(t30_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2620 $T # label(t8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2621 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),C) = D -> v3_pre_topc(D,A)) & (E = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),C) -> v3_pre_topc(E,B))))))))))))) # label(t59_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 2622 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) -> (exists F (r1_tarski(k4_pre_topc(A,B,C,F),E) & m1_connsp_2(F,A,D))))))) <-> v5_pre_topc(C,A,B)))))))) # label(d2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2623 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k2_funct_2(k2_zfmisc_1(B,C),C,k10_funct_3(B,C),A) = k1_funct_1(k1_funct_3(k10_funct_3(B,C)),A))) # label(t10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2624 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m2_connsp_2(E,A,C) -> (all F (m2_connsp_2(F,B,D) -> m2_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)))))))))))))) # label(t49_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2625 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(r2_hidden(E,C) & k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),E) = D))) & r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),C)))))))))) # label(t58_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2626 (all A (-v1_xboole_0(A) -> (exists B (m1_eqrel_1(B,A) & v1_setfam_1(B) & -v1_xboole_0(B))))) # label(rc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2627 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(k5_setfam_1(A,B)) = k3_tarski(a_2_0_borsuk_1(A,B)))) # label(t17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2628 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> k12_borsuk_1(A,B) = k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B))))))) # label(d7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2629 $T # label(t22_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2630 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (D = k3_tarski(C) -> k3_tarski(k3_subset_1(B,C)) = k3_subset_1(A,D)))))))))) # label(t27_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2631 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> k3_funct_2(A,B,k2_borsuk_1(A,B),C) = k3_tarski(C))))))) # label(t31_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2632 (all A all B (l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & -v1_xboole_0(C))))) # label(rc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2633 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> -v1_xboole_0(k8_eqrel_1(A,B)))))) # label(t28_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2634 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(k15_borsuk_1(A)) & v1_setfam_1(k15_borsuk_1(A)))) # label(fc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2635 (all A all B (v2_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> v1_pre_topc(k16_borsuk_1(A,B)) & l1_pre_topc(k16_borsuk_1(A,B)) & v2_pre_topc(k16_borsuk_1(A,B)))) # label(dt_k16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2636 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2637 $T # label(t1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2638 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_borsuk_1(C,B) & v2_borsuk_1(C,B) -> (r2_borsuk_1(A,B) -> r2_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t85_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2639 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (A = k5_setfam_1(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k3_tarski(C) = D -> r1_tarski(k3_subset_1(A,D),k3_tarski(k3_subset_1(B,C))))))))))) # label(t18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2640 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k10_relat_1(C,B)) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2641 (all A all B all C all D all E (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(B) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & m1_connsp_2(E,B,C) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) -> m2_connsp_2(k5_borsuk_1(A,B,C,D,E),A,k5_pre_topc(A,B,D,k1_struct_0(B,C))))) # label(dt_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2642 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_compts_1(k6_borsuk_1(A,B),C,k7_borsuk_1(A,B,D,E)) -> (k1_xboole_0 != E -> r1_compts_1(A,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),D)) & (k1_xboole_0 != D -> r1_compts_1(B,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),E))))))))))))) # label(t62_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2643 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_borsuk_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (all D (m2_connsp_2(D,A,k5_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),k1_struct_0(k16_borsuk_1(A,B),C))) -> m1_connsp_2(k4_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),D),k16_borsuk_1(A,B),C))))))))) # label(t81_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2644 (all A all B all C (v2_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & l1_pre_topc(A) & -v3_struct_0(A) -> k19_borsuk_1(A,B,C) = k18_borsuk_1(A,B,C))) # label(redefinition_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2645 (all A all B all C all D (v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k7_borsuk_1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))) # label(dt_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2646 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,C) -> k8_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k1_domain_1(A,C,E,F)) = k1_domain_1(B,C,k8_funct_2(A,B,D,E),F))))))))))))) # label(t21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2647 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B))))) # label(dt_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2648 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & v1_setfam_1(B) & v2_borsuk_1(B,A) & m1_borsuk_1(B,A))))) # label(rc5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2649 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))) -> r2_hidden(D,u1_struct_0(B))))))))))) # label(t79_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2650 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(A) & v1_borsuk_1(B,A) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & -v3_struct_0(B) & -v3_struct_0(A) -> m1_borsuk_1(k19_borsuk_1(A,B,C),A))) # label(dt_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2651 (all A all B all C (l1_pre_topc(B) & l1_pre_topc(C) & v2_pre_topc(C) & v2_pre_topc(B) -> (r2_hidden(A,a_2_1_borsuk_1(B,C)) <-> (exists D exists E (r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) & k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E) = A & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2652 $T # label(t11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2653 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> r1_tarski(u1_struct_0(B),u1_struct_0(A)))))) # label(t35_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2654 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(C,k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),C)))))))) # label(t70_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2655 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> -v3_struct_0(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)))) # label(fc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2656 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_pre_topc(k6_borsuk_1(A,B)) & l1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)))) # label(dt_k6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2657 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> k1_struct_0(A,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D)))))))))) # label(t77_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2658 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) -> k2_funcop_1(B,C) = k1_borsuk_1(A,B,C))) # label(redefinition_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2659 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v1_borsuk_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2660 (all A all B all C (v2_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) & v2_pre_topc(B) & l1_pre_topc(A) -> m1_subset_1(k11_borsuk_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))))) # label(dt_k11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2661 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k1_funct_1(k17_borsuk_1(B,C),D)))))))))) # label(t76_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2662 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_funct_1(D) & v5_pre_topc(D,B,A) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (all E (m1_connsp_2(E,A,C) -> m2_connsp_2(k5_pre_topc(B,A,D,E),B,k5_pre_topc(B,A,D,k1_struct_0(A,C))))))))))))) # label(t38_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2663 (all A all B all C all D (v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & v1_funct_1(C) -> k9_relat_1(C,D) = k14_borsuk_1(A,B,C,D))) # label(redefinition_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2664 (all A all B all C (v2_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & l1_pre_topc(A) & -v3_struct_0(A) -> k20_borsuk_1(A,B,C) = k18_borsuk_1(A,B,C))) # label(redefinition_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2665 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)),C))))))) # label(t53_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2666 $T # label(t34_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2667 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_borsuk_1(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = D)))))))))) # label(d19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2668 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k15_borsuk_1(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_struct_0(A,C) != B))))))) # label(t68_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2669 $T # label(t40_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2670 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_funct_1(k13_borsuk_1(A,B)) & m2_relset_1(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))) & v1_funct_2(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))))) # label(dt_k13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2671 $T # label(t43_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2672 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_borsuk_1(C,B) & v2_borsuk_1(C,B) -> (r1_borsuk_1(A,B) -> r1_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t84_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2673 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> v5_pre_topc(k3_borsuk_1(B,A,C),B,A))))))) # label(t36_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2674 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) -> m1_subset_1(k14_borsuk_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))))) # label(dt_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2675 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F ((exists G (m1_subset_1(G,k1_zfmisc_1(B)) & E = k12_mcart_1(A,B,F,G))) & m1_subset_1(F,k1_zfmisc_1(A)))))) -> r1_tarski(k2_zfmisc_1(k3_tarski(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k1_setfam_1(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2676 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_connsp_2(E,A,C) -> (all F (m1_connsp_2(F,B,D) -> m1_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))))))))))))) # label(t48_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2677 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k12_mcart_1(A,B,C,D) != k1_xboole_0 -> D = k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) & C = k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),k12_mcart_1(A,B,C,D))))))) # label(t12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2678 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_funct_1(k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))))))))))) # label(t80_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2679 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) & (all E -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) -> -(E = k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G) & v3_pre_topc(F,A) & v3_pre_topc(G,B)))))) & r2_hidden(E,D))) & C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D)))))))))) # label(t45_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2680 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> v1_tops_2(k11_borsuk_1(A,B,C),k6_borsuk_1(A,B)))))))) # label(t51_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2681 (all A all B all C all D all E all F (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m2_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> k2_zfmisc_1(E,F) = k10_borsuk_1(A,B,C,D,E,F))) # label(redefinition_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2682 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,k18_borsuk_1(A,B,C)) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(-r2_hidden(E,k2_pre_topc(B)) & k1_struct_0(A,E) = D))) & -r2_hidden(D,C)))))))))) # label(t74_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2683 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k11_borsuk_1(A,B,C) = a_3_1_borsuk_1(A,B,C))))))) # label(d6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2684 (all A all B all C all D all E (v2_pre_topc(A) & -v3_struct_0(C) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & l1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> k5_relat_1(D,E) = k4_borsuk_1(A,B,C,D,E))) # label(redefinition_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2685 (all A all B all C all D all E (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(C) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & v5_pre_topc(E,B,C) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & l1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) -> v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C) & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(k4_borsuk_1(A,B,C,D,E)))) # label(dt_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2686 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> r2_hidden(D,k8_funct_2(A,B,C,D)))) <-> k2_borsuk_1(A,B) = C))))))) # label(d1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2687 (all A all B (v2_pre_topc(A) & -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_pre_topc(k16_borsuk_1(A,B)) & v2_pre_topc(k16_borsuk_1(A,B)) & -v3_struct_0(k16_borsuk_1(A,B)))) # label(fc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2688 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) -> r1_xboole_0(D,C) | r1_tarski(D,C)))) -> C = k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C))))))))) # label(t33_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2689 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & l1_pre_topc(A) -> m1_pre_topc(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & v1_borsuk_1(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & v1_pre_topc(k21_borsuk_1(A,B,C)))) # label(dt_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2690 (all A (l1_struct_0(A) -> k15_borsuk_1(A) = k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))))) # label(d9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2691 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> k2_xboole_0(C,a_2_3_borsuk_1(A,B)) = k18_borsuk_1(A,B,C))))))) # label(d12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2692 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) -> (all C (v1_pre_topc(C) & l1_pre_topc(C) & v2_pre_topc(C) -> (C = k16_borsuk_1(A,B) <-> u1_struct_0(C) = B & a_2_2_borsuk_1(A,B) = u1_pre_topc(C)))))))) # label(d10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2693 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> k1_funct_1(k13_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k1_funct_1(k12_borsuk_1(A,B),k1_xboole_0))))) # label(t66_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2694 (all A all B all C all D (-v3_struct_0(A) & -v3_struct_0(B) & v2_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(B) & l1_pre_topc(A) & v2_pre_topc(A) -> k4_tarski(C,D) = k8_borsuk_1(A,B,C,D))) # label(redefinition_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2695 (all A all B all C all D (v2_pre_topc(A) & l1_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v2_pre_topc(B) -> k2_zfmisc_1(C,D) = k7_borsuk_1(A,B,C,D))) # label(redefinition_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2696 (all A all B all C (l1_pre_topc(B) & m1_eqrel_1(C,u1_struct_0(B)) & v2_pre_topc(B) -> (r2_hidden(A,a_2_2_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(C)) & A = D & r2_hidden(k3_tarski(D),u1_pre_topc(B))))))) # label(fraenkel_a_2_2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2697 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> r1_tarski(k3_funct_2(A,B,E,k6_domain_1(B,D)),k3_funct_2(A,C,k7_funct_2(A,B,C,E,F),k6_domain_1(C,k8_funct_2(B,C,F,D)))))))))))))))) # label(t20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2698 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & (exists E (m1_subset_1(E,u1_struct_0(B)) & C = k8_borsuk_1(A,B,D,E))))))))))) # label(t50_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2699 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v6_compts_1(D,B) <-> v6_compts_1(C,A))))))))))) # label(t42_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2700 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k7_borsuk_1(A,B,C,D) != k1_xboole_0 -> C = k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) & D = k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),k7_borsuk_1(A,B,C,D))))))))))) # label(t65_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2701 (all A all B all C (v2_pre_topc(A) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> m1_borsuk_1(k20_borsuk_1(A,B,C),A) & v2_borsuk_1(k20_borsuk_1(A,B,C),A))) # label(dt_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2702 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k5_pre_topc(A,B,C,k1_tops_1(B,D)),k1_tops_1(A,k5_pre_topc(A,B,C,D))))))))))) # label(t37_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2703 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B))) = k13_borsuk_1(A,B))))) # label(d8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2704 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (k1_xboole_0 = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C) | k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C) = k1_xboole_0 -> C = k1_xboole_0))))))) # label(t61_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2705 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),E) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) -> E = D | r2_hidden(D,u1_struct_0(B))))))))))))) # label(t78_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2706 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> k2_relat_1(k17_borsuk_1(A,B)) = u1_struct_0(k16_borsuk_1(A,B)))))) # label(t72_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2707 (all A all B all C (l1_struct_0(A) & -v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_struct_0(B) -> m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k3_borsuk_1(A,B,C)))) # label(dt_k3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2708 (all A all B all C all D (l1_pre_topc(B) & v2_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,C)))) & l1_pre_topc(C) & v2_pre_topc(B) -> (r2_hidden(A,a_3_1_borsuk_1(B,C,D)) <-> (exists E exists F (r1_tarski(k7_borsuk_1(B,C,E,F),D) & v3_pre_topc(E,B) & v3_pre_topc(F,C) & k7_borsuk_1(B,C,E,F) = A & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_3_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2709 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (r1_tarski(C,D) -> r1_tarski(k11_borsuk_1(A,B,C),k11_borsuk_1(A,B,D))))))))))) # label(t52_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2710 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> v1_funct_1(k12_borsuk_1(A,B)) & v1_funct_2(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) & m2_relset_1(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))))) # label(dt_k12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2711 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_struct_0(A,D),k18_borsuk_1(A,B,C))))))))))) # label(t75_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2712 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k1_funct_1(k1_funct_3(k9_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),A))) # label(t9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2713 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_funct_2(A,A,k6_partfun1(A),B) = B)) # label(t4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2714 (all A all B all C all D all E all F (l1_pre_topc(A) & v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & m1_connsp_2(F,B,D) & m1_connsp_2(E,A,C) & l1_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) & -v3_struct_0(A) -> m1_connsp_2(k9_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))) # label(dt_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2715 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> (all D (m2_connsp_2(D,A,C) -> (exists E (v3_pre_topc(E,A) & r1_tarski(C,E) & r1_tarski(E,D) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(F,B) -> r1_xboole_0(F,E) | r1_tarski(F,E)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))))) <-> m1_borsuk_1(B,A)))))) # label(d13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2716 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_compts_1(D,B) -> (all E (m2_connsp_2(E,k6_borsuk_1(B,A),k7_borsuk_1(B,A,D,k1_struct_0(A,C))) -> (exists F (m2_connsp_2(F,B,D) & (exists G (r1_tarski(k10_borsuk_1(B,A,D,C,F,G),E) & m1_connsp_2(G,A,C)))))))))))))))) # label(t67_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2717 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> (exists D (m1_subset_1(D,A) & C = k8_funct_2(A,B,k2_borsuk_1(A,B),D))))))))) # label(t32_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2718 (all A all B all C all D (v2_pre_topc(B) & l1_pre_topc(C) & l1_pre_topc(D) & v2_pre_topc(D) & v1_pre_topc(D) & v2_pre_topc(C) & l1_pre_topc(B) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D)))) & r1_tarski(E,a_2_1_borsuk_1(B,C)) & k5_setfam_1(u1_struct_0(D),E) = A)) <-> r2_hidden(A,a_3_0_borsuk_1(B,C,D))))) # label(fraenkel_a_3_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2719 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> k2_borsuk_1(u1_struct_0(A),B) = k17_borsuk_1(A,B))))) # label(d11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2720 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(v1_finset_1(C) & r1_tarski(C,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),D)) & (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(v1_finset_1(E) & C = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),E) & r1_tarski(E,D))))))))))))) # label(t64_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2721 (all A all B all C (v2_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & v1_borsuk_1(B,A) & l1_pre_topc(A) & -v3_struct_0(A) -> k21_borsuk_1(A,B,C) = k16_borsuk_1(B,C))) # label(redefinition_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2722 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -(r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),C)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),E) & r2_hidden(E,C)))))))))))) # label(t57_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2723 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & m1_connsp_2(E,B,C) & v5_pre_topc(D,A,B) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> k10_relat_1(D,E) = k5_borsuk_1(A,B,C,D,E))) # label(redefinition_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2724 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_funct_1(k17_borsuk_1(A,B)) & m2_relset_1(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B)) & v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))))) # label(dt_k17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2725 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(A) -> -v1_xboole_0(k3_borsuk_1(A,B,C)) & v1_relat_1(k3_borsuk_1(A,B,C)) & v1_funct_1(k3_borsuk_1(A,B,C)) & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k3_borsuk_1(A,B,C),A,B) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)))) # label(fc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2726 $T # label(t3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2727 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> k5_setfam_1(B,k2_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(B),k2_funct_3(A,B,C),D)) = k2_funct_2(A,B,C,k5_setfam_1(A,D)))))))) # label(t16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2728 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) -> v1_funct_1(k1_borsuk_1(A,B,C)) & m2_relset_1(k1_borsuk_1(A,B,C),B,A) & v1_funct_2(k1_borsuk_1(A,B,C),B,A))) # label(dt_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2729 $T # label(t2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2730 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_borsuk_1(A,B,C) = k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C))))))) # label(d3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2731 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (v1_tops_2(C,k6_borsuk_1(A,B)) -> v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),B) & v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),A)))))))) # label(t60_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2732 $T # label(t7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2733 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & v3_pre_topc(D,B) -> v3_pre_topc(k7_borsuk_1(A,B,C,D),k6_borsuk_1(A,B))))))))))) # label(t46_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2734 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & -v3_struct_0(C) & m1_pre_topc(C,B) & l1_pre_topc(B) -> (r2_hidden(A,a_2_3_borsuk_1(B,C)) <-> (exists D (-r2_hidden(D,u1_struct_0(C)) & A = k1_struct_0(B,D) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2735 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & v1_pre_topc(C) -> (k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(C) & u1_pre_topc(C) = a_3_0_borsuk_1(A,B,C) <-> C = k6_borsuk_1(A,B)))))))) # label(d5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2736 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v6_compts_1(C,A)))) <-> v2_borsuk_1(B,A)))))) # label(d15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2737 $T # label(t44_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2738 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B m1_borsuk_1(B,A)))) # label(existence_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2739 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B))) <-> r2_hidden(k3_tarski(C),u1_pre_topc(A))))))))) # label(t69_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2740 (all A all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> k3_tarski(k5_subset_1(B,C,D)) = k3_xboole_0(k3_tarski(C),k3_tarski(D)))))))) # label(t26_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2741 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> m1_subset_1(k3_tarski(C),k1_zfmisc_1(A)))))))) # label(t25_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.08 2742 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & -v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) & m1_pre_topc(B,A) & -v3_struct_0(B) & l1_pre_topc(A) -> -v1_xboole_0(k18_borsuk_1(A,B,C)) & m1_eqrel_1(k18_borsuk_1(A,B,C),u1_struct_0(A)))) # label(dt_k18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2743 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(B)) & r2_hidden(D,C) & A = k3_tarski(D))) <-> r2_hidden(A,a_2_0_borsuk_1(B,C))))) # label(fraenkel_a_2_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2744 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> k2_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k12_mcart_1(A,C,E,F)) = k12_mcart_1(B,C,k2_funct_2(A,B,D,E),F))))))))))))) # label(t23_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2745 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k8_metric_1)))) -> (B = k1_rcomp_1(np__0,np__1) -> k3_pre_topc(k5_pcomps_1(k8_metric_1),B) = A))) <-> k22_borsuk_1 = A))) # label(d16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2746 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> m1_borsuk_1(k15_borsuk_1(A),A))) # label(t82_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2747 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k12_mcart_1(A,B,C,D) != k1_xboole_0 -> k1_funct_1(k1_funct_3(k10_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = D & k1_funct_1(k1_funct_3(k9_funct_3(A,B)),k12_mcart_1(A,B,C,D)) = C))))) # label(t13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2748 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,D),k5_subset_1(u1_struct_0(A),C,D))))))))))) # label(t43_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2749 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & (exists E (-v3_struct_0(E) & m1_pre_topc(C,E) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & v1_borsuk_1(E,A))) & v1_borsuk_1(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t81_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2750 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,B) & v1_borsuk_1(C,B) -> v1_borsuk_1(C,A) & m1_pre_topc(C,A))))))) # label(t13_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2751 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> r2_tsep_1(A,B,C)))))))) # label(t53_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2752 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(D,B) & r1_tarski(E,C) & r2_tsep_1(A,C,B) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),C,D),k4_subset_1(u1_struct_0(A),B,E))))))))))))) # label(t56_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2753 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r4_tsep_1(A,B,C) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (E = u1_struct_0(C) & u1_struct_0(B) = D -> r2_tsep_1(A,D,E))))))))))))) # label(d9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2754 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(B,A) & -v3_struct_0(C) & m1_pre_topc(C,A) & -v3_struct_0(B) & -v3_struct_0(A) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_pre_topc(k2_tsep_1(A,B,C)) & -v3_struct_0(k2_tsep_1(A,B,C)))) # label(dt_k2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2755 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & D = E & r1_tarski(D,C) & v4_pre_topc(C,A) -> (v4_pre_topc(D,A) <-> v4_pre_topc(E,B))))))))))))) # label(t8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2756 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_borsuk_1(k2_tsep_1(A,B,C),A)))))))) # label(t32_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2757 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) -> (m1_pre_topc(D,B) & r3_tsep_1(A,B,C) & m1_pre_topc(E,C) -> r3_tsep_1(A,D,E)))))))))))) # label(t77_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2758 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v2_pre_topc(B) & v1_tsep_1(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2759 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (-v3_struct_0(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2760 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (v1_tsep_1(C,B) & m1_pre_topc(C,B) -> m1_pre_topc(C,A) & v1_tsep_1(C,A))))))) # label(t18_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2761 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (r1_tarski(B,D) & r1_tarski(C,E) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))))))))) # label(t47_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2762 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),C) & m1_pre_topc(k2_tsep_1(A,B,C),B)))))))) # label(t30_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2763 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> -((all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) -> (all E (v1_borsuk_1(E,A) & m1_pre_topc(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & -((all F (m1_pre_topc(F,A) & v1_tsep_1(F,A) & -v3_struct_0(F) -> -(m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F)))) & -m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E))) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C)))))))))) # label(t93_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2764 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (A = k1_tsep_1(A,B,C) -> r1_tsep_1(A,B,C) | (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(C,B) & (all D (-v3_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) & v1_tsep_1(E,A) -> -(-(k1_tsep_1(A,D,E) != A & (all F (-v3_struct_0(F) & v1_borsuk_1(F,A) & m1_pre_topc(F,A) -> -(m1_pre_topc(F,k2_tsep_1(A,B,C)) & k1_tsep_1(A,k1_tsep_1(A,D,E),F) = A)))) & m1_pre_topc(E,C) & m1_pre_topc(D,B)))))) & -m1_pre_topc(B,C)))))))))) # label(t97_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2765 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (-r1_tsep_1(A,C,D) -> (r4_tsep_1(A,B,C) & r4_tsep_1(A,B,D) -> r4_tsep_1(A,B,k2_tsep_1(A,C,D))) & (r4_tsep_1(A,C,B) & r4_tsep_1(A,D,B) -> r4_tsep_1(A,k2_tsep_1(A,C,D),B))))))))))) # label(t91_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2766 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (v1_tsep_1(D,A) & (exists E (v1_tsep_1(E,A) & m1_pre_topc(B,D) & r1_tsep_1(A,D,C) & r1_tsep_1(A,E,B) & m1_pre_topc(C,E) & m1_pre_topc(E,A) & -v3_struct_0(E))) & m1_pre_topc(D,A) & -v3_struct_0(D))) <-> r3_tsep_1(A,B,C)))))))) # label(t82_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2767 (all A all B all C (m1_pre_topc(B,A) & m1_pre_topc(C,A) & l1_pre_topc(A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,C,B)))) # label(symmetry_r4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2768 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,D) & r2_tsep_1(A,C,D) -> r2_tsep_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t57_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2769 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_tsep_1(A,B,C) & -r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(E,A) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(F,A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F)))) & -r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E))) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & v4_pre_topc(D,A)))))) & -r1_tarski(B,C)))))))) # label(t60_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2770 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v4_pre_topc(C,A) <-> v1_borsuk_1(B,A) & m1_pre_topc(B,A))))))))) # label(t11_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2771 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))))))) # label(t17_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2772 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) & v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) -> v3_pre_topc(B,A) & v3_pre_topc(C,A)))))))) # label(t42_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2773 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> r4_tsep_1(A,B,C))))))) # label(t87_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2774 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v3_pre_topc(C,A)))) <-> v1_tsep_1(B,A)))))) # label(d1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2775 (all A all B all C (-v3_struct_0(B) & m1_pre_topc(B,A) & m1_pre_topc(C,A) & -v3_struct_0(C) & l1_pre_topc(A) & -v3_struct_0(A) -> k1_tsep_1(A,C,B) = k1_tsep_1(A,B,C))) # label(commutativity_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2776 $T # label(t84_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2777 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E ((exists F (k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C) & r1_tarski(E,C) & v3_pre_topc(E,A) & v4_pre_topc(F,A) & v3_pre_topc(D,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(D,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))) <-> r2_tsep_1(A,B,C))))))))) # label(t65_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2778 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,D),k4_subset_1(u1_struct_0(A),C,D))))))))))) # label(t55_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2779 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r1_xboole_0(B,C) -> r1_xboole_0(B,k6_pre_topc(A,C))))))))) # label(t40_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2780 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> r1_tsep_1(A,B,C)))))))) # label(t70_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2781 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) & v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) -> v4_pre_topc(C,A) & v4_pre_topc(B,A)))))))) # label(t39_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2782 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A & r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> v1_tsep_1(B,A) & m1_pre_topc(B,A) & m1_pre_topc(C,A) & v1_tsep_1(C,A))))))))) # label(t98_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2783 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> v1_borsuk_1(B,C) & m1_pre_topc(B,C) & -v3_struct_0(B)))))))) # label(t14_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2784 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (A = k1_tsep_1(A,B,C) & r1_tsep_1(A,B,C) -> (m1_pre_topc(B,A) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & v1_borsuk_1(B,A) <-> r4_tsep_1(A,B,C))))))))) # label(t95_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2785 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) & r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C)))))))) # label(t51_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2786 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (all E (m1_pre_topc(E,A) & -v3_struct_0(E) -> (m1_pre_topc(D,B) & m1_pre_topc(E,C) & r4_tsep_1(A,C,B) -> r4_tsep_1(A,k1_tsep_1(A,C,D),k1_tsep_1(A,B,E)) & r4_tsep_1(A,k1_tsep_1(A,D,C),k1_tsep_1(A,E,B))))))))))))) # label(t90_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2787 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v1_tsep_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t75_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2788 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E ((exists F (k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(D,A) & v4_pre_topc(E,A) & v3_pre_topc(F,A) & r1_tarski(E,C) & r1_tarski(D,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))) <-> r2_tsep_1(A,B,C))))))))) # label(t61_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2789 $T # label(t50_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2790 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,B,D) -> r1_tsep_1(A,B,C) | r3_tsep_1(A,k2_tsep_1(A,B,C),D)))))))))) # label(t78_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2791 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v1_borsuk_1(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) & m1_pre_topc(k1_tsep_1(A,B,C),A) -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t72_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2792 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_tsep_1(k1_tsep_1(A,B,C),A))))))) # label(t25_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2793 (all A (l1_pre_topc(A) -> m1_pre_topc(A,A))) # label(t2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2794 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k1_tsep_1(A,B,C) <-> m1_pre_topc(B,C)))))))) # label(t23_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2795 (all A all B all C (-v3_struct_0(A) & -v3_struct_0(B) & -v3_struct_0(C) & m1_pre_topc(C,A) & m1_pre_topc(B,A) & l1_pre_topc(A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_pre_topc(k1_tsep_1(A,B,C)) & -v3_struct_0(k1_tsep_1(A,B,C)))) # label(dt_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2796 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2797 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> (r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C))))))))) # label(t41_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2798 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E ((exists F (r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_tsep_1(A,B,C)))))))) # label(t63_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2799 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> v1_tsep_1(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t33_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2800 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> m1_pre_topc(B,k1_tsep_1(A,B,C)))))))) # label(t22_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2801 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r1_tsep_1(A,B,C) <-> r1_xboole_0(u1_struct_0(B),u1_struct_0(C))))))))) # label(d3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2802 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (m1_pre_topc(C,B) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_tsep_1(A,B,C)) & (g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_tsep_1(A,B,C) -> m1_pre_topc(C,B)) & (k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> m1_pre_topc(B,C)) & (m1_pre_topc(B,C) -> k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))))))))) # label(t31_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2803 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> r2_tsep_1(A,B,C)))))))) # label(t54_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2804 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D))))))))))) # label(t89_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2805 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D,A) & v4_pre_topc(E,A) & r1_xboole_0(E,B) & r1_xboole_0(D,C) & r1_tarski(C,E) & r1_tarski(B,D))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r1_connsp_1(A,B,C)))))))) # label(t46_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2806 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (all D (m1_pre_topc(D,A) & v1_pre_topc(D) & -v3_struct_0(D) -> (k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D) <-> k2_tsep_1(A,B,C) = D)))))))))) # label(d5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2807 $T # label(t28_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2808 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,D) | r1_connsp_1(A,C,D) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t44_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2809 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (-v3_struct_0(D) & (exists E (r4_tsep_1(A,D,E) & m1_pre_topc(C,E) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & -v3_struct_0(E))) & m1_pre_topc(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t99_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2810 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> -(-r1_tsep_1(A,B,D) & -(k2_tsep_1(A,D,k1_tsep_1(A,B,C)) = k1_tsep_1(A,k2_tsep_1(A,D,B),k2_tsep_1(A,D,C)) & k1_tsep_1(A,k2_tsep_1(A,B,D),k2_tsep_1(A,C,D)) = k2_tsep_1(A,k1_tsep_1(A,B,C),D)) & -r1_tsep_1(A,D,C)))))))))) # label(t35_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2811 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (m1_pre_topc(B,C) -> r4_tsep_1(A,B,C)))))))) # label(t86_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2812 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r3_tsep_1(A,C,D) -> r1_tsep_1(A,C,B) | r3_tsep_1(A,k2_tsep_1(A,C,B),k2_tsep_1(A,D,B)) & r3_tsep_1(A,k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) | r1_tsep_1(A,D,B)))))))))) # label(t76_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2813 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (-(-m1_pre_topc(B,C) & (all D (m1_pre_topc(D,A) & v1_tsep_1(D,A) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & v1_tsep_1(E,A) & m1_pre_topc(E,A) -> -(m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C) & -((all F (m1_pre_topc(F,A) & v1_borsuk_1(F,A) & -v3_struct_0(F) -> -(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C))))) & -m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E)))))))) & -m1_pre_topc(C,B)) <-> r4_tsep_1(A,B,C))))))))) # label(t96_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2814 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r4_tsep_1(A,D,C) & r4_tsep_1(A,D,B) -> r4_tsep_1(A,D,k1_tsep_1(A,B,C))) & (r4_tsep_1(A,B,D) & r4_tsep_1(A,C,D) -> r4_tsep_1(A,k1_tsep_1(A,B,C),D)))))))))) # label(t92_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2815 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (u1_struct_0(B) = u1_struct_0(C) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))))) # label(t5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2816 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t73_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2817 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (D = u1_struct_0(B) & E = u1_struct_0(C) -> r1_connsp_1(A,D,E))))))))))))) # label(d8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2818 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) -> r4_tsep_1(A,B,C))))))) # label(t88_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2819 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A & r3_tsep_1(A,B,C) -> v1_borsuk_1(B,A) & m1_pre_topc(B,A)))))))) # label(t71_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2820 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,C,D) & -r1_tsep_1(A,B,k2_tsep_1(A,C,D)) | -r1_tsep_1(A,k2_tsep_1(A,B,C),D) & -r1_tsep_1(A,B,C) -> k2_tsep_1(A,k2_tsep_1(A,B,C),D) = k2_tsep_1(A,B,k2_tsep_1(A,C,D))) & (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,C,B) = k2_tsep_1(A,B,C)))))))))) # label(t29_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2821 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,k4_subset_1(u1_struct_0(A),B,C),D) <-> r1_connsp_1(A,C,D) & r1_connsp_1(A,B,D)))))))))) # label(t45_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2822 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tsep_1(B,A) & m1_pre_topc(B,A) <-> v3_pre_topc(C,A))))))))) # label(t16_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2823 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> k1_tsep_1(A,k1_tsep_1(A,B,C),D) = k1_tsep_1(A,B,k1_tsep_1(A,C,D)))))))))) # label(t21_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2824 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r2_tsep_1(A,B,C)))))))) # label(t52_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2825 $T # label(d4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2826 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> (r1_connsp_1(A,B,C) <-> r1_xboole_0(B,C))))))))) # label(t38_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2827 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),k1_tsep_1(A,B,C))))))))) # label(t34_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2828 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) & (exists E (-v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(C,E) & r1_tsep_1(A,E,B) & r1_tsep_1(A,D,C) & m1_pre_topc(B,D) & m1_pre_topc(E,A)))))))))))) # label(t80_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2829 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> B != u1_struct_0(C))) & v4_pre_topc(B,A)))))) # label(t15_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2830 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) & r2_tsep_1(A,B,C) & -r1_tarski(B,C) & -r1_tarski(C,B) & (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(E) -> -(v3_pre_topc(D,A) & r1_tarski(D,B) & r1_tarski(E,C) & -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C) & v4_pre_topc(F,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C))))) & k4_subset_1(u1_struct_0(A),D,E) != k4_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(E,A))))))))))))) # label(t66_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2831 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,D) & r2_tsep_1(A,C,D) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t58_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2832 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,C),k6_subset_1(u1_struct_0(A),C,B)) <-> r2_tsep_1(A,B,C)))))))) # label(d7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2833 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) & D = E & r1_tarski(C,u1_struct_0(B)) & v3_pre_topc(C,A) -> (v3_pre_topc(E,B) <-> v3_pre_topc(D,A))))))))))))) # label(t9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2834 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (A = k1_tsep_1(A,B,C) & r3_tsep_1(A,B,C) -> m1_pre_topc(B,A) & v1_tsep_1(B,A)))))))) # label(t74_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2835 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (r1_xboole_0(D,C) & r1_xboole_0(E,B) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(C,E) & r1_tarski(B,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))) <-> r1_connsp_1(A,B,C)))))))) # label(t48_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2836 $T # label(t26_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2837 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) <-> m1_pre_topc(B,C)))))))) # label(t4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2838 $T # label(d6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2839 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (v1_pre_topc(D) & m1_pre_topc(D,A) & -v3_struct_0(D) -> (k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D) <-> D = k1_tsep_1(A,B,C)))))))))) # label(d2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2840 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v4_pre_topc(C,A) <-> v4_pre_topc(D,B))))))))))) # label(t12_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2841 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) -> (r1_tsep_1(A,B,C) -> r1_tsep_1(A,C,B)))) # label(symmetry_r1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2842 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,B) -> m1_pre_topc(C,A))))))) # label(t7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.09 2843 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(C,B) & m1_pre_topc(B,C) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))))) # label(t6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2844 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_tsep_1(A,B,C) & -r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & -(-r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E)) & (all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A))))) & v3_pre_topc(D,A)))))) & -r1_tarski(B,C)))))))) # label(t64_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2845 (all A all B all C (m1_pre_topc(C,A) & m1_pre_topc(B,A) & l1_pre_topc(A) -> (r3_tsep_1(A,B,C) -> r3_tsep_1(A,C,B)))) # label(symmetry_r3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2846 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,B,D) & r3_tsep_1(A,C,D) <-> r3_tsep_1(A,k1_tsep_1(A,B,C),D)))))))))) # label(t79_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2847 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (m1_pre_topc(D,A) & (exists E (v1_tsep_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(C,E) & -v3_struct_0(E))) & v1_tsep_1(D,A) & -v3_struct_0(D))) <-> r3_tsep_1(A,B,C)))))))) # label(t83_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2848 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (k1_tsep_1(A,B,C) = A -> r1_tsep_1(A,B,C) | (-(-m1_pre_topc(B,C) & (all D (m1_pre_topc(D,A) & v1_borsuk_1(D,A) & -v3_struct_0(D) -> (all E (m1_pre_topc(E,A) & v1_borsuk_1(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(D,B) & m1_pre_topc(E,C) & -((all F (-v3_struct_0(F) & v1_tsep_1(F,A) & m1_pre_topc(F,A) -> -(m1_pre_topc(F,k2_tsep_1(A,B,C)) & k1_tsep_1(A,k1_tsep_1(A,D,E),F) = A))) & A != k1_tsep_1(A,D,E))))))) & -m1_pre_topc(C,B)) <-> r4_tsep_1(A,B,C))))))))) # label(t94_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2849 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r4_tsep_1(A,B,C) & r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t85_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2850 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) & -r1_tarski(C,B) & (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,B) & -(k4_subset_1(u1_struct_0(A),D,E) != k4_subset_1(u1_struct_0(A),B,C) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C) & v3_pre_topc(F,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)))))) & r1_tarski(E,C) & v4_pre_topc(E,A) & v4_pre_topc(D,A)))))) & -r1_tarski(B,C) & r2_tsep_1(A,B,C)))))))) # label(t62_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2851 $T # label(t27_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2852 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,B,C) -> k1_tsep_1(A,D,k2_tsep_1(A,B,C)) = k2_tsep_1(A,k1_tsep_1(A,D,B),k1_tsep_1(A,D,C)) & k2_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D)) = k1_tsep_1(A,k2_tsep_1(A,B,C),D)))))))))) # label(t36_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2853 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D ((exists E (r2_tsep_1(A,D,E) & r1_tarski(C,E) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(B,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r1_connsp_1(A,B,C)))))))) # label(t67_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2854 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C (v1_pre_topc(C) & m1_pre_topc(C,A) & B = u1_struct_0(C) & -v3_struct_0(C))))))) # label(t10_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2855 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & v3_pre_topc(F,A) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B))))))) <-> r2_tsep_1(A,B,C)))))))) # label(t59_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2856 $T # label(t37_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2857 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(C,E) & r1_tarski(B,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))))) <-> r1_connsp_1(A,B,C)))))))) # label(t49_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2858 (all A (v1_pre_topc(A) & l1_pre_topc(A) -> k3_pre_topc(A,k2_pre_topc(A)) = A)) # label(t3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2859 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_pre_topc(B,C) & v1_tsep_1(B,C)))))))) # label(t19_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2860 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) -> r1_tsep_1(A,B,C)))))))) # label(t68_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2861 (all A all B all C (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,C,B)))) # label(symmetry_r2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2862 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (m1_pre_topc(C,A) & v1_tsep_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v3_pre_topc(B,A)))))) # label(t20_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2863 $T # label(t69_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2864 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> v1_borsuk_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A))))))) # label(t24_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2865 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> r1_tarski(k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)),k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B)))))))))) # label(t5_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2866 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(B,A) & v1_tops_3(B,A)))))) # label(t37_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2867 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (u1_struct_0(A) = u1_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(B),D) <-> D = C)))))))))) # label(t71_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2868 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) & v1_tops_3(B,A) -> v1_tops_3(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t48_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2869 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> v3_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t39_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2870 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v2_tops_1(D,B) <-> v2_tops_1(C,A))))))))))) # label(t67_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2871 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> (exists C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(C,B) & v3_pre_topc(C,A) & v1_tops_1(C,A)))))))) # label(t41_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2872 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (D = E & r1_tarski(D,C) & r1_tarski(C,u1_struct_0(B)) & v3_pre_topc(C,A) -> k1_tops_1(A,D) = k1_tops_1(B,E)))))))))))) # label(t57_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2873 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(C,A) | v1_tops_3(B,A) -> v1_tops_3(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t43_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2874 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k1_tops_1(A,C) = k1_tops_1(B,D)))))) & u1_struct_0(B) = u1_struct_0(A) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))) # label(t74_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2875 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> k1_tops_1(B,D) = k1_tops_1(A,C)))))))))) # label(t77_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2876 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (u1_struct_0(B) = u1_struct_0(A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k6_pre_topc(A,C) = k6_pre_topc(B,D)))))) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))))) # label(t75_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2877 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = k6_pre_topc(A,k1_tops_1(A,B)) <-> v1_tops_3(B,A)))))) # label(d5_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2878 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,C) & D != k1_xboole_0 & v3_pre_topc(D,A) & r1_xboole_0(B,D)))) & C != k1_xboole_0)))))))) # label(t28_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2879 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,C) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B))))) <-> v1_tops_1(B,A)))))) # label(t20_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2880 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_1(B,A) & B = k1_xboole_0))))) # label(t17_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2881 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> v2_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t18_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2882 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(D,A) & r1_xboole_0(C,D) & k4_subset_1(u1_struct_0(A),C,D) = B & v1_tops_1(C,A) & v3_pre_topc(C,A)))))) & v1_tops_3(B,A)))))) # label(t49_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2883 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(C,A) & v1_tops_3(D,A) & B = k5_subset_1(u1_struct_0(A),C,D) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D) & v4_pre_topc(C,A))))))))))) # label(t51_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2884 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(B,A) & u1_struct_0(A) = B))))) # label(t23_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2885 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (u1_struct_0(A) = u1_struct_0(B) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v4_pre_topc(C,A) <-> v4_pre_topc(D,B))))))) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))))) # label(t73_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2886 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = u1_struct_0(A) -> k1_xboole_0 = k3_subset_1(u1_struct_0(A),B)) & (k3_subset_1(u1_struct_0(A),B) = k1_xboole_0 -> u1_struct_0(A) = B) & (k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),B) -> k2_pre_topc(A) = B) & (B = k2_pre_topc(A) -> k3_subset_1(u1_struct_0(A),B) = k1_pre_topc(A)))))) # label(t2_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2887 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & r1_tarski(C,D) -> r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D))))))))))) # label(t78_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2888 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B))) = u1_struct_0(A) -> u1_struct_0(A) = k6_pre_topc(A,k1_tops_1(A,B))))))) # label(t8_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2889 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) & v3_tops_1(D,B) -> v3_tops_1(C,A)))))))))) # label(t68_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2890 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v2_tops_1(B,A) -> v2_tops_1(C,A)))))))) # label(t11_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2891 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v1_tops_3(B,A) -> v1_tops_3(C,A)))))))) # label(t38_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2892 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B = u1_struct_0(A) & v2_tops_1(B,A)))))) # label(t10_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2893 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v1_tops_1(C,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t45_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2894 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) & E = D & v3_tops_1(D,A) & r1_tarski(D,C) -> v3_tops_1(E,B)))))))))))) # label(t69_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2895 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & E = D & r1_tarski(D,C) & r1_tarski(C,u1_struct_0(B)) -> (v1_tops_3(D,A) <-> v1_tops_1(C,A) & v1_tops_3(E,B))))))))))))) # label(t62_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2896 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> (exists C (r1_tarski(B,C) & v2_tops_1(C,A) & v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t27_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2897 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k6_pre_topc(A,B) = u1_struct_0(A) <-> v1_tops_1(B,A)))))) # label(d2_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2898 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> r1_tarski(k6_pre_topc(A,C),k6_pre_topc(B,D))))))))))) # label(t81_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2899 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) & v1_tops_1(C,A) -> v1_tops_1(D,B)))))))))) # label(t59_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2900 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k1_tops_1(A,B),A) <-> v1_tops_3(B,A)))))) # label(t35_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2901 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v3_tops_1(B,A) -> v3_tops_1(C,A)))))))) # label(t26_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2902 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k6_pre_topc(A,C) = k6_pre_topc(B,D)))))))))) # label(t55_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2903 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B)))))))))) # label(t6_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2904 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v3_tops_1(k1_pre_topc(A),A))) # label(t22_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2905 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v3_tops_1(k6_pre_topc(A,B),A)))))) # label(t24_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2906 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v3_pre_topc(B,A) -> v1_tops_3(B,A)))))) # label(t36_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2907 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & E = D & r1_tarski(D,C) -> (v1_tops_3(D,A) <-> v1_tops_3(C,A) & v1_tops_3(E,B))))))))))))) # label(t64_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2908 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(C,A) | v2_tops_1(B,A) -> v2_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t15_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2909 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(t16_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2910 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) -> v1_tops_3(k1_tops_1(A,B),A)))))) # label(t32_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2911 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_tops_1(C,A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & r1_tarski(D,C) -> v2_tops_1(D,B)))))))))) # label(t82_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2912 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_tops_3(k2_pre_topc(A),A))) # label(t31_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2913 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) | v3_tops_1(B,A) -> v3_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2914 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k1_tops_1(A,C))))))))) # label(t4_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2915 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,k1_tops_1(A,k6_pre_topc(A,B))) -> k1_xboole_0 = k1_tops_1(A,k6_pre_topc(A,B))))))) # label(t7_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2916 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(C,A) & E = D & r1_tarski(D,C) & r1_tarski(C,u1_struct_0(B)) -> k6_pre_topc(A,D) = k6_pre_topc(B,E)))))))))))) # label(t54_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2917 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> k6_pre_topc(A,k1_tops_1(A,B)) = k2_pre_topc(A)))))) # label(d4_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2918 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (E = C & D = u1_struct_0(B) -> (v1_tops_1(D,A) & v1_tops_3(E,B) <-> v1_tops_3(C,A))))))))))))) # label(t63_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2919 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,D) -> r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D))))))))))) # label(t56_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2920 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) -> r1_tarski(k6_pre_topc(B,D),k6_pre_topc(A,C))))))))))) # label(t53_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2921 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v3_tops_1(C,A) <-> v3_tops_1(D,B))))))))))) # label(t70_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2922 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(D != u1_struct_0(A) & v4_pre_topc(D,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,D) & r1_tarski(C,D)))) & v4_pre_topc(C,A) & C != u1_struct_0(A))))))))) # label(t42_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2923 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(C,A) & v1_tops_3(B,A) -> v1_tops_3(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t44_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2924 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) -> v1_tops_1(B,A)))))) # label(t33_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2925 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v2_tops_1(C,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t30_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2926 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v3_pre_topc(D,B) <-> v3_pre_topc(C,A))))))) & u1_struct_0(A) = u1_struct_0(B) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))) # label(t72_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2927 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(C,A) | v1_tops_1(B,A) -> v1_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t21_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2928 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(C,A) & v1_tops_1(D,A) & B = k5_subset_1(u1_struct_0(A),C,k4_subset_1(u1_struct_0(A),B,D)) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D) & r1_xboole_0(C,D) & v3_pre_topc(D,A) & v4_pre_topc(C,A)))))) & v3_tops_1(B,A)))))) # label(t52_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2929 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B = k1_xboole_0 & v1_tops_3(B,A)))))) # label(t34_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2930 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & r1_tarski(D,C) & v2_tops_1(D,A) & D = E & r1_tarski(C,u1_struct_0(B)) -> v2_tops_1(E,B)))))))))))) # label(t66_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2931 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_tops_1(A,k6_pre_topc(A,B)) = k1_xboole_0 <-> v3_tops_1(B,A)))))) # label(d3_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2932 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> k1_tops_1(A,B) = k1_xboole_0))))) # label(d1_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2933 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_xboole_0 -> k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A)) & (k3_subset_1(u1_struct_0(A),B) = u1_struct_0(A) -> B = k1_xboole_0) & (k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),B) -> B = k1_pre_topc(A)) & (k1_pre_topc(A) = B -> k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),B)))))) # label(t1_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2934 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (D = E & r1_tarski(D,C) & r1_tarski(C,u1_struct_0(B)) -> (v1_tops_1(D,A) <-> v1_tops_1(C,A) & v1_tops_1(E,B))))))))))))) # label(t60_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2935 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v2_tops_1(k1_pre_topc(A),A))) # label(t9_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2936 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_1(C,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D) & r1_xboole_0(C,D) & B = k4_subset_1(u1_struct_0(A),C,k5_subset_1(u1_struct_0(A),B,D)) & v2_tops_1(D,A) & v4_pre_topc(D,A) & v3_pre_topc(C,A)))))) & v1_tops_3(B,A)))))) # label(t50_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2937 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))))))))) # label(t3_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2938 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v3_tops_1(C,A) -> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t46_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2939 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & v3_tops_1(C,A) & r1_tarski(D,C) -> v3_tops_1(D,B)))))))))) # label(t84_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2940 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & C = D -> k6_pre_topc(A,C) = k6_pre_topc(B,D)))))))))) # label(t80_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2941 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C & v4_pre_topc(C,A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v4_pre_topc(D,B)))))))))) # label(t79_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2942 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_tops_3(C,A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & r1_tarski(C,D) -> v1_tops_3(D,B)))))))))) # label(t85_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2943 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != k1_xboole_0 & v3_pre_topc(C,A) & r1_xboole_0(k3_subset_1(u1_struct_0(A),B),C))))))))) # label(t13_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2944 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(C,A) & v1_tops_3(B,A) -> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t47_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2945 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v4_pre_topc(C,A) -> u1_struct_0(A) = C))) <-> v1_tops_1(B,A)))))) # label(t19_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2946 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) = k1_tops_1(A,C))))))))) # label(t14_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2947 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_tops_1(D,B) & r1_tarski(C,D) -> v2_tops_1(C,A)))))))))) # label(t65_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2948 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v3_pre_topc(C,A) & C = D -> v3_pre_topc(D,B)))))))))) # label(t76_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2949 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(B,A) & v1_tops_1(B,A)))))) # label(t25_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2950 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tops_1(C,A) & r1_tarski(C,D) -> v1_tops_1(D,B)))))))))) # label(t83_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2951 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(k3_subset_1(u1_struct_0(A),B),A) <-> v3_tops_1(B,A)))))) # label(t40_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2952 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k1_tops_1(B,D) = k1_tops_1(A,C)))))))))) # label(t58_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2953 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & r1_tarski(k3_subset_1(u1_struct_0(A),B),C) -> u1_struct_0(A) = C))) <-> v2_tops_1(B,A)))))) # label(t12_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2954 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_tops_3(C,A) & r1_tarski(C,D) -> v1_tops_3(D,B)))))))))) # label(t61_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2955 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) <-> -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t49_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2956 (all A (l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (exists B (v2_tex_2(B,A) & v3_realset2(B) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc13_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2957 (all A all B all C (v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v3_tdlat_3(B) & -v3_struct_0(B) -> ((exists D (A = k6_pre_topc(B,k1_struct_0(B,D)) & r2_hidden(D,C) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_tex_2(B,C))))) # label(fraenkel_a_2_0_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2958 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k5_subset_1(u1_struct_0(A),B,D) = C & v4_pre_topc(D,A))))))) <-> v3_tex_2(B,A)))))) # label(d6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2959 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)) & v1_realset1(B) & -v1_xboole_0(B))))) # label(rc6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2960 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(rc10_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2961 (all A (-v1_xboole_0(A) & v1_realset1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_tex_2(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> v1_realset1(B) & -v1_tex_2(B,k1_zfmisc_1(A)) & -v1_xboole_0(B)))))) # label(cc5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2962 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A)))))) # label(rc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2963 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_borsuk_1(B,A) -> v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc30_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2964 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((all C (v1_tdlat_3(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (m1_pre_topc(B,C) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))) & v1_tdlat_3(B) <-> v5_tex_2(B,A)))))) # label(t52_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2965 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v5_tex_2(B,A) -> -v3_struct_0(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc37_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2966 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k3_tarski(a_2_0_tex_2(A,B)))))) # label(t54_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2967 (all A (l1_pre_topc(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) & -v3_struct_0(B) -> v3_realset2(B) & -v3_struct_0(B)))))) # label(cc13_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2968 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C & v4_tex_2(C,A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v4_tex_2(D,B)))))))))) # label(t45_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2969 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(C,A) | v3_tex_2(B,A) -> v3_tex_2(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2970 (all A (-v1_xboole_0(A) -> (exists B (v1_realset1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2971 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v3_tex_2(B,A) -> v3_pre_topc(B,A)))))) # label(t40_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2972 (all A (l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_tex_2(B,A) -> -v3_struct_0(B) & -v3_realset2(B)))))) # label(cc15_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2973 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_pre_topc(k1_tex_2(A,B),A) & v1_pre_topc(k1_tex_2(A,B)) & -v3_struct_0(k1_tex_2(A,B)))) # label(dt_k1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2974 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_tex_2(B,A))))) # label(t35_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2975 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))) <-> v2_tex_2(B,A))))))))) # label(t13_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2976 (all A (v2_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v3_realset2(B) -> -v3_struct_0(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & -v5_tex_2(B,A) & v5_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc44_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2977 (all A (v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_xboole_0(B) -> -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A))))))) # label(cc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2978 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C))) | k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,B)))))))) # label(t56_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2979 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_tex_2(B,A))))) # label(t43_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2980 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_tex_2(B,k1_zfmisc_1(A)) -> -v1_xboole_0(B)))))) # label(cc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2981 (all A (-v3_realset2(A) & l1_struct_0(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc8_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2982 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) & v2_tex_2(B,A) -> v2_tex_2(C,A)))))))) # label(t14_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2983 (all A (-v3_struct_0(A) & l1_struct_0(A) & -v3_realset2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -v1_realset1(B) & -v1_xboole_0(B)))))) # label(cc11_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2984 $T # label(t10_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2985 (all A (-v3_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v5_tex_2(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & -v5_tex_2(B,A) & -v3_realset2(B) & v4_tdlat_3(B) & -v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc46_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2986 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (-v3_struct_0(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) -> r1_borsuk_1(A,B))))) # label(t79_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2987 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v5_tex_2(B,A) -> v2_pre_topc(B) & v1_borsuk_1(B,A) & v2_tex_2(B,A) & v3_tdlat_3(B) & v1_tdlat_3(B) & v1_tsep_1(B,A)))))) # label(cc42_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2988 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & k1_tarski(C) = k5_subset_1(u1_struct_0(A),B,D)))))))))))) # label(t32_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.10 2989 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C)))) & r2_hidden(C,B))))))))) # label(t33_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2990 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) -> v3_tdlat_3(B)))))) # label(cc22_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2991 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_tex_2(B,k1_zfmisc_1(A)) <-> B != A))) # label(t5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2992 (all A exists B (-v1_tex_2(B,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2993 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_realset2(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_realset2(B) -> -v3_struct_0(B) & v2_tex_2(B,A)))))) # label(cc14_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2994 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v3_tex_2(B,A) -> v4_tex_2(B,A)))))) # label(t48_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2995 (all A (v2_pre_topc(A) & -v1_tdlat_3(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) & -v3_struct_0(B) -> v2_pre_topc(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc47_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2996 (all A (-v1_xboole_0(A) & -v1_realset1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_realset1(B) & -v1_xboole_0(B) -> v1_tex_2(B,k1_zfmisc_1(A)) & -v1_xboole_0(B)))))) # label(cc6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2997 (all A (-v3_struct_0(A) & l1_struct_0(A) & -v3_realset2(A) -> (exists B (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc9_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2998 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v4_tex_2(B,A) & (all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) -> -(B = u1_struct_0(C) & v5_tex_2(C,A))))))))) # label(t53_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 2999 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) & v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_tex_2(B,A) & v3_tex_2(C,A) & v3_pre_topc(B,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t30_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3000 (all A (v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_pre_topc(B) & -v1_tdlat_3(B) & v2_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & -v3_realset2(B) & v3_tdlat_3(B)))))) # label(cc34_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3001 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc28_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3002 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) -> -v3_struct_0(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)) & v2_pre_topc(k1_tex_2(A,B)) & v1_tdlat_3(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & v5_tdlat_3(k1_tex_2(A,B)) & v4_tdlat_3(k1_tex_2(A,B)) & v3_tdlat_3(k1_tex_2(A,B)))) # label(fc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3003 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tex_2(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & v4_tex_2(C,A))))))))) # label(t65_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3004 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> -(v2_tex_2(B,A) & u1_struct_0(A) = u1_struct_0(B)))))) # label(t15_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3005 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_realset2(B) & v2_pre_topc(B) -> v4_tdlat_3(B) & v3_realset2(B) & v5_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc27_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3006 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = C))))))))))) # label(d5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3007 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))) # label(fc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3008 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) -> v2_pre_topc(B)))))) # label(cc17_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3009 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v4_tex_2(C,A) <-> v5_tex_2(B,A))))))))) # label(t51_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3010 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k1_struct_0(A,C) = k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C)))))) -> v3_tex_2(B,A)))))) # label(t58_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3011 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v4_tex_2(B,A) -> v1_tops_1(B,A)))))) # label(t47_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3012 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> C = D | r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,D)))))))) <-> v3_tex_2(B,A)))))) # label(t59_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3013 (all A (v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (exists C (v1_funct_1(C) & v5_pre_topc(C,A,B) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)))))))) # label(t72_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3014 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v3_tdlat_3(B) & v5_tex_2(B,A) & v1_tdlat_3(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc41_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3015 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> v2_pre_topc(B) & v3_tdlat_3(B) & -v5_tex_2(B,A) & v1_tdlat_3(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A)))))) # label(cc40_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3016 (all A (-v1_xboole_0(A) -> (all B (v1_realset1(B) & -v1_xboole_0(B) -> (r1_tarski(A,B) -> A = B))))) # label(t1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3017 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all 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))))))) # label(t68_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3018 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = u1_struct_0(A) -> (v3_tex_2(B,A) <-> v1_tdlat_3(A))))))) # label(t27_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3019 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) -> -v3_struct_0(k1_tex_2(A,B)) & v4_tdlat_3(k1_tex_2(A,B)) & v5_tdlat_3(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & v3_tdlat_3(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B)) & v1_tdlat_3(k1_tex_2(A,B)) & v2_pre_topc(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)))) # label(fc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3020 (all A (v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_tex_2(B,k1_zfmisc_1(A)) -> v3_membered(B) & v4_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) & v5_membered(B) & v2_membered(B) & v1_membered(B) & v1_xboole_0(B)))))) # label(cc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3021 (all A (-v1_xboole_0(A) & v1_realset1(A) -> (all B (-v1_xboole_0(k3_xboole_0(A,B)) -> r1_tarski(A,B))))) # label(t2_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3022 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tsep_1(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc29_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3023 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_pre_topc(B) -> -v1_tdlat_3(B)))))) # label(cc18_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3024 (all A (l1_struct_0(A) & -v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t9_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3025 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v5_tex_2(B,A) & -v3_struct_0(B) -> (all C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_borsuk_1(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (E = D -> k6_pre_topc(A,E) = k5_pre_topc(A,B,C,D))))))))))))) # label(t76_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3026 (all A (-v1_xboole_0(A) & -v1_realset1(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_realset1(B) & -v1_tex_2(B,k1_zfmisc_1(A)))))) # label(rc7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3027 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v1_pre_topc(B))))) # label(rc16_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3028 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_xboole_0(B) -> v1_tex_2(B,k1_zfmisc_1(A))))))) # label(cc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3029 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> ((all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> v5_pre_topc(C,A,B))))) -> v1_tdlat_3(A)))) # label(t69_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3030 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r2_hidden(D,B) & k1_struct_0(A,D) = k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) & m1_subset_1(D,u1_struct_0(A)))))) <-> v4_tex_2(B,A)))))) # label(t64_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3031 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_tdlat_3(B) -> -v1_tdlat_3(B)))))) # label(cc21_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3032 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> -(v1_realset1(A) & v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A))))))) # label(t6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3033 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_tdlat_3(B) -> -v2_tdlat_3(B)))))) # label(cc23_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3034 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))))))))))) # label(d3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3035 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) -> v3_tdlat_3(B)))))) # label(cc20_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3036 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) & v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_tex_2(C,A) & v3_tex_2(B,A) & v4_pre_topc(C,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t31_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3037 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) -> v5_pre_topc(C,B,A))))) -> v2_tdlat_3(A)))) # label(t71_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3038 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v2_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_realset2(B) & -v3_struct_0(B) -> v2_pre_topc(B) & v4_tdlat_3(B) & -v5_tex_2(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc50_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3039 (all A (-v1_xboole_0(A) & -v1_realset1(A) -> (all B (m1_subset_1(B,A) -> v1_tex_2(k6_domain_1(A,B),k1_zfmisc_1(A)))))) # label(t7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3040 (all A (v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> r1_borsuk_1(A,B))))) # label(t73_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3041 $T # label(t3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3042 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & v2_pre_topc(A) -> v2_pre_topc(B)))))) # label(t12_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3043 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & v2_tdlat_3(B) & -v3_struct_0(B) -> (all 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)) & v1_funct_1(C) -> v5_pre_topc(C,A,B))))))) # label(t70_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3044 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v1_tdlat_3(B) -> -v3_struct_0(B) & -v5_tex_2(B,A)))))) # label(cc38_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3045 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_pre_topc(B) -> -v2_tdlat_3(B)))))) # label(cc19_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3046 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) -> v1_tops_1(B,A)))))) # label(t62_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3047 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_tdlat_3(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v2_tdlat_3(B) & v2_pre_topc(B) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc14_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3048 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v1_tdlat_3(B) & -v3_realset2(B) -> -v2_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc26_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3049 $T # label(t11_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3050 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,k6_pre_topc(A,B)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(k1_struct_0(A,D) = k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) & r2_hidden(D,B)))))))))))) # label(t60_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3051 (all A all B (m1_subset_1(B,A) -> (v1_tex_2(B,A) <-> B != k3_tarski(A)))) # label(d2_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3052 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tex_2(B,A) & (all C (v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tdlat_3(C) & -v3_struct_0(C) -> B != u1_struct_0(C)))))))) # label(t34_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3053 (all A (-v3_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v3_tex_2(B,A) <-> v1_realset1(B)))))) # label(t44_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3054 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (v2_tdlat_3(A) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v2_tdlat_3(B)))))) # label(t18_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3055 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_tex_2(B,A) & v3_tex_2(C,A) & v4_pre_topc(C,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t39_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3056 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (exists B (v3_tdlat_3(B) & v5_tdlat_3(B) & v2_tex_2(B,A) & v4_tdlat_3(B) & v2_pre_topc(B) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc19_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3057 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (u1_struct_0(A) = u1_struct_0(B) & v3_realset2(A) -> v3_realset2(B)))))) # label(t4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3058 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v5_tex_2(B,A) & -v3_struct_0(B) -> (exists C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)))))))) # label(t74_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3059 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) -> v2_pre_topc(B)))))) # label(cc16_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3060 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v3_tex_2(k1_struct_0(A,B),A))))) # label(t36_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3061 (all A (-v1_xboole_0(A) -> (exists B (v1_tex_2(B,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3062 (all A (-v1_xboole_0(A) -> (v1_realset1(A) <-> (exists B (m1_subset_1(B,A) & k6_domain_1(A,B) = A))))) # label(d1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3063 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & v3_tex_2(C,A) -> B = C))) & v3_tex_2(B,A) <-> v4_tex_2(B,A)))))) # label(d7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3064 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tdlat_3(B) -> v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v1_tsep_1(B,A) & -v3_struct_0(B)))))) # label(cc31_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3065 (all A (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2))) -> -((all B (m1_subset_1(B,u1_struct_0(f1_s1_tex_2)) -> -p1_s1_tex_2(A,B))) & r2_hidden(A,f2_s1_tex_2)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2)) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_tex_2))) -> (r2_hidden(B,f2_s1_tex_2) -> p1_s1_tex_2(B,k1_funct_1(A,B))))) & m2_relset_1(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2)))) # label(s1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3066 (all A (-v3_struct_0(A) & l1_struct_0(A) & v3_realset2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(B) & v1_realset1(B)))))) # label(cc9_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3067 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v3_realset2(B) & v1_pre_topc(B))))) # label(rc12_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3068 (all A (-v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) -> (exists B (-v1_tsep_1(B,A) & v3_tdlat_3(B) & v2_tex_2(B,A) & v2_tdlat_3(B) & -v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc18_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3069 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v2_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_realset2(B) -> -v3_struct_0(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v5_tex_2(B,A) & v3_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc45_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3070 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)) = C))) <-> v3_tex_2(B,A)))))) # label(t41_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3071 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) & v2_tdlat_3(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_realset2(B)))))) # label(cc24_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3072 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))) -> k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C))))))))) # label(t55_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3073 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & v2_tdlat_3(B) & -v3_struct_0(B) -> -v1_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc25_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3074 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) -> k3_tarski(a_2_0_tex_2(A,B)) = u1_struct_0(A)))))) # label(t63_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3075 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A)) -> -v1_realset1(B) & -v1_xboole_0(B)))))) # label(cc7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3076 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) & v3_tex_2(B,A) & v3_tex_2(C,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3077 (all A (-v3_realset2(A) & l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v1_tdlat_3(B) -> -v3_struct_0(B) & v1_tdlat_3(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v3_realset2(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & v4_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc36_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3078 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_realset2(A)))))) # label(t8_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3079 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v3_realset2(B) & m1_pre_topc(B,A) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(k1_tex_2(A,C)),u1_pre_topc(k1_tex_2(A,C))))))))) # label(t23_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3080 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) & v2_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & -v1_tsep_1(B,A) & -v1_borsuk_1(B,A) & v2_tdlat_3(B) & v4_tdlat_3(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc35_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3081 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C) & v3_pre_topc(D,A))))))) -> v3_tex_2(B,A)))))) # label(t37_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3082 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v1_tdlat_3(B) -> v1_tdlat_3(B) & v2_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc33_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3083 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v5_tex_2(B,A) -> -v3_struct_0(B) & v2_pre_topc(B) & v5_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_tdlat_3(B)))))) # label(cc43_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3084 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v4_tex_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t66_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3085 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & -v2_tex_2(B,A) & v1_pre_topc(B))))) # label(rc11_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3086 (all A (v2_pre_topc(A) & -v2_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) & -v3_struct_0(B) -> v2_pre_topc(B) & v5_tdlat_3(B) & -v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc49_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3087 (all A (-v3_struct_0(A) & l1_struct_0(A) & -v3_realset2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) & v1_realset1(B) -> v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B)))))) # label(cc10_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3088 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v1_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v3_tdlat_3(B) & v5_tdlat_3(B) & -v3_realset2(B) & v4_tdlat_3(B) & -v2_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc32_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.11 3089 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) & -v3_struct_0(B) -> v2_pre_topc(B) & v3_tdlat_3(B) & -v5_tex_2(B,A) & v5_tdlat_3(B) & v4_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc48_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3090 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v1_realset1(B) <-> v4_tex_2(B,A)))))) # label(t50_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3091 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_struct_0(A,C))) = k1_struct_0(A,C))))))))) # label(t42_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3092 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = k1_struct_0(A,C))))))) -> v3_tex_2(B,A)))))) # label(t57_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3093 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v2_tex_2(k1_tex_2(A,B),A) <-> v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t20_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3094 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v2_tex_2(B,A) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))))) # label(t16_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3095 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_tdlat_3(B) -> (exists C (v1_pre_topc(C) & m1_pre_topc(C,A) & m1_pre_topc(B,C) & v5_tex_2(C,A) & -v3_struct_0(C))))))) # label(t67_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3096 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (v3_tdlat_3(A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v3_tdlat_3(B)))))) # label(t19_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3097 (all A (v3_realset2(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & -v2_tex_2(B,A)))))) # label(cc12_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3098 (all A (v3_realset2(A) & l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) -> -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(cc8_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3099 (exists A (v1_realset1(A) & -v1_xboole_0(A))) # label(rc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3100 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v2_tex_2(B,A) & v3_tdlat_3(B) & v1_tsep_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc17_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3101 $T # label(t22_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3102 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_pre_topc(B) & v5_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & v1_tdlat_3(B) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc15_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3103 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v2_tex_2(k1_tex_2(A,B),A) & v3_realset2(A)))))) # label(t21_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3104 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v2_pre_topc(k1_tex_2(A,B)) -> v1_tdlat_3(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B))))))) # label(t24_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3105 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) & r1_tarski(C,B) -> v3_tex_2(C,A)))))))) # label(t28_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3106 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> v1_pre_topc(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & -v3_struct_0(k1_tex_2(A,B)))) # label(fc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3107 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v4_tex_2(C,A))))))))) # label(d8_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3108 (all A (v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v5_tex_2(B,A) -> (all C (v1_funct_1(C) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_borsuk_1(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (E = D -> k5_pre_topc(A,B,C,k1_struct_0(B,D)) = k6_pre_topc(A,k1_struct_0(A,E)))))))))))))) # label(t77_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3109 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) -> -v4_tex_2(B,A))))) # label(t46_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3110 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v1_tdlat_3(B) <-> v3_tex_2(C,A))))))))) # label(t26_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3111 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((v3_pre_topc(B,A) | v4_pre_topc(B,A)) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v4_tex_2(B,A)))))) # label(t61_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3112 (all A (v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tdlat_3(B) & -v3_struct_0(B) -> (exists C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & v5_pre_topc(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))))))) # label(t78_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3113 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tdlat_3(A) -> v1_tdlat_3(B)))))) # label(t17_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3114 (all A (-v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) -> v2_pre_topc(B) & v1_tdlat_3(B) & -v2_tex_2(B,A) & v3_tdlat_3(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A)))))) # label(cc39_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3115 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_tex_2(B,A) & m1_pre_topc(B,A) -> r1_borsuk_1(A,B))))) # label(t75_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3116 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v5_tex_2(B,A) & v4_tdlat_3(B))))) # label(rc20_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3117 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_pre_topc(C) -> (k1_tex_2(A,B) = C <-> u1_struct_0(C) = k1_struct_0(A,B)))))))) # label(d4_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3118 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & v3_tex_2(C,A) & D = C -> v3_tex_2(D,B)))))))))) # label(t25_tex_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3119 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tex_3(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> v1_tex_3(C,A)))))))) # label(t12_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3120 (all A (l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_pre_topc(B) & -v1_borsuk_1(B,A) & v2_tex_2(B,A) & v1_tex_3(B,A) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & v2_tex_3(B,A) & v1_tsep_1(B,A) & v1_pre_topc(B))))) # label(rc13_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3121 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v4_tex_3(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v2_tex_2(C,A) & v1_tex_3(C,A) & (exists D (-v3_struct_0(D) & v1_borsuk_1(D,A) & v3_tex_3(D,A) & m1_pre_topc(B,D) & r4_tsep_2(A,C,D) & m1_pre_topc(D,A) & v1_pre_topc(D))) & m1_pre_topc(C,A) & v1_tsep_1(C,A) & v1_pre_topc(C))))))) # label(t74_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3122 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -(v3_tdlat_3(A) & (exists B (v2_tex_3(B,A) & v2_tex_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B)))))) # label(t60_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3123 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_pre_topc(B,A) -> -v3_tex_3(B,A))) -> v1_tdlat_3(A)))) # label(t47_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3124 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> -((v4_tex_3(C,A) | v4_tex_3(B,A)) & -v4_tex_3(k2_tsep_1(A,B,C),A) & -r1_tsep_1(A,B,C)))))))) # label(t46_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3125 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> v3_tdlat_3(B) & v4_tdlat_3(B) & -v4_tex_3(B,A) & v5_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc25_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3126 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) & v1_borsuk_1(B,A) -> -v2_tex_3(B,A) & v3_tex_3(B,A) & v4_tex_3(B,A) & -v1_tex_3(B,A) & v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc19_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3127 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v2_tex_2(B,A) -> -v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc3_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3128 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tops_3(C,A) <-> v2_tex_3(B,A))))))))) # label(t16_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3129 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v2_pre_topc(B) & v2_tex_3(B,A) & v1_tex_3(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc2_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3130 (all A (l1_pre_topc(A) & -v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v2_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & v1_pre_topc(C) -> B != u1_struct_0(C))) & v1_tops_1(B,A)))))) # label(t52_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3131 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v1_tops_3(C,A) <-> v3_tops_1(B,A))))))))) # label(t5_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3132 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r3_tsep_2(A,B,C) -> (v3_tex_3(C,A) <-> v1_tex_3(B,A))))))))) # label(t31_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3133 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) <-> (exists C (v1_pre_topc(C) & v1_tsep_1(C,A) & m1_pre_topc(C,B) & m1_pre_topc(C,A) & v1_tex_3(C,A)))))))) # label(t24_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3134 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v1_tops_1(B,A) <-> v2_tops_1(C,A))))))))) # label(t2_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3135 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,B) & v1_tex_3(C,B) -> -v3_struct_0(C) & v1_tex_3(C,A) & m1_pre_topc(C,A))))))) # label(t14_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3136 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v4_tex_3(B,A) <-> v3_tops_1(C,A))))))))) # label(t35_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3137 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A)))))) # label(cc14_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3138 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -(v1_tdlat_3(A) & (exists B (-v3_struct_0(B) & v1_tex_3(B,A) & v2_tex_2(B,A) & m1_pre_topc(B,A)))))) # label(t50_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3139 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> -((v3_tex_3(B,A) | v3_tex_3(C,A)) & -v3_tex_3(k2_tsep_1(A,B,C),A) & -r1_tsep_1(A,B,C)))))))) # label(t43_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3140 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -((exists B (m1_pre_topc(B,A) & v4_tex_3(B,A) & -v3_struct_0(B))) & v3_tdlat_3(A)))) # label(t58_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3141 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -(v3_tdlat_3(A) & (exists B (v3_tex_3(B,A) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B)))))) # label(t59_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3142 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_tex_2(B,A) & m1_pre_topc(B,A) & v2_tex_3(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v4_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C))))))) # label(t65_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3143 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(C,B) & v4_tex_3(B,A) -> v4_tex_3(C,A)))))))) # label(t40_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3144 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> v2_tex_3(C,A)))))))) # label(t19_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3145 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) & v1_tex_3(B,A) -> v2_pre_topc(B) & -v1_borsuk_1(B,A) & v2_tex_2(B,A)))))) # label(cc2_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.11 3146 (all A (-v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v1_tsep_1(B,A) & v2_tex_2(B,A) & v3_tex_3(B,A) & v4_tex_3(B,A) & -v2_tex_3(B,A) & -v1_tex_3(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc10_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3147 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_pre_topc(B,A) -> -v4_tex_3(B,A))) -> v3_tdlat_3(A)))) # label(t56_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3148 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (-v1_xboole_0(B) <-> v1_tex_2(C,k1_zfmisc_1(u1_struct_0(A))))))))))) # label(t1_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3149 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,u1_struct_0(B)) -> v3_tops_1(C,A))))))))) # label(t39_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3150 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v3_tops_1(C,A)))) <-> v4_tex_3(B,A)))))) # label(d4_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3151 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v2_tops_1(B,A) <-> v1_tops_1(C,A))))))))) # label(t3_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3152 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v2_tex_3(B,A) & v2_tex_2(B,A) -> (exists C (v1_pre_topc(C) & v1_tsep_1(C,A) & v2_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & (exists D (v3_tex_3(D,A) & r3_tsep_2(A,C,D) & m1_pre_topc(C,B) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) & v1_pre_topc(D))))))))) # label(t75_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3153 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (v1_pre_topc(C) & m1_pre_topc(C,A) & v3_tex_3(C,A) -> u1_struct_0(C) != B)) & v2_tops_1(B,A)))))) # label(t51_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3154 (all A (v2_pre_topc(A) & -v3_realset2(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A))))) # label(rc9_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3155 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v1_tops_1(D,B) <-> v1_tops_1(C,A))))))))))) # label(t11_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3156 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_3(B,A) & v1_tex_3(B,A) -> v2_tex_2(B,A) & -v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc9_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3157 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_tsep_1(B,A) & v2_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (v1_pre_topc(C) & v1_borsuk_1(C,A) & v3_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & -v3_struct_0(C))))))) # label(t70_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3158 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v4_tex_3(B,A) & v3_tex_3(C,A) | v4_tex_3(C,A) & v3_tex_3(B,A) -> v3_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t45_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3159 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (v4_tex_3(B,A) & v4_tex_3(C,A) -> v4_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t44_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3160 (all A (l1_pre_topc(A) & -v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v3_tex_3(B,A) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v2_tex_2(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v1_tex_3(C,A))))))) # label(t53_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3161 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) -> -v2_tex_3(B,A) & -v1_tex_3(B,A) & v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc17_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3162 (all A (v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v4_tdlat_3(B) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B) & v1_tdlat_3(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B))))) # label(rc4_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3163 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (v4_tex_3(B,A) <-> (exists C (v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & m1_pre_topc(B,C) & v3_tex_3(C,A) & -v3_struct_0(C)))))))) # label(t71_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3164 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> v1_tex_3(B,A) & v2_tex_3(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & -v2_tex_2(B,A) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc27_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3165 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tops_1(B,A) & (all C (v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & v2_tex_2(C,A) -> B != u1_struct_0(C))) & v3_pre_topc(B,A)))))) # label(t68_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3166 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v4_tex_3(B,A) & v3_tex_3(B,A) -> v2_tex_2(B,A) & -v1_borsuk_1(B,A) & v2_pre_topc(B)))))) # label(cc20_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3167 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_tex_3(B,A) -> -v4_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc16_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3168 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v3_tex_3(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v2_tex_2(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v1_tex_3(C,A) & v1_tsep_1(C,A))))))) # label(t69_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3169 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(B,A) & (all C (v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> u1_struct_0(C) != B)) & v1_tops_1(B,A)))))) # label(t23_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3170 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(C,B) & v3_tex_3(B,A) -> v3_tex_3(C,A)))))))) # label(t34_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3171 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> ((all B (m1_pre_topc(B,A) & v2_tex_2(B,A) -> -v1_tex_3(B,A))) -> v1_tdlat_3(A)))) # label(t48_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3172 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_pre_topc(B) & v1_tex_3(B,A) & v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc1_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3173 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_3(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & v3_tex_3(B,A) & -v2_tex_3(B,A)))))) # label(cc15_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3174 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_3(B,A) -> v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc7_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3175 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v1_tex_3(B,A) <-> v1_tops_1(C,A))))))))) # label(t9_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3176 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_tex_2(B,A) & v2_tex_3(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v1_tex_3(B,A) & -v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc11_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3177 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,u1_struct_0(B)) -> v2_tops_1(C,A))))))))) # label(t33_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3178 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) -> v2_pre_topc(B) & -v4_tex_3(B,A)))))) # label(cc18_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3179 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) & -v3_struct_0(B) -> v2_pre_topc(B) & -v1_borsuk_1(B,A) & v4_tdlat_3(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc28_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3180 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tex_3(B,A) & v2_tex_3(B,A) & v1_tsep_1(B,A) & m1_pre_topc(B,A))))) # label(rc3_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3181 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc29_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3182 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v1_tsep_1(B,A) -> v1_tex_3(B,A) & v2_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc8_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3183 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v3_realset2(A) & l1_pre_topc(A) -> ((all B (v2_tex_2(B,A) & m1_pre_topc(B,A) -> -v2_tex_3(B,A))) -> v3_tdlat_3(A)))) # label(t57_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3184 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A)))))) # label(cc26_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3185 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (v2_tex_3(B,A) & m1_pre_topc(B,A) <-> v2_tex_3(C,A) & m1_pre_topc(C,A))))))))) # label(t22_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3186 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v2_tex_3(C,A) | v2_tex_3(B,A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v2_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t26_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3187 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_2(A,B,C) -> (v1_tops_3(B,A) <-> v3_tops_1(C,A))))))))) # label(t4_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3188 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r3_tsep_2(A,B,C) -> (v2_tex_3(B,A) <-> v4_tex_3(C,A))))))))) # label(t37_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3189 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_tex_3(B,A) -> v2_pre_topc(B) & -v1_tsep_1(B,A) & v2_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc12_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3190 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) & v1_tex_3(B,A) -> v2_pre_topc(B) & -v2_tex_2(B,A) & v1_tsep_1(B,A) & v1_borsuk_1(B,A)))))) # label(cc1_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3191 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v2_tex_3(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v1_tops_3(D,B) <-> v1_tops_3(C,A))))))))))) # label(t18_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3192 (all A (-v3_struct_0(A) & -v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_pre_topc(C) & v2_pre_topc(C) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = C -> (m1_pre_topc(B,A) & v3_tex_3(B,A) <-> m1_pre_topc(C,A) & v3_tex_3(C,A))))))))) # label(t55_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3193 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tops_1(B,A) & (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> -(u1_struct_0(C) = B & v4_tex_3(C,A))))))))) # label(t36_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3194 (all A (-v3_struct_0(A) & -v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & v3_tex_3(B,A) & -v1_tsep_1(B,A))))) # label(rc6_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3195 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v2_tops_1(C,A))))))))) # label(d3_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3196 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> (v2_tops_1(C,A) <-> v3_tex_3(B,A))))))))) # label(t29_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3197 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,B) & v2_tex_3(C,B) & -v3_struct_0(C) -> v2_tex_3(C,A) & m1_pre_topc(C,A))))))) # label(t21_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3198 (all A (v2_pre_topc(A) & v1_tdlat_3(A) & -v3_realset2(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v1_borsuk_1(B,A) & v3_tdlat_3(B) & -v2_tex_3(B,A) & -v1_tex_3(B,A) & -v5_tex_2(B,A) & v2_tex_2(B,A) & v1_tdlat_3(B) & v1_tsep_1(B,A) & v2_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3199 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v4_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v2_tex_2(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v2_tex_3(C,A))))))) # label(t64_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3200 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v1_tops_1(C,A)))) <-> v1_tex_3(B,A)))))) # label(d1_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3201 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (v1_tex_3(B,A) | v1_tex_3(C,A) -> v1_tex_3(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A)))))))) # label(t25_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3202 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (m1_pre_topc(B,C) -> m1_pre_topc(B,C) & v2_tex_3(B,C)))))))) # label(t20_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3203 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v2_tex_2(B,A) & -v5_tex_2(B,A) & -v2_tex_3(B,A) & -v1_tex_3(B,A) & v3_tdlat_3(B) & v1_tsep_1(B,A)))))) # label(cc23_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3204 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tex_2(B,A) & m1_pre_topc(B,A) & v1_tex_3(B,A) -> (exists C (-v3_struct_0(C) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & v3_tex_3(C,A) & v1_pre_topc(C))))))) # label(t54_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3205 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -(v3_tdlat_3(A) & (exists B (v1_tsep_1(B,A) & v2_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B)))))) # label(t61_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3206 (all A (v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> v1_tdlat_3(B) & v5_tdlat_3(B) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v4_tdlat_3(B) & v3_tdlat_3(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc22_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3207 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & -v2_tex_3(B,A) -> v2_pre_topc(B) & -v1_tex_3(B,A) & -v2_tex_3(B,A) & v2_tex_2(B,A)))))) # label(cc10_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3208 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> -(v1_tdlat_3(A) & (exists B (-v3_struct_0(B) & v3_tex_3(B,A) & m1_pre_topc(B,A)))))) # label(t49_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3209 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r4_tsep_2(A,B,C) -> (v3_tex_3(B,A) <-> v1_tex_3(C,A))))))))) # label(t32_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3210 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & -v3_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc11_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3211 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v1_tops_3(C,A)))) <-> v2_tex_3(B,A)))))) # label(d2_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3212 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r4_tsep_2(A,B,C) -> (v4_tex_3(B,A) <-> v2_tex_3(C,A))))))))) # label(t38_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3213 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r4_tsep_2(A,B,C) -> v2_tex_2(C,A) & v2_tex_2(B,A)))))))) # label(t6_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3214 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v4_tex_3(C,A) -> u1_struct_0(C) != B)) & v3_tops_1(B,A)))))) # label(t62_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3215 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v2_tex_2(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v1_tsep_1(B,A)))))) # label(cc30_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3216 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & -v3_struct_0(C) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = C -> (v4_tex_3(C,A) & m1_pre_topc(C,A) <-> v4_tex_3(B,A) & m1_pre_topc(B,A))))))))) # label(t66_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3217 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v2_tex_2(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v2_tex_2(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A))))))) # label(t8_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3218 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_tdlat_3(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_pre_topc(C,A) & v3_tex_3(C,A) & v1_borsuk_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v4_pre_topc(B,A) & v2_tops_1(B,A)))))) # label(t67_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3219 (all A (l1_pre_topc(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v1_tops_3(B,A) & (all C (m1_pre_topc(C,A) & v2_tex_3(C,A) & v2_tex_2(C,A) & v1_pre_topc(C) -> u1_struct_0(C) != B))))))) # label(t63_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3220 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (v2_tex_3(B,A) & v2_tex_3(C,A) -> v2_tex_3(k2_tsep_1(A,B,C),A) & m1_pre_topc(k2_tsep_1(A,B,C),A)))))))) # label(t27_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3221 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (-v3_struct_0(C) & v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> -(v3_tex_3(C,A) & B = u1_struct_0(C)))) & v4_pre_topc(B,A) & v2_tops_1(B,A)))))) # label(t41_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3222 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v4_tex_3(B,A) & v1_borsuk_1(B,A) -> v2_pre_topc(B) & -v4_tex_3(B,A) & -v3_tex_3(B,A)))))) # label(cc21_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3223 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_tdlat_3(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_pre_topc(B) & -v1_tsep_1(B,A) & v2_tex_2(B,A) & -v1_tex_3(B,A) & -v2_tex_3(B,A) & v4_tex_3(B,A) & v3_tex_3(B,A) & v1_borsuk_1(B,A) & v1_pre_topc(B))))) # label(rc12_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3224 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) -> -((all C (-v3_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) & v1_tex_3(C,A) & v2_tex_2(C,A) & v1_pre_topc(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v4_tex_3(D,A) & v1_pre_topc(D) -> -(k1_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & r1_tsep_1(A,C,D)))))) & -(v1_tex_3(B,A) & v1_tsep_1(B,A))))))) # label(t73_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3225 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (l1_pre_topc(C) & v2_pre_topc(C) & -v3_struct_0(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (v1_tex_3(C,A) & m1_pre_topc(C,A) <-> m1_pre_topc(B,A) & v1_tex_3(B,A))))))))) # label(t15_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3226 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_tex_3(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> v1_tex_3(B,C) & m1_pre_topc(B,C)))))))) # label(t13_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3227 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> -v3_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc13_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3228 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v2_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc6_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3229 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v1_tex_3(C,A) & m1_pre_topc(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> u1_struct_0(C) != B)) & v1_tops_1(B,A)))))) # label(t10_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3230 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) -> v2_pre_topc(B) & v1_tdlat_3(B) & -v2_tex_2(B,A) & v5_tex_2(B,A) & -v4_tex_3(B,A) & -v3_tex_3(B,A) & v2_tex_3(B,A) & v1_tex_3(B,A) & v3_tdlat_3(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A)))))) # label(cc24_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3231 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (v2_tex_3(B,A) & v1_tex_3(C,A) | v2_tex_3(C,A) & v1_tex_3(B,A) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_tex_3(k2_tsep_1(A,B,C),A)))))))) # label(t28_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3232 (all A (v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v5_tdlat_3(B) & -v4_tex_3(B,A) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B))))) # label(rc8_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3233 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (v4_tex_3(B,A) <-> (exists C (-v3_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & v3_tex_3(C,A) & m1_pre_topc(B,C) & v1_pre_topc(C)))))))) # label(t42_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3234 (all A (-v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A) -> -(-(v3_tex_3(B,A) & v1_borsuk_1(B,A)) & (all C (-v3_struct_0(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & v2_tex_3(C,A) & v1_pre_topc(C) -> (all D (v1_pre_topc(D) & v3_tex_3(D,A) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) & -v3_struct_0(D) -> -(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,C,D) & k2_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))))))))))) # label(t72_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3235 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & v2_tex_2(B,A) -> v2_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & -v1_tex_3(B,A)))))) # label(cc32_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3236 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> v2_pre_topc(B) & v1_tex_3(B,A)))))) # label(cc4_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3237 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(B,A) & (all C (v1_pre_topc(C) & m1_pre_topc(C,A) -> -(v3_tex_3(C,A) & u1_struct_0(C) = B)))))))) # label(t30_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3238 (all A (l1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C (-v3_struct_0(C) & u1_struct_0(C) = B & m1_pre_topc(C,A) & v2_tex_2(C,A) & v1_pre_topc(C))))))) # label(t7_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3239 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v2_tex_3(C,A) & m1_pre_topc(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v1_tops_3(B,A)))))) # label(t17_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3240 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v1_tsep_1(B,A) -> v2_pre_topc(B) & v1_tex_3(B,A) & v2_tex_3(B,A) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & -v2_tex_2(B,A) & v1_tsep_1(B,A) & v1_borsuk_1(B,A)))))) # label(cc31_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3241 (all A (v2_pre_topc(A) & -v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v2_tex_2(B,A) & -v4_tex_3(B,A) & v1_tex_3(B,A) & -v1_borsuk_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc7_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3242 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tex_3(B,A) -> -v2_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc5_tex_3) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3243 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> -v1_xboole_0(k2_t_0topsp(A)) & m1_eqrel_1(k2_t_0topsp(A),u1_struct_0(A)))) # label(dt_k2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3244 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all 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) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_pre_topc(A,B,C,k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),D)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))))))))) # label(t16_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3245 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v2_pre_topc(k3_t_0topsp(A)) & l1_pre_topc(k3_t_0topsp(A)) & v2_t_0topsp(k3_t_0topsp(A)) & -v3_struct_0(k3_t_0topsp(A)))) # label(t13_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3246 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B))))) # label(t8_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3247 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (r2_hidden(E,D) & k8_funct_2(A,B,C,E) = k8_funct_2(A,B,C,F) -> r2_hidden(F,D)))))) -> D = k3_funct_2(A,B,C,k2_funct_2(A,B,C,D))))))))))) # label(t2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3248 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> u1_struct_0(k3_t_0topsp(A)) = k2_t_0topsp(A) & u1_pre_topc(k3_t_0topsp(A)) = a_1_0_t_0topsp(A))) # label(t5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3249 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_funct_2(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))) & m2_relset_1(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))) & v5_pre_topc(k4_t_0topsp(A),A,k3_t_0topsp(A)) & v1_funct_1(k4_t_0topsp(A)))) # label(dt_k4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3250 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & v2_t_0topsp(B) & -v3_struct_0(B) -> (all C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & v5_pre_topc(D,k3_t_0topsp(A),B) & m2_relset_1(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & C = k4_borsuk_1(A,k3_t_0topsp(A),B,k4_t_0topsp(A),D))))))))) # label(t17_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3251 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & B = k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),C))))))) # label(t7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3252 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> k17_borsuk_1(A,k2_t_0topsp(A)) = k4_t_0topsp(A))) # label(d6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3253 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> ((exists C (v1_funct_1(C) & r1_rfinseq(k4_t_0topsp(A),k7_funct_2(u1_struct_0(B),u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(B),C)) & v3_tops_2(C,k3_t_0topsp(B),k3_t_0topsp(A)) & m2_relset_1(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v1_funct_2(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))))) -> r1_t_0topsp(A,B)))))) # label(t14_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3254 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) -> v3_pre_topc(k4_pre_topc(A,B,C,D),B)))) <-> v1_t_0topsp(C,A,B)))))))) # label(d2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3255 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),D) -> r2_hidden(D,B))))))))))) # label(t10_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3256 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,k2_t_0topsp(A)) -> r1_tarski(C,B) | r1_xboole_0(C,B))))))))) # label(t11_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3257 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(fc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3258 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k16_borsuk_1(A,k2_t_0topsp(A)) = k3_t_0topsp(A))) # label(d5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3259 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> v3_relat_2(k1_t_0topsp(A)) & v1_partfun1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k1_t_0topsp(A)))) # label(dt_k1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3260 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(B) & v3_relat_2(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(E,A) -> (r2_hidden(C,E) <-> r2_hidden(D,E))))) <-> r2_hidden(k4_tarski(C,D),B)))))) <-> B = k1_t_0topsp(A)))))) # label(d3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3261 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_t_0topsp(k4_t_0topsp(A),A,k3_t_0topsp(A)))) # label(t12_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3262 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) -> (all C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k8_borsuk_1(A,A,D,E),k1_t_0topsp(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))))))))))) # label(t15_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3263 (all A (l1_pre_topc(A) -> (v3_struct_0(A) | (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & (r2_hidden(B,D) & -r2_hidden(C,D) | -r2_hidden(B,D) & r2_hidden(C,D)))))))))) <-> v2_t_0topsp(A)))) # label(d7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3264 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> u1_struct_0(A) = k1_relat_1(k4_t_0topsp(A)) & r1_tarski(k2_relat_1(k4_t_0topsp(A)),u1_struct_0(k3_t_0topsp(A))))) # label(t4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3265 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> l1_pre_topc(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(dt_k3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3266 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_t_0topsp(A)))) -> (r2_hidden(k3_tarski(B),u1_pre_topc(A)) <-> v3_pre_topc(B,k3_t_0topsp(A))))))) # label(t6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3267 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((exists 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))) <-> r1_t_0topsp(A,B)))))) # label(d1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3268 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) <-> r2_hidden(k8_borsuk_1(A,A,C,B),k1_t_0topsp(A))))))))) # label(t9_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3269 (exists A (-v3_struct_0(A) & v2_t_0topsp(A) & v2_pre_topc(A) & l1_pre_topc(A))) # label(rc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3270 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> k8_eqrel_1(u1_struct_0(A),k1_t_0topsp(A)) = k2_t_0topsp(A))) # label(d4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3271 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_0_t_0topsp(B)) <-> (exists C (m1_subset_1(C,k1_zfmisc_1(k2_t_0topsp(B))) & C = A & r2_hidden(k3_tarski(C),u1_pre_topc(B))))))) # label(fraenkel_a_1_0_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3272 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(k4_tarski(E,F),D) <-> r2_hidden(k4_tarski(E,F),C)))))) -> C = D))))))))) # label(t1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3273 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B)))))) # label(t3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3274 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k3_tex_4(A,B) = B))))) # label(t62_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3275 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tex_4(k1_struct_0(A,B),A))))) # label(t8_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.12 3276 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,k3_tex_4(A,B))),u1_pre_topc(k7_tex_4(A,k3_tex_4(A,B)))))))) # label(t87_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3277 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> -v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(k6_pre_topc(A,B),A) & -v1_xboole_0(k6_pre_topc(A,B)))) # label(fc3_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3278 (all A all B (-v3_realset2(A) & l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & -v3_struct_0(A) -> -v3_struct_0(k7_tex_4(A,B)) & v1_pre_topc(k7_tex_4(A,B)) & -v3_realset2(k7_tex_4(A,B)))) # label(fc20_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3279 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> v1_pre_topc(k6_tex_4(A,B)) & -v3_struct_0(k6_tex_4(A,B)))) # label(fc16_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3280 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v1_tex_4(B,A) -> r1_tarski(B,k2_tex_4(A,C))))))))) # label(t21_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3281 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tex_4(B,A) & v2_tdlat_3(B))))) # label(rc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3282 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k1_tex_4(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3283 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) | v4_pre_topc(C,A) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t66_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3284 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k3_tex_4(A,B)) = k6_pre_topc(A,B))))) # label(t64_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3285 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_tex_4(B,A))))) # label(t9_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3286 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_9_tex_4(A,B))))))) # label(t48_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3287 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v2_tdlat_3(B) -> (all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> m1_pre_topc(B,C) | r1_tsep_1(A,B,C))))))) # label(t73_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3288 (all A all B (v2_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> -v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3289 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k3_tex_4(A,C)) -> r1_tarski(k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t36_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3290 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tex_4(B,A) -> v1_tex_4(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t11_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3291 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> -v1_xboole_0(k4_tex_4(A,B)) & m1_subset_1(k4_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3292 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> v1_pre_topc(k5_tex_4(A,B)) & m1_pre_topc(k5_tex_4(A,B),A))) # label(dt_k5_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3293 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> -v1_xboole_0(k3_tex_4(A,B)) & -v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(fc12_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3294 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k6_tex_4(A,B)) & m1_pre_topc(k6_tex_4(A,B),A))) # label(dt_k6_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3295 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,B) = k3_tex_4(A,k3_tex_4(A,B)))))) # label(t35_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3296 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C)))))))) # label(t38_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3297 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v3_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> B = k2_tex_4(A,C))))))))) # label(d10_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3298 $T # label(t5_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3299 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v3_tex_4(C,A) <-> v4_tex_4(B,A))))))))) # label(t74_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3300 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_pre_topc(A,k1_struct_0(A,B)) = k1_setfam_1(a_2_1_tex_4(A,B)))))) # label(t2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3301 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_1_tex_4(A,B))))))) # label(t49_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3302 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> g1_pre_topc(u1_struct_0(k7_tex_4(A,k1_struct_0(A,B))),u1_pre_topc(k7_tex_4(A,k1_struct_0(A,B)))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))))))) # label(t85_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3303 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_7_tex_4(A,B) != k1_xboole_0 -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_7_tex_4(A,B)))))))) # label(t41_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3304 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_pre_topc(k7_tex_4(A,C),B)))))))) # label(t91_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3305 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tex_4(B,A) -> k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0 | v1_tex_4(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t10_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3306 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_struct_0(A,B) = k6_pre_topc(A,k1_struct_0(A,B)) -> v3_tex_4(k1_struct_0(A,B),A)))))) # label(t47_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3307 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tex_4(k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)),A))))) # label(t15_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3308 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists D (A = D & r2_hidden(C,D) & v4_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_1_tex_4(B,C))))) # label(fraenkel_a_2_1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3309 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),C) & v1_tex_4(C,A) -> k6_pre_topc(A,k1_struct_0(A,B)) = C))))))) # label(t44_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3310 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_pre_topc(A,k1_struct_0(A,B)) != k6_pre_topc(A,k1_struct_0(A,C)) <-> r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C))))))))) # label(t52_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3311 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r1_tarski(B,k6_pre_topc(A,k1_struct_0(A,C)))))) <-> v1_tex_4(B,A)))))) # label(d12_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3312 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D & v1_tex_4(C,A) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v1_tex_4(D,B)))))))))) # label(t6_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3313 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) | r1_subset_1(u1_struct_0(k5_tex_4(A,B)),u1_struct_0(k5_tex_4(A,C))))))))) # label(t77_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3314 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_tarski(a_2_2_tex_4(A,B)))))) # label(t4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3315 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_tex_4(C,A) & D = C & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v3_tex_4(D,B)))))))))) # label(t16_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3316 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_tex_4(A,B) = k3_tex_4(A,k1_struct_0(A,B)))))) # label(t30_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3317 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-r1_tarski(B,C) & -r1_xboole_0(B,C) & v4_pre_topc(C,A)))) <-> v1_tex_4(B,A)))))) # label(d4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3318 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_4(B,A) <-> v2_tdlat_3(B) & (all C (m1_pre_topc(C,A) -> (v2_tdlat_3(C) & r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> u1_struct_0(B) = u1_struct_0(C))))))))) # label(d16_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3319 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k3_tex_4(A,B)))))) # label(t34_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3320 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) & r2_hidden(C,D) & r2_hidden(C,B) -> r1_tarski(B,D)))))) <-> v1_tex_4(B,A)))))) # label(d2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3321 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (a_2_4_tex_4(A,B) != k1_xboole_0 -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_4_tex_4(A,B)))))))) # label(t27_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3322 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> -v1_xboole_0(k1_tex_4(A,B)))) # label(fc8_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3323 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v3_pre_topc(B,A) & r2_hidden(C,B) -> r1_tarski(k2_tex_4(A,C),B)))))))) # label(t26_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3324 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) & v3_pre_topc(B,A) -> v3_tex_4(B,A)))))) # label(t18_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3325 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) -> (r2_hidden(A,a_2_4_tex_4(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(C,D) & v4_pre_topc(D,B)))))) # label(fraenkel_a_2_4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3326 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) & v2_membered(k3_tex_4(A,B)) & v5_membered(k3_tex_4(A,B)) & v4_membered(k3_tex_4(A,B)) & v3_membered(k3_tex_4(A,B)) & v1_membered(k3_tex_4(A,B)) & v2_tops_1(k3_tex_4(A,B),A) & v1_xboole_0(k3_tex_4(A,B)))) # label(fc11_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3327 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tdlat_3(B) -> -v4_tex_4(B,A)))))) # label(cc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3328 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_struct_0(A,B) = k6_pre_topc(A,k1_struct_0(A,B)) -> v4_tex_4(k1_tex_2(A,B),A)))))) # label(t80_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3329 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_pre_topc(C) & m1_pre_topc(C,A) -> (C = k5_tex_4(A,B) <-> k2_tex_4(A,B) = u1_struct_0(C)))))))) # label(d17_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3330 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v3_pre_topc(k1_tops_1(A,B),A) & v2_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v1_membered(k1_tops_1(A,B)) & v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_tops_1(k1_tops_1(A,B),A) & v2_tops_1(k1_tops_1(A,B),A) & v4_pre_topc(k1_tops_1(A,B),A) & v1_xboole_0(k1_tops_1(A,B)))) # label(fc7_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3331 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v1_xboole_0(k6_pre_topc(A,B)) & v3_pre_topc(k6_pre_topc(A,B),A) & v4_pre_topc(k6_pre_topc(A,B),A) & v2_tops_1(k6_pre_topc(A,B),A) & v3_tops_1(k6_pre_topc(A,B),A) & v1_membered(k6_pre_topc(A,B)) & v2_membered(k6_pre_topc(A,B)) & v4_membered(k6_pre_topc(A,B)) & v5_membered(k6_pre_topc(A,B)) & v3_membered(k6_pre_topc(A,B)) & v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(fc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3332 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v1_tex_4(C,A)))) <-> v2_tex_4(B,A)))))) # label(d5_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3333 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v4_pre_topc(B,A) & r2_hidden(C,B) -> r1_tarski(k2_tex_4(A,C),B)))))))) # label(t25_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3334 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v1_borsuk_1(B,A) & v2_tdlat_3(B) -> v2_pre_topc(B) & v2_tdlat_3(B) & v4_tex_4(B,A) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc6_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3335 (all A all B all C (v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_2_tex_4(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & D = A & v3_pre_topc(D,B) & r1_tarski(D,C)))))) # label(fraenkel_a_2_2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3336 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k4_tex_4(A,C),D) & r1_xboole_0(D,k4_tex_4(A,B)) & v4_pre_topc(D,A)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k4_tex_4(A,B),D) & r1_xboole_0(D,k4_tex_4(A,C)) & v4_pre_topc(D,A))))) <-> r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C))))))))) # label(t56_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3337 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_tex_4(A,C) = k3_tex_4(A,B) -> k6_pre_topc(A,B) = k6_pre_topc(A,C)))))))) # label(t65_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3338 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -v2_tex_2(k7_tex_4(A,B),A) & v1_pre_topc(k7_tex_4(A,B)) & -v3_struct_0(k7_tex_4(A,B)))) # label(fc21_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3339 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> ((all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> r1_tsep_1(A,B,C) | m1_pre_topc(B,C))) -> v2_tdlat_3(B)))))) # label(t71_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3340 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v4_tex_4(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_pre_topc(B) & -v2_tdlat_3(B) & -v4_tex_4(B,A) & -v3_realset2(B)))))) # label(cc7_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3341 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) & v3_tex_4(B,A) -> B = k2_tex_4(A,C)))))))) # label(t29_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3342 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_subset_1(C,u1_struct_0(B)) -> m1_pre_topc(k5_tex_4(A,C),B)))))))) # label(t78_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3343 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) & -v4_tex_4(B,A) & -v3_struct_0(B) -> v2_tex_2(B,A) & -v1_borsuk_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc8_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3344 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> k6_pre_topc(A,k1_struct_0(A,D)) = k6_pre_topc(A,k1_struct_0(A,C)))))))))))) # label(d14_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3345 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3346 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-r1_xboole_0(B,C) & -r1_tarski(B,C) & v3_pre_topc(C,A))))))))) # label(d3_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3347 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t39_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3348 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> B = k6_pre_topc(A,k1_struct_0(A,C)))))))))) # label(t45_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3349 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k3_tex_4(A,k6_pre_topc(A,B)))))) # label(t63_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3350 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k2_tex_4(A,B),k6_pre_topc(A,k1_struct_0(A,B))))))) # label(t50_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3351 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k3_tex_4(A,B)) & r1_tarski(B,k3_tex_4(A,C)) <-> k3_tex_4(A,B) = k3_tex_4(A,C)))))))) # label(t37_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3352 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_tex_4(D,B) & r2_hidden(C,D) & A = D)) <-> r2_hidden(A,a_2_3_tex_4(B,C))))) # label(fraenkel_a_2_3_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3353 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_subset_1(C,u1_struct_0(B)) -> m1_pre_topc(k5_tex_4(A,C),B)))))))) # label(t79_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3354 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & -v1_xboole_0(B) & -v3_realset2(A) -> -v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A) & -v1_realset1(k6_pre_topc(A,B)))) # label(fc4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3355 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C)) | k2_tex_4(A,C) = k2_tex_4(A,B))))))) # label(t24_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3356 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_10_tex_4(A,B))))))) # label(t57_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3357 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_xboole_0 != a_2_5_tex_4(A,B) -> r1_tarski(k2_tex_4(A,B),k1_setfam_1(a_2_5_tex_4(A,B)))))))) # label(t28_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3358 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_struct_0(A,B),k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B))))))) # label(t14_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3359 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,B)))))))) # label(t81_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3360 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v3_tex_4(B,A))))) # label(t17_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3361 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & r1_tarski(C,B) -> r1_tarski(k3_tex_4(A,C),B)))))))) # label(t42_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3362 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k2_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3363 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (k6_tex_4(A,B) = C <-> u1_struct_0(C) = B))))))) # label(d18_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3364 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & D = A & r2_hidden(C,D) & v3_pre_topc(D,B))) <-> r2_hidden(A,a_2_5_tex_4(B,C))))) # label(fraenkel_a_2_5_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3365 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> m1_pre_topc(k6_tex_4(A,B),k7_tex_4(A,B)))))) # label(t84_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3366 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_pre_topc(A) -> -v3_struct_0(k7_tex_4(A,B)) & v1_pre_topc(k7_tex_4(A,B)))) # label(fc19_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3367 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v2_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_9_tex_4(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(C,D) & v3_pre_topc(D,B)))))) # label(fraenkel_a_2_9_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3368 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_setfam_1(u1_struct_0(A),k1_tex_4(A,B)) = k1_struct_0(A,B))))) # label(t13_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3369 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) -> -v3_struct_0(k5_tex_4(A,B)) & v2_pre_topc(k5_tex_4(A,B)) & v4_tex_4(k5_tex_4(A,B),A) & v3_tdlat_3(k5_tex_4(A,B)) & v2_tdlat_3(k5_tex_4(A,B)) & v1_pre_topc(k5_tex_4(A,B)))) # label(fc15_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3370 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_pre_topc(k7_tex_4(A,B)) & m1_pre_topc(k7_tex_4(A,B),A))) # label(dt_k7_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3371 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_7_tex_4(B,C)) <-> (exists D (r1_tarski(C,D) & v3_pre_topc(D,B) & A = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_7_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3372 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A) & -v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(k1_tops_1(A,B)))) # label(fc5_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3373 (all A all B (v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> k2_tex_4(A,B) = k4_tex_4(A,B))) # label(redefinition_k4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3374 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) & v4_pre_topc(B,A) -> v3_tex_4(B,A)))))) # label(t19_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3375 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_realset2(A) -> (exists B (v1_pre_topc(B) & -v2_tex_2(B,A) & m1_pre_topc(B,A))))) # label(rc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3376 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) & r2_hidden(C,B) & r2_hidden(C,D) -> r1_tarski(B,D))))))))))) # label(d1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3377 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_4(B,A) <-> v1_tex_4(B,A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(C,A) & r1_tarski(B,C) -> C = B)))))))) # label(d7_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3378 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_struct_0(A,B),k2_tex_4(A,B)))))) # label(t20_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3379 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_tex_4(A,B) = k2_tex_4(A,C) <-> k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C))))))))) # label(t51_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3380 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r1_tarski(B,C) -> m1_pre_topc(k7_tex_4(A,B),k7_tex_4(A,C))))))))) # label(t86_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3381 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k4_tex_4(A,C),D) & r1_xboole_0(D,k4_tex_4(A,B)) & v3_pre_topc(D,A)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_xboole_0(D,k4_tex_4(A,C)) & r1_tarski(k4_tex_4(A,B),D) & v3_pre_topc(D,A))))) <-> r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C))))))))) # label(t55_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3382 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tdlat_3(B) & C = u1_struct_0(B) -> v1_tex_4(C,A)))))))) # label(t68_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3383 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) | v3_pre_topc(C,A) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t67_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3384 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & -v4_tex_4(B,A) & -v3_struct_0(B) -> -v3_realset2(B) & v2_pre_topc(B) & -v4_tex_4(B,A) & -v2_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc4_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3385 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v3_tex_4(k2_tex_4(A,B),A))))) # label(t22_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3386 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(k6_tex_4(A,B)) & v1_pre_topc(k6_tex_4(A,B)) & -v2_tex_2(k6_tex_4(A,B),A))) # label(fc18_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3387 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B)) -> r1_tarski(k2_tex_4(A,C),k3_tex_4(A,B))))))))) # label(t32_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3388 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_0_tex_4(A,B))))))) # label(t60_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3389 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v2_tex_4(k1_tex_4(A,B),A))))) # label(t12_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3390 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_tex_4(A,C) = k2_tex_4(A,B) <-> r2_hidden(C,k2_tex_4(A,B))))))))) # label(t23_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3391 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,B)))))))) # label(t83_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3392 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v1_tex_4(B,A) -> v1_tex_4(C,A)))))))) # label(t7_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3393 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> m1_pre_topc(k1_tex_2(A,B),k5_tex_4(A,B)))))) # label(t75_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3394 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,B)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,C)))) <-> g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,C)),u1_pre_topc(k7_tex_4(A,C)))))))))) # label(t89_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3395 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) & v1_tex_4(C,A) -> v2_tdlat_3(B))))))))) # label(t69_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3396 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,a_2_10_tex_4(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v3_pre_topc(D,B) & r1_tarski(C,D) & D = A))))) # label(fraenkel_a_2_10_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3397 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,B) = k3_tarski(a_2_6_tex_4(A,B)))))) # label(d11_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3398 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_struct_0(A) -> -v1_xboole_0(k3_tex_4(A,B)))) # label(fc10_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3399 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,k1_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t59_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3400 $T # label(t3_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3401 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_tarski(k1_setfam_1(a_2_9_tex_4(A,C)),k1_setfam_1(a_2_9_tex_4(A,B))) <-> r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C)))))))))) # label(t53_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3402 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k3_tex_4(A,B) = B))))) # label(t58_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3403 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) -> ((exists D (D = A & r1_tarski(C,D) & v4_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_0_tex_4(B,C))))) # label(fraenkel_a_2_0_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3404 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k1_setfam_1(a_2_0_tex_4(A,B)))))) # label(t1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3405 (all A all B all C (-v3_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (r2_hidden(D,C) & A = k2_tex_4(B,D) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_6_tex_4(B,C))))) # label(fraenkel_a_2_6_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3406 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_pre_topc(k6_tex_4(A,C),B)))))))) # label(t82_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3407 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tdlat_3(B) & m1_pre_topc(B,A) -> (all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) -> m1_pre_topc(B,C) | r1_tsep_1(A,B,C))))))) # label(t72_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3408 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) -> v2_tops_1(B,A) | v3_pre_topc(B,A)))))) # label(t46_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3409 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_tex_4(A,B) = k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)))))) # label(d8_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3410 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & -v3_realset2(A) -> -v1_realset1(k3_tex_4(A,B)) & -v1_xboole_0(k3_tex_4(A,B)))) # label(fc13_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3411 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) -> r1_tsep_1(A,B,C) | m1_pre_topc(B,C))) -> v2_tdlat_3(B)))))) # label(t70_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3412 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t33_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3413 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) & v2_tdlat_3(B) & -v3_struct_0(B) -> v3_tdlat_3(B) & v4_tex_4(B,A) & v2_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc3_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3414 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_tex_4(A,B) = k3_xboole_0(k6_pre_topc(A,k1_struct_0(A,B)),k1_setfam_1(a_2_9_tex_4(A,B))))))) # label(d15_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3415 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_tex_4(A,B) = a_2_3_tex_4(A,B))))) # label(d6_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3416 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> m1_subset_1(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3417 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),k6_pre_topc(A,k1_struct_0(A,C))) <-> r1_tarski(k4_tex_4(A,C),k1_setfam_1(a_2_9_tex_4(A,B)))))))))) # label(t54_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3418 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_subset_1(C,u1_struct_0(k5_tex_4(A,B))) <-> g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C)))))))))) # label(t76_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3419 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k6_pre_topc(A,B) = k6_pre_topc(A,k1_struct_0(A,C)))))))))) # label(d13_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3420 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((exists C (m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & k2_tex_4(A,C) = B)) <-> v3_tex_4(B,A)))))) # label(d9_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3421 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(-r1_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B)) & r1_xboole_0(k2_tex_4(A,C),B)))))))) # label(t31_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3422 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_tex_4(A,B),k6_pre_topc(A,B)))))) # label(t61_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3423 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_tex_4(A,C)))) -> m1_pre_topc(k7_tex_4(A,B),k7_tex_4(A,C))))))))) # label(t88_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3424 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (k3_tex_4(A,B) = u1_struct_0(C) <-> k7_tex_4(A,B) = C))))))) # label(d19_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3425 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tdlat_3(B) & -v4_tex_4(B,A) -> v2_tex_2(B,A) & -v1_tsep_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc5_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3426 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_4(B,A) -> v2_pre_topc(B) & v3_tdlat_3(B) & v2_tdlat_3(B)))))) # label(cc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3427 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> -v3_struct_0(k5_tex_4(A,B)) & v1_pre_topc(k5_tex_4(A,B)))) # label(fc14_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3428 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_pre_topc(B) -> (r2_hidden(A,a_2_8_tex_4(B,C)) <-> (exists D (v4_pre_topc(D,B) & r1_tarski(C,D) & A = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_8_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3429 (all A all B (-v3_realset2(A) & l1_pre_topc(A) & -v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & -v3_struct_0(A) -> -v3_struct_0(k6_tex_4(A,B)) & v1_pre_topc(k6_tex_4(A,B)) & -v3_realset2(k6_tex_4(A,B)))) # label(fc17_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3430 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> -v1_xboole_0(k2_tex_4(A,B)))) # label(fc9_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3431 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_pre_topc(k7_tex_4(A,C),B)))))))) # label(t90_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3432 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r1_tarski(C,B) -> r1_tarski(k3_tex_4(A,C),B)))))))) # label(t40_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3433 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_8_tex_4(A,B) != k1_xboole_0 -> r1_tarski(k3_tex_4(A,B),k1_setfam_1(a_2_8_tex_4(A,B)))))))) # label(t43_tex_4) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3434 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tsp_1(C,A) <-> v2_t_0topsp(B))))))))) # label(t15_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3435 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> -(D = k3_xboole_0(C,u1_struct_0(B)) & v4_pre_topc(D,B))))))))))) # label(t4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3436 (all A (-v3_realset2(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v2_tex_2(B,A) & v2_t_0topsp(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3437 $T # label(t3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3438 (all A (l1_pre_topc(A) -> (-v3_realset2(A) & v2_pre_topc(A) & v2_tdlat_3(A) & -v3_struct_0(A) -> -v3_struct_0(A) & -v2_t_0topsp(A) & v2_pre_topc(A) & -v3_realset2(A)))) # label(cc5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3439 (all A all B (m1_pre_topc(B,A) & l1_pre_topc(A) -> (v3_tsp_1(B,A) <-> v2_t_0topsp(B)))) # label(redefinition_v3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3440 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v2_t_0topsp(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(-v1_tsp_1(B,A) & (all C (v1_pre_topc(C) & m2_tsp_1(C,A) & -v2_t_0topsp(C) -> B != u1_struct_0(C)))))))) # label(t21_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3441 (all A (l1_pre_topc(A) -> (all B (m1_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> -(v3_pre_topc(D,B) & D = k3_xboole_0(C,u1_struct_0(B))))) & v3_pre_topc(C,A)))))))) # label(t2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3442 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & -v1_tdlat_3(A) -> -v3_realset2(A) & -v1_tdlat_3(A) & -v3_tdlat_3(A) & -v2_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A)))) # label(cc10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3443 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,D))) & r2_hidden(D,k6_pre_topc(A,k1_struct_0(A,C))) & D != C)))))))))) # label(d11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3444 (all A (l1_pre_topc(A) -> (v3_tdlat_3(A) & v2_t_0topsp(A) & v2_pre_topc(A) & -v3_struct_0(A) -> v2_pre_topc(A) & v3_tdlat_3(A) & v5_tdlat_3(A) & v2_t_0topsp(A) & v4_tdlat_3(A) & v1_tdlat_3(A) & -v3_struct_0(A)))) # label(cc8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3445 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & C != D & k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,D)) & r2_hidden(D,B))))))))))) # label(d10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3446 $T # label(t1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3447 (all A (l1_pre_topc(A) -> (exists B m2_tsp_1(B,A)))) # label(existence_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.13 3448 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & r2_hidden(D,B) & r1_tarski(k6_pre_topc(A,k1_struct_0(A,D)),k6_pre_topc(A,k1_struct_0(A,C))) & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,D))) & D != C))))) <-> v1_tsp_1(B,A)))))) # label(d12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3449 (all A all B (m1_pre_topc(B,A) & l1_pre_topc(A) -> (v2_t_0topsp(B) <-> v2_tsp_1(B,A)))) # label(redefinition_v2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3450 (all A (l1_pre_topc(A) -> (all B (m1_tsp_1(B,A) -> l1_pre_topc(B))))) # label(dt_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3451 (all A (l1_pre_topc(A) -> (-v1_tdlat_3(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(A) & -v3_realset2(A) & -v1_tdlat_3(A) & -v2_t_0topsp(A) & v2_pre_topc(A)))) # label(cc9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3452 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v2_t_0topsp(A) -> (all B (m1_pre_topc(B,A) -> (v2_t_0topsp(B) & -v3_struct_0(B) -> v2_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3453 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) -> v1_tsp_1(B,A))))) # label(t13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3454 (all A (-v2_t_0topsp(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & -v3_realset2(B) & -v2_t_0topsp(B)))))) # label(cc12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3455 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = B -> (v2_t_0topsp(A) <-> v1_tsp_1(B,A))))))) # label(t6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3456 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_t_0topsp(A) & v2_tdlat_3(A) & v2_pre_topc(A) -> -v3_struct_0(A) & v3_realset2(A) & v1_tdlat_3(A) & v2_tdlat_3(A) & v3_tdlat_3(A) & v2_t_0topsp(A) & v5_tdlat_3(A) & v4_tdlat_3(A) & v2_pre_topc(A)))) # label(cc6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3457 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> -v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A)))) # label(cc3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3458 (all A (l1_pre_topc(A) -> (-v3_realset2(A) & v2_t_0topsp(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v2_pre_topc(A) & -v2_tdlat_3(A) & -v3_realset2(A)))) # label(cc7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3459 (all A (l1_pre_topc(A) -> (-v2_t_0topsp(A) & -v3_struct_0(A) -> -v3_realset2(A) & -v3_struct_0(A)))) # label(cc2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3460 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) <-> m1_pre_topc(B,A))))) # label(redefinition_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3461 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_t_0topsp(B) & -v3_struct_0(B) -> (all C (m2_tsp_1(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> v2_t_0topsp(k2_tsep_1(A,B,C))))))))) # label(t17_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3462 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & -v2_t_0topsp(A) & v2_pre_topc(A) -> -v3_struct_0(A) & -v1_tdlat_3(A) & v2_pre_topc(A) & -v3_realset2(A)))) # label(cc4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3463 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & -r2_hidden(B,D) & v3_pre_topc(D,A)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & -r2_hidden(C,D) & r2_hidden(B,D)))) & C != B))))) | v3_struct_0(A) <-> v2_t_0topsp(A)))) # label(d3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3464 (all A (l1_pre_topc(A) -> (exists B m1_tsp_1(B,A)))) # label(existence_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3465 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(k6_pre_topc(A,k1_struct_0(A,C)) = k6_pre_topc(A,k1_struct_0(A,B)) & C != B))))) <-> v2_t_0topsp(A)))) # label(d5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3466 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> l1_pre_topc(B))))) # label(dt_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3467 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & -v2_tdlat_3(A) & v2_t_0topsp(A) & v2_pre_topc(A) & -v3_realset2(A))) # label(rc3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3468 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & -r2_hidden(B,D) & v4_pre_topc(D,A)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r2_hidden(B,D) & -r2_hidden(C,D))))))))) | v3_struct_0(A) <-> v2_t_0topsp(A)))) # label(d4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3469 (all A (l1_pre_topc(A) -> (v3_realset2(A) & -v3_struct_0(A) -> v2_t_0topsp(A) & -v3_struct_0(A)))) # label(cc1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3470 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(C,A) & v1_tsp_1(B,A) -> -v4_pre_topc(C,A) & -v4_pre_topc(B,A) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3471 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,E) & -r2_hidden(C,E) & v4_pre_topc(E,A)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(D,E) & r2_hidden(C,E) & v4_pre_topc(E,A)))) & D != C & m1_subset_1(C,u1_struct_0(B))))))) | v3_struct_0(B) <-> v2_t_0topsp(B)))))) # label(d14_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3472 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v1_tsp_1(B,A) -> v1_tsp_1(C,A)))))))) # label(t7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3473 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (m2_tsp_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(C,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(D,A) & k3_xboole_0(D,u1_struct_0(B)) = C))))) & r1_tarski(u1_struct_0(B),u1_struct_0(A))))))) # label(d2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3474 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))) & r1_tarski(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,B))) & B != C))))) <-> v2_t_0topsp(A)))) # label(d7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3475 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_tsp_1(k1_struct_0(A,B),A))))) # label(t14_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3476 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v2_t_0topsp(A) & v2_pre_topc(A) & v1_pre_topc(A))) # label(rc1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3477 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(C,A) | v1_tsp_1(B,A) -> v1_tsp_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3478 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_t_0topsp(B) & m2_tsp_1(B,A) -> (all C (-v3_struct_0(C) & v2_t_0topsp(C) & m2_tsp_1(C,A) -> (v1_borsuk_1(C,A) | v1_borsuk_1(B,A) -> v2_t_0topsp(k1_tsep_1(A,B,C))))))))) # label(t19_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3479 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v2_t_0topsp(C) & m2_tsp_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> u1_struct_0(C) != B)) & v1_tsp_1(B,A)))))) # label(t20_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3480 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & r2_hidden(D,B) & C != D & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & -r2_hidden(C,E) & r2_hidden(D,E)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & -r2_hidden(D,E) & r2_hidden(C,E)))))))))))))) # label(d8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3481 (exists A (-v3_realset2(A) & v2_pre_topc(A) & -v2_t_0topsp(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3482 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_t_0topsp(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v2_t_0topsp(B)))))) # label(cc11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3483 (all A (l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (v3_struct_0(B) | (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(m1_subset_1(C,u1_struct_0(B)) & D != C & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(C,E) & r2_hidden(D,E) & v3_pre_topc(E,A)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(D,E) & r2_hidden(C,E) & v3_pre_topc(E,A)))) & m1_subset_1(D,u1_struct_0(B))))))) <-> v2_t_0topsp(B)))))) # label(d13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3484 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_t_0topsp(B) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v2_t_0topsp(C) & m2_tsp_1(C,A) -> (v1_tsep_1(B,A) | v1_tsep_1(C,A) -> v2_t_0topsp(k1_tsep_1(A,B,C))))))))) # label(t18_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3485 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tsp_1(B,A) & -v1_realset1(B) & v1_tex_4(B,A)))))) # label(t12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3486 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (r1_tarski(u1_struct_0(B),u1_struct_0(A)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & k3_xboole_0(D,u1_struct_0(B)) = C & v3_pre_topc(D,A)))))) <-> m1_tsp_1(B,A)))))) # label(d1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3487 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) & v1_tsp_1(C,A) -> -v3_pre_topc(C,A) & -v3_pre_topc(B,A) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3488 (all A (l1_pre_topc(A) -> (all B (m1_tsp_1(B,A) <-> m1_pre_topc(B,A))))) # label(redefinition_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3489 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & v1_tsp_1(C,A) & D = C -> v1_tsp_1(D,B)))))))))) # label(t5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3490 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v2_t_0topsp(B) & m1_pre_topc(B,A))))) # label(rc5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3491 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tex_2(B,A) -> v1_tsp_1(B,A)))))) # label(t11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3492 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(C,E) & r2_hidden(D,E) & v4_pre_topc(E,A)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(E,A) & r2_hidden(C,E) & -r2_hidden(D,E)))) & D != C & r2_hidden(D,B)))))) <-> v1_tsp_1(B,A)))))) # label(d9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3493 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) -> (all C (-v3_struct_0(C) & m2_tsp_1(C,A) & v2_t_0topsp(C) -> (m2_tsp_1(B,C) -> v2_t_0topsp(B)))))))) # label(t16_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3494 (exists A (l1_pre_topc(A) & v1_pre_topc(A) & v2_pre_topc(A) & -v1_tdlat_3(A) & -v2_t_0topsp(A) & -v3_realset2(A) & -v3_struct_0(A))) # label(rc4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3495 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v2_t_0topsp(A) -> (exists B (-v2_t_0topsp(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3496 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_t_0topsp(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != C & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,B))) & r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))))))))))) # label(d6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3497 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) & u1_struct_0(A) = k3_tex_4(A,B) <-> v1_tsp_2(B,A)))))) # label(d5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3498 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> C = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)))))))))) # label(t6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3499 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) & v2_pre_topc(A) -> v1_funct_1(k1_tsp_2(A,B)) & v5_pre_topc(k1_tsp_2(A,B),A,B) & m2_relset_1(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k1_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3500 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B,A) & (v3_pre_topc(B,A) | v4_pre_topc(B,A))))))) # label(t3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3501 (all A all B (l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_funct_2(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A,B),A,B) & m2_relset_1(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k4_tsp_2(A,B)))) # label(dt_k4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3502 (all A all B (l1_pre_topc(A) & -v3_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & v2_pre_topc(A) & -v3_struct_0(A) -> v1_funct_1(k2_tsp_2(A,B)) & v5_pre_topc(k2_tsp_2(A,B),A,B) & m2_relset_1(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3503 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C))) = k6_pre_topc(A,C)))))))) # label(t7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3504 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r1_subset_1(k4_tex_4(A,C),k4_tex_4(A,D)) | C = D))))) <-> v1_tsp_1(B,A)))))) # label(d1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3505 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) = k1_tops_1(A,C)))))))) # label(t8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3506 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(C,A) & r1_tarski(B,C) -> C = B))) & v1_tsp_1(B,A)))))) # label(d4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3507 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = C)))))))) # label(t5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3508 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & -v3_struct_0(A) -> k1_tsp_2(A,B) = k4_tsp_2(A,B))) # label(redefinition_k4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3509 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_tex_4(D,A) & k1_struct_0(A,C) = k5_subset_1(u1_struct_0(A),B,D)))))))))))) # label(d3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3510 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) -> v1_tops_1(B,A)))))) # label(t2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3511 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) -> k2_tsp_2(A,B) = k1_tsp_2(A,B))) # label(redefinition_k2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3512 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) -> -v1_tsp_2(B,A))))) # label(t4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3513 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & k1_struct_0(A,D) = k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C))))))))))) # label(d6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3514 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) & l1_pre_topc(A) -> k1_tsp_2(A,B) = k3_tsp_2(A,B))) # label(redefinition_k3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3515 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k1_struct_0(A,C) = k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)))))))))) # label(d2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.06/5.14 3516 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) & -v3_struct_0(A) -> v1_funct_2(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k3_tsp_2(A,B),A,B) & m2_relset_1(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k3_tsp_2(A,B)))) # label(dt_k3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3517 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & v1_tsp_2(C,A) & C = D -> v1_tsp_2(D,B)))))))))) # label(t1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3518 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & v1_tsp_2(C,A)))) & v1_tsp_1(B,A)))))) # label(t9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.48/5.59 3519 -(all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B,A))))) # label(t10_tsp_2) # label(negated_conjecture) # label(non_clause). [assumption]. 5.48/5.59 5.48/5.59 ============================== end of process non-clausal formulas === 5.48/5.59 5.48/5.59 ============================== PROCESS INITIAL CLAUSES =============== 5.48/5.59 5.48/5.59 ============================== PREDICATE ELIMINATION ================= 5.48/5.59 3520 -r2_tarski(A,B) | r2_hidden(k4_tarski(f10(A,B,C),C),f9(A,B)) | -r2_hidden(C,B) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 3521 r2_tarski(A,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)) # label(t9_tarski) # label(axiom). [clausify(10)]. 5.48/5.59 Derived: r2_hidden(k4_tarski(f10(A,f7(B),C),C),f9(A,f7(B))) | -r2_hidden(C,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(3520,a,3521,a)]. 5.48/5.59 3522 -r2_tarski(A,B) | r2_hidden(f10(A,B,C),A) | -r2_hidden(C,B) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 Derived: r2_hidden(f10(A,f7(B),C),A) | -r2_hidden(C,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(3522,a,3521,a)]. 5.48/5.59 3523 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f9(A,B)) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | C != E | D = F # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 Derived: -r2_hidden(k4_tarski(A,B),f9(C,f7(D))) | -r2_hidden(k4_tarski(E,F),f9(C,f7(D))) | A != E | B = F | r2_hidden(C,f7(D)) | -r1_tarski(C,f7(D)). [resolve(3523,a,3521,a)]. 5.48/5.59 3524 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f9(A,B)) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | C = E | D != F # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 Derived: -r2_hidden(k4_tarski(A,B),f9(C,f7(D))) | -r2_hidden(k4_tarski(E,F),f9(C,f7(D))) | A = E | B != F | r2_hidden(C,f7(D)) | -r1_tarski(C,f7(D)). [resolve(3524,a,3521,a)]. 5.48/5.59 3525 -r2_tarski(A,B) | r2_hidden(f11(A,B,C),B) | -r2_hidden(C,A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 Derived: r2_hidden(f11(A,f7(B),C),f7(B)) | -r2_hidden(C,A) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(3525,a,3521,a)]. 5.48/5.59 3526 -r2_tarski(A,B) | r2_hidden(k4_tarski(C,f11(A,B,C)),f9(A,B)) | -r2_hidden(C,A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 Derived: r2_hidden(k4_tarski(A,f11(B,f7(C),A)),f9(B,f7(C))) | -r2_hidden(A,B) | r2_hidden(B,f7(C)) | -r1_tarski(B,f7(C)). [resolve(3526,a,3521,a)]. 5.48/5.59 3527 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f15(A,B,D),f16(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.59 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(3527,a,3520,a)]. 5.48/5.59 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(3527,a,3522,a)]. 5.48/5.59 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(3527,a,3523,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(3527,a,3524,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(3527,a,3525,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(3527,a,3526,a)]. 5.48/5.61 3528 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f15(A,B,D),f16(A,B,D)),D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(3528,a,3520,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(3528,a,3522,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(3528,a,3523,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(3528,a,3524,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(3528,a,3525,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(3528,a,3526,a)]. 5.48/5.61 3529 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(3529,a,3520,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(3529,a,3522,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(3529,a,3523,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(3529,a,3524,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(3529,a,3525,a)]. 5.48/5.61 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(3529,a,3526,a)]. 5.48/5.64 3530 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(3530,a,3520,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(3530,a,3522,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(3530,a,3523,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(3530,a,3524,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(3530,a,3525,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(3530,a,3526,a)]. 5.48/5.64 3531 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) = f13(A,B,D) | f16(A,B,D) = f14(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(3531,a,3520,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(3531,a,3522,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(3531,a,3523,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(3531,a,3524,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(3531,a,3525,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(3531,a,3526,a)]. 5.48/5.64 3532 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) = f13(A,B,D) | f16(A,B,D) = f14(A,B,D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(3532,a,3520,a)]. 5.48/5.64 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(3532,a,3522,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(3532,a,3523,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(3532,a,3524,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(3532,a,3525,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(3532,a,3526,a)]. 5.59/5.66 3533 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) != f13(A,B,D) | f16(A,B,D) != f14(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(3533,a,3520,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(3533,a,3522,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(3533,a,3523,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(3533,a,3524,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(3533,a,3525,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(3533,a,3526,a)]. 5.59/5.66 3534 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) != f13(A,B,D) | f16(A,B,D) != f14(A,B,D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(3534,a,3520,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(3534,a,3522,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(3534,a,3523,a)]. 5.59/5.66 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(3534,a,3524,a)]. 5.59/5.69 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(3534,a,3525,a)]. 5.59/5.69 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(3534,a,3526,a)]. 5.59/5.69 3535 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(3535,a,3520,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(3535,a,3522,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(3535,a,3523,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(3535,a,3524,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(3535,a,3525,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(3535,a,3526,a)]. 5.59/5.69 3536 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(3536,a,3520,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(3536,a,3522,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(3536,a,3523,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(3536,a,3524,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(3536,a,3525,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(3536,a,3526,a)]. 5.59/5.69 3537 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(3537,a,3520,a)]. 5.59/5.69 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(3537,a,3522,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(3537,a,3523,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(3537,a,3524,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(3537,a,3525,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(3537,a,3526,a)]. 5.67/5.71 3538 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(3538,a,3520,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(3538,a,3522,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(3538,a,3523,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(3538,a,3524,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(3538,a,3525,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(3538,a,3526,a)]. 5.67/5.71 3539 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(3539,a,3520,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(3539,a,3522,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(3539,a,3523,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(3539,a,3524,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(3539,a,3525,a)]. 5.67/5.71 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(3539,a,3526,a)]. 5.67/5.74 3540 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(3540,a,3520,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(3540,a,3522,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(3540,a,3523,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(3540,a,3524,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(3540,a,3525,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(3540,a,3526,a)]. 5.67/5.74 3541 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(3541,a,3520,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(3541,a,3522,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(3541,a,3523,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(3541,a,3524,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(3541,a,3525,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(3541,a,3526,a)]. 5.67/5.74 3542 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(3542,a,3520,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(3542,a,3522,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(3542,a,3523,a)]. 5.67/5.74 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(3542,a,3524,a)]. 61.08/61.24 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(3542,a,3525,a)]. 61.08/61.24 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(3542,a,3526,a)]. 61.08/61.24 3543 r2_tarski(A,f55(B)) | r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) # label(t136_zfmisc_1) # label(axiom). [clausify(308)]. 61.08/61.24 Derived: r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) | r2_hidden(k4_tarski(f10(A,f55(B),C),C),f9(A,f55(B))) | -r2_hidden(C,f55(B)). [resolve(3543,a,3520,a)]. 61.08/61.24 Derived: r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) | r2_hidden(f10(A,f55(B),C),A) | -r2_hidden(C,f55(B)). [resolve(3543,a,3522,a)]. 61.08/61.24 Derived: r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) | -r2_hidden(k4_tarski(C,D),f9(A,f55(B))) | -r2_hidden(k4_tarski(E,F),f9(A,f55(B))) | C != E | D = F. [resolve(3543,a,3523,a)]. 61.08/61.24 Derived: r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) | -r2_hidden(k4_tarski(C,D),f9(A,f55(B))) | -r2_hidden(k4_tarski(E,F),f9(A,f55(B))) | C = E | D != F. [resolve(3543,a,3524,a)]. 61.08/61.24 Derived: r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) | r2_hidden(f11(A,f55(B),C),f55(B)) | -r2_hidden(C,A). [resolve(3543,a,3525,a)]. 61.08/61.24 Derived: r2_hidden(A,f55(B)) | -r1_tarski(A,f55(B)) | r2_hidden(k4_tarski(C,f11(A,f55(B),C)),f9(A,f55(B))) | -r2_hidden(C,A). [resolve(3543,a,3526,a)]. 61.08/61.24 3544 r2_hidden(A,c8) | -r2_hidden(A,f1_s1_xboole_0) | -p1_s1_xboole_0(A) # label(s1_xboole_0) # label(axiom). [clausify(39)]. 61.08/61.24 3545 -r2_hidden(A,c8) | p1_s1_xboole_0(A) # label(s1_xboole_0) # label(axiom). [clausify(39)]. 61.08/61.24 3546 -m1_subset_1(A,f1_s3_subset_1) | r2_hidden(A,c12) | -p1_s3_subset_1(A) # label(s3_subset_1) # label(axiom). [clausify(396)]. 61.08/61.24 3547 -m1_subset_1(A,f1_s3_subset_1) | -r2_hidden(A,c12) | p1_s3_subset_1(A) # label(s3_subset_1) # label(axiom). [clausify(396)]. 61.08/61.24 3548 r2_hidden(A,c13) | -p1_s1_subset_1(A) | -r2_hidden(A,f1_s1_subset_1) # label(s1_subset_1) # label(axiom). [clausify(408)]. 61.08/61.24 3549 -r2_hidden(A,c13) | p1_s1_subset_1(A) # label(s1_subset_1) # label(axiom). [clausify(408)]. 61.08/61.24 3550 -v1_relat_1(A) | v2_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)) # label(d9_relat_1) # label(axiom). [clausify(501)]. 61.08/61.24 3551 -v1_relat_1(A) | -v2_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)) # label(d9_relat_1) # label(axiom). [clausify(501)]. 61.08/61.24 3552 -v1_funct_1(A) | -v2_relat_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)) # label(fc6_funct_1) # label(axiom). [clausify(683)]. 61.08/61.24 Derived: -v1_funct_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)) | -v1_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3552,b,3550,b)]. 61.08/61.24 3553 -v1_relat_1(A) | -v1_funct_1(A) | -v2_relat_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)) # label(d15_funct_1) # label(axiom). [clausify(781)]. 61.08/61.24 Derived: -v1_relat_1(A) | -v1_funct_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)) | -v1_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3553,c,3550,b)]. 61.08/61.24 3554 -v1_relat_1(A) | -v1_funct_1(A) | v2_relat_1(A) | v1_xboole_0(k1_funct_1(A,f153(A))) # label(d15_funct_1) # label(axiom). [clausify(781)]. 61.08/61.24 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_xboole_0(k1_funct_1(A,f153(A))) | -v1_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3554,c,3551,b)]. 61.08/61.24 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_xboole_0(k1_funct_1(A,f153(A))) | -v1_funct_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)). [resolve(3554,c,3552,b)]. 61.08/61.24 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_xboole_0(k1_funct_1(A,f153(A))) | -v1_relat_1(A) | -v1_funct_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)). [resolve(3554,c,3553,c)]. 61.08/61.24 3555 -v1_relat_1(A) | -v1_funct_1(A) | v2_relat_1(A) | r2_hidden(f153(A),k1_relat_1(A)) # label(d15_funct_1) # label(axiom). [clausify(781)]. 61.08/61.24 Derived: -v1_relat_1(A) | -v1_funct_1(A) | r2_hidden(f153(A),k1_relat_1(A)) | -v1_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3555,c,3551,b)]. 103.20/103.26 Derived: -v1_relat_1(A) | -v1_funct_1(A) | r2_hidden(f153(A),k1_relat_1(A)) | -v1_funct_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)). [resolve(3555,c,3552,b)]. 103.20/103.26 Derived: -v1_relat_1(A) | -v1_funct_1(A) | r2_hidden(f153(A),k1_relat_1(A)) | -v1_relat_1(A) | -v1_funct_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)). [resolve(3555,c,3553,c)]. 103.20/103.26 3556 v2_relat_1(c33) # label(rc5_funct_1) # label(axiom). [clausify(869)]. 103.20/103.26 Derived: -v1_relat_1(c33) | -r2_hidden(k1_xboole_0,k2_relat_1(c33)). [resolve(3556,a,3551,b)]. 103.20/103.26 Derived: -v1_funct_1(c33) | -v1_relat_1(c33) | v1_setfam_1(k2_relat_1(c33)). [resolve(3556,a,3552,b)]. 103.20/103.26 Derived: -v1_relat_1(c33) | -v1_funct_1(c33) | -v1_xboole_0(k1_funct_1(c33,A)) | -r2_hidden(A,k1_relat_1(c33)). [resolve(3556,a,3553,c)]. 103.20/103.26 3557 v1_xboole_0(A) | v2_relat_1(k2_funcop_1(B,A)) # label(fc9_funcop_1) # label(axiom). [clausify(1659)]. 103.20/103.26 Derived: v1_xboole_0(A) | -v1_relat_1(k2_funcop_1(B,A)) | -r2_hidden(k1_xboole_0,k2_relat_1(k2_funcop_1(B,A))). [resolve(3557,b,3551,b)]. 103.20/103.26 Derived: v1_xboole_0(A) | -v1_funct_1(k2_funcop_1(B,A)) | -v1_relat_1(k2_funcop_1(B,A)) | v1_setfam_1(k2_relat_1(k2_funcop_1(B,A))). [resolve(3557,b,3552,b)]. 103.20/103.26 Derived: v1_xboole_0(A) | -v1_relat_1(k2_funcop_1(B,A)) | -v1_funct_1(k2_funcop_1(B,A)) | -v1_xboole_0(k1_funct_1(k2_funcop_1(B,A),C)) | -r2_hidden(C,k1_relat_1(k2_funcop_1(B,A))). [resolve(3557,b,3553,c)]. 103.20/103.26 3558 p1_s1_relat_1(A,B) | -r2_hidden(k4_tarski(A,B),c17) # label(s1_relat_1) # label(axiom). [clausify(608)]. 103.20/103.26 3559 -p1_s1_relat_1(A,B) | -r2_hidden(B,f2_s1_relat_1) | -r2_hidden(A,f1_s1_relat_1) | r2_hidden(k4_tarski(A,B),c17) # label(s1_relat_1) # label(axiom). [clausify(608)]. 103.20/103.26 3560 -v1_relat_1(A) | v7_relat_2(A) | -r7_relat_2(A,k3_relat_1(A)) # label(d15_relat_2) # label(axiom). [clausify(930)]. 103.20/103.26 3561 -v1_relat_1(A) | -v7_relat_2(A) | v6_relat_2(A) # label(t46_relat_2) # label(axiom). [clausify(885)]. 103.20/103.26 3562 -v1_relat_1(A) | -v7_relat_2(A) | v1_relat_2(A) # label(t46_relat_2) # label(axiom). [clausify(885)]. 103.20/103.26 3563 -v1_relat_1(A) | -v7_relat_2(A) | r7_relat_2(A,k3_relat_1(A)) # label(d15_relat_2) # label(axiom). [clausify(930)]. 103.20/103.26 Derived: -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | v6_relat_2(A). [resolve(3560,b,3561,b)]. 103.20/103.26 Derived: -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | v1_relat_2(A). [resolve(3560,b,3562,b)]. 103.20/103.26 3564 -v1_relat_1(A) | -v7_relat_2(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) = k2_xboole_0(A,k4_relat_1(A)) # label(t47_relat_2) # label(axiom). [clausify(931)]. 103.20/103.26 Derived: -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) = k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)). [resolve(3564,b,3560,b)]. 103.20/103.26 3565 -v1_relat_1(A) | v7_relat_2(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) # label(t47_relat_2) # label(axiom). [clausify(931)]. 103.20/103.26 Derived: -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | v6_relat_2(A). [resolve(3565,b,3561,b)]. 103.20/103.26 Derived: -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | v1_relat_2(A). [resolve(3565,b,3562,b)]. 103.20/103.26 Derived: -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | r7_relat_2(A,k3_relat_1(A)). [resolve(3565,b,3563,b)]. 103.20/103.26 3566 -v1_relat_1(A) | v6_relat_2(A) | -r6_relat_2(A,k3_relat_1(A)) # label(d14_relat_2) # label(axiom). [clausify(915)]. 103.20/103.26 3567 -v1_relat_1(A) | -v6_relat_2(A) | r6_relat_2(A,k3_relat_1(A)) # label(d14_relat_2) # label(axiom). [clausify(915)]. 103.20/103.26 3568 -v1_relat_1(A) | -v6_relat_2(A) | r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))) # label(t45_relat_2) # label(axiom). [clausify(923)]. 103.20/103.26 Derived: -v1_relat_1(A) | r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))) | -v1_relat_1(A) | -r6_relat_2(A,k3_relat_1(A)). [resolve(3568,b,3566,b)]. 103.20/103.26 3569 -v1_relat_1(A) | v6_relat_2(A) | -r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))) # label(t45_relat_2) # label(axiom). [clausify(923)]. 116.87/116.94 Derived: -v1_relat_1(A) | -r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))) | -v1_relat_1(A) | r6_relat_2(A,k3_relat_1(A)). [resolve(3569,b,3567,b)]. 116.87/116.94 3570 -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | v6_relat_2(A). [resolve(3560,b,3561,b)]. 116.87/116.94 Derived: -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | -v1_relat_1(A) | r6_relat_2(A,k3_relat_1(A)). [resolve(3570,d,3567,b)]. 116.87/116.94 Derived: -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | -v1_relat_1(A) | r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))). [resolve(3570,d,3568,b)]. 116.87/116.94 3571 -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | v6_relat_2(A). [resolve(3565,b,3561,b)]. 116.87/116.94 Derived: -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | -v1_relat_1(A) | r6_relat_2(A,k3_relat_1(A)). [resolve(3571,d,3567,b)]. 116.87/116.94 Derived: -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | -v1_relat_1(A) | -v1_relat_1(A) | r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A))). [resolve(3571,d,3568,b)]. 116.87/116.94 3572 v3_ordinal1(A) | -v1_ordinal1(A) | -v2_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(963)]. 116.87/116.94 3573 -v3_ordinal1(A) | v1_ordinal1(k3_tarski(A)) # label(fc4_ordinal1) # label(axiom). [clausify(939)]. 116.87/116.94 3574 v1_ordinal1(c34) # label(rc3_ordinal1) # label(axiom). [clausify(942)]. 116.87/116.94 3575 -v3_ordinal1(A) | v1_ordinal1(k1_ordinal1(A)) # label(fc3_ordinal1) # label(axiom). [clausify(956)]. 116.87/116.94 3576 -v3_ordinal1(A) | v1_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(963)]. 116.87/116.94 Derived: v3_ordinal1(k3_tarski(A)) | -v2_ordinal1(k3_tarski(A)) | -v3_ordinal1(A). [resolve(3572,b,3573,b)]. 116.87/116.94 Derived: v3_ordinal1(c34) | -v2_ordinal1(c34). [resolve(3572,b,3574,a)]. 116.87/116.94 3577 v1_ordinal1(c36) # label(rc2_ordinal1) # label(axiom). [clausify(967)]. 116.87/116.94 3578 -v1_ordinal1(A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r1_tarski(A,B) | -r2_hidden(B,C) | r2_hidden(A,C) # label(t22_ordinal1) # label(axiom). [clausify(970)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(k3_tarski(C),A) | -r2_hidden(A,B) | r2_hidden(k3_tarski(C),B) | -v3_ordinal1(C). [resolve(3578,a,3573,b)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(c34,A) | -r2_hidden(A,B) | r2_hidden(c34,B). [resolve(3578,a,3574,a)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(k1_ordinal1(C),A) | -r2_hidden(A,B) | r2_hidden(k1_ordinal1(C),B) | -v3_ordinal1(C). [resolve(3578,a,3575,b)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(C,A) | -r2_hidden(A,B) | r2_hidden(C,B) | -v3_ordinal1(C). [resolve(3578,a,3576,b)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(c36,A) | -r2_hidden(A,B) | r2_hidden(c36,B). [resolve(3578,a,3577,a)]. 116.87/116.94 3579 -v3_ordinal1(A) | -v3_ordinal1(B) | -v1_ordinal1(C) | -r2_hidden(C,A) | -r2_hidden(A,B) | r2_hidden(C,B) # label(t19_ordinal1) # label(axiom). [clausify(975)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(k3_tarski(C),A) | -r2_hidden(A,B) | r2_hidden(k3_tarski(C),B) | -v3_ordinal1(C). [resolve(3579,c,3573,b)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(c34,A) | -r2_hidden(A,B) | r2_hidden(c34,B). [resolve(3579,c,3574,a)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(k1_ordinal1(C),A) | -r2_hidden(A,B) | r2_hidden(k1_ordinal1(C),B) | -v3_ordinal1(C). [resolve(3579,c,3575,b)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(C,A) | -r2_hidden(A,B) | r2_hidden(C,B) | -v3_ordinal1(C). [resolve(3579,c,3576,b)]. 116.87/116.94 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(c36,A) | -r2_hidden(A,B) | r2_hidden(c36,B). [resolve(3579,c,3577,a)]. 116.87/116.94 3580 -v1_ordinal1(A) | -v2_ordinal1(A) | v3_ordinal1(A) # label(cc2_ordinal1) # label(axiom). [clausify(977)]. 116.93/117.00 Derived: -v2_ordinal1(c36) | v3_ordinal1(c36). [resolve(3580,a,3577,a)]. 116.93/117.00 3581 -v1_ordinal1(A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B) # label(t21_ordinal1) # label(axiom). [clausify(979)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(k3_tarski(B),A) | r2_hidden(k3_tarski(B),A) | -v3_ordinal1(B). [resolve(3581,a,3573,b)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(c34,A) | r2_hidden(c34,A). [resolve(3581,a,3574,a)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(k1_ordinal1(B),A) | r2_hidden(k1_ordinal1(B),A) | -v3_ordinal1(B). [resolve(3581,a,3575,b)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(B,A) | r2_hidden(B,A) | -v3_ordinal1(B). [resolve(3581,a,3576,b)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(c36,A) | r2_hidden(c36,A). [resolve(3581,a,3577,a)]. 116.93/117.00 3582 -v3_ordinal1(A) | v1_ordinal1(A) # label(cc1_ordinal1) # label(axiom). [clausify(983)]. 116.93/117.00 3583 v1_ordinal1(c38) # label(rc1_ordinal1) # label(axiom). [clausify(991)]. 116.93/117.00 Derived: v3_ordinal1(c38) | -v2_ordinal1(c38). [resolve(3583,a,3572,b)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(c38,A) | -r2_hidden(A,B) | r2_hidden(c38,B). [resolve(3583,a,3578,a)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(c38,A) | -r2_hidden(A,B) | r2_hidden(c38,B). [resolve(3583,a,3579,c)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(c38,A) | r2_hidden(c38,A). [resolve(3583,a,3581,a)]. 116.93/117.00 3584 -v1_xboole_0(A) | v1_ordinal1(A) # label(cc3_ordinal1) # label(axiom). [clausify(996)]. 116.93/117.00 Derived: -v1_xboole_0(A) | v3_ordinal1(A) | -v2_ordinal1(A). [resolve(3584,b,3572,b)]. 116.93/117.00 Derived: -v1_xboole_0(A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r1_tarski(A,B) | -r2_hidden(B,C) | r2_hidden(A,C). [resolve(3584,b,3578,a)]. 116.93/117.00 Derived: -v1_xboole_0(A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r2_hidden(A,B) | -r2_hidden(B,C) | r2_hidden(A,C). [resolve(3584,b,3579,c)]. 116.93/117.00 Derived: -v1_xboole_0(A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B). [resolve(3584,b,3581,a)]. 116.93/117.00 3585 v1_ordinal1(k1_xboole_0) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 116.93/117.00 Derived: v3_ordinal1(k1_xboole_0) | -v2_ordinal1(k1_xboole_0). [resolve(3585,a,3572,b)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r1_tarski(k1_xboole_0,A) | -r2_hidden(A,B) | r2_hidden(k1_xboole_0,B). [resolve(3585,a,3578,a)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(k1_xboole_0,A) | -r2_hidden(A,B) | r2_hidden(k1_xboole_0,B). [resolve(3585,a,3579,c)]. 116.93/117.00 Derived: -v3_ordinal1(A) | -r2_xboole_0(k1_xboole_0,A) | r2_hidden(k1_xboole_0,A). [resolve(3585,a,3581,a)]. 116.93/117.00 3586 -v1_ordinal1(A) | -r2_hidden(B,A) | r1_tarski(B,A) # label(d2_ordinal1) # label(axiom). [clausify(1008)]. 116.93/117.00 Derived: -r2_hidden(A,k3_tarski(B)) | r1_tarski(A,k3_tarski(B)) | -v3_ordinal1(B). [resolve(3586,a,3573,b)]. 116.93/117.00 Derived: -r2_hidden(A,c34) | r1_tarski(A,c34). [resolve(3586,a,3574,a)]. 116.93/117.00 Derived: -r2_hidden(A,k1_ordinal1(B)) | r1_tarski(A,k1_ordinal1(B)) | -v3_ordinal1(B). [resolve(3586,a,3575,b)]. 116.93/117.00 Derived: -r2_hidden(A,B) | r1_tarski(A,B) | -v3_ordinal1(B). [resolve(3586,a,3576,b)]. 116.93/117.00 Derived: -r2_hidden(A,c36) | r1_tarski(A,c36). [resolve(3586,a,3577,a)]. 116.93/117.00 Derived: -r2_hidden(A,c38) | r1_tarski(A,c38). [resolve(3586,a,3583,a)]. 116.93/117.00 Derived: -r2_hidden(A,B) | r1_tarski(A,B) | -v1_xboole_0(B). [resolve(3586,a,3584,b)]. 116.93/117.00 Derived: -r2_hidden(A,k1_xboole_0) | r1_tarski(A,k1_xboole_0). [resolve(3586,a,3585,a)]. 116.93/117.00 3587 v1_ordinal1(A) | r2_hidden(f199(A),A) # label(d2_ordinal1) # label(axiom). [clausify(1008)]. 116.93/117.00 Derived: r2_hidden(f199(A),A) | v3_ordinal1(A) | -v2_ordinal1(A). [resolve(3587,a,3572,b)]. 116.93/117.00 Derived: r2_hidden(f199(A),A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r1_tarski(A,B) | -r2_hidden(B,C) | r2_hidden(A,C). [resolve(3587,a,3578,a)]. 116.93/117.00 Derived: r2_hidden(f199(A),A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r2_hidden(A,B) | -r2_hidden(B,C) | r2_hidden(A,C). [resolve(3587,a,3579,c)]. 116.93/117.00 Derived: r2_hidden(f199(A),A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B). [resolve(3587,a,3581,a)]. 116.93/117.00 Derived: r2_hidden(f199(A),A) | -r2_Alarm clock 120.01/120.04 Prover9 interrupted 120.01/120.04 EOF