0.01/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n007.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 : 960 0.12/0.33 % DateTime : Thu Jul 2 14:33:26 EDT 2020 0.12/0.33 % CPUTime : 3.87/4.35 ============================== Prover9 =============================== 3.87/4.35 Prover9 (32) version 2009-11A, November 2009. 3.87/4.35 Process 2566 was started by sandbox2 on n007.cluster.edu, 3.87/4.35 Thu Jul 2 14:33:30 2020 3.87/4.35 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_2238_n007.cluster.edu". 3.87/4.35 ============================== end of head =========================== 3.87/4.35 3.87/4.35 ============================== INPUT ================================= 3.87/4.35 3.87/4.35 % Reading from file /tmp/Prover9_2238_n007.cluster.edu 3.87/4.35 3.87/4.35 set(prolog_style_variables). 3.87/4.35 set(auto2). 3.87/4.35 % set(auto2) -> set(auto). 3.87/4.35 % set(auto) -> set(auto_inference). 3.87/4.35 % set(auto) -> set(auto_setup). 3.87/4.35 % set(auto_setup) -> set(predicate_elim). 3.87/4.35 % set(auto_setup) -> assign(eq_defs, unfold). 3.87/4.35 % set(auto) -> set(auto_limits). 3.87/4.35 % set(auto_limits) -> assign(max_weight, "100.000"). 3.87/4.35 % set(auto_limits) -> assign(sos_limit, 20000). 3.87/4.35 % set(auto) -> set(auto_denials). 3.87/4.35 % set(auto) -> set(auto_process). 3.87/4.35 % set(auto2) -> assign(new_constants, 1). 3.87/4.35 % set(auto2) -> assign(fold_denial_max, 3). 3.87/4.35 % set(auto2) -> assign(max_weight, "200.000"). 3.87/4.35 % set(auto2) -> assign(max_hours, 1). 3.87/4.35 % assign(max_hours, 1) -> assign(max_seconds, 3600). 3.87/4.35 % set(auto2) -> assign(max_seconds, 0). 3.87/4.35 % set(auto2) -> assign(max_minutes, 5). 3.87/4.35 % assign(max_minutes, 5) -> assign(max_seconds, 300). 3.87/4.35 % set(auto2) -> set(sort_initial_sos). 3.87/4.35 % set(auto2) -> assign(sos_limit, -1). 3.87/4.35 % set(auto2) -> assign(lrs_ticks, 3000). 3.87/4.35 % set(auto2) -> assign(max_megs, 400). 3.87/4.35 % set(auto2) -> assign(stats, some). 3.87/4.35 % set(auto2) -> clear(echo_input). 3.87/4.35 % set(auto2) -> set(quiet). 3.87/4.35 % set(auto2) -> clear(print_initial_clauses). 3.87/4.35 % set(auto2) -> clear(print_given). 3.87/4.35 assign(lrs_ticks,-1). 3.87/4.35 assign(sos_limit,10000). 3.87/4.35 assign(order,kbo). 3.87/4.35 set(lex_order_vars). 3.87/4.35 clear(print_given). 3.87/4.35 3.87/4.35 % formulas(sos). % not echoed (3677 formulas) 3.87/4.35 3.87/4.35 ============================== end of input ========================== 3.87/4.35 3.87/4.35 % From the command line: assign(max_seconds, 960). 3.87/4.35 3.87/4.35 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.87/4.35 3.87/4.35 % Formulas that are not ordinary clauses: 3.87/4.35 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 2 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 3 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 4 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 5 (all A all B ((all C ((exists D (r2_hidden(C,D) & r2_hidden(D,A))) <-> r2_hidden(C,B))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 6 (all A all B all C (C = k2_tarski(A,B) <-> (all D (D = A | D = B <-> r2_hidden(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 7 (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]. 3.87/4.35 8 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 9 (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]. 3.87/4.35 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 11 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 12 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 13 (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]. 3.87/4.35 14 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 15 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 16 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 17 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C))) & 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) -> (G = E <-> F = D))) & (all D -((all E -(r2_hidden(k4_tarski(D,E),C) & r2_hidden(E,B))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 18 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 19 (all A all B (k1_tarski(A) = B <-> (all C (r2_hidden(C,B) <-> A = C)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 20 (all A all B -((all C -((all D -(r2_hidden(D,C) & r2_hidden(D,B))) & r2_hidden(C,B))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 21 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 22 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 23 (all A exists B (r2_hidden(A,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 all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 24 (all A all B all C -(r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)) & r1_xboole_0(A,B) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 25 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 26 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 27 (all A (k1_xboole_0 = A <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 28 (all A all B all C ((all D (-r2_hidden(D,B) & r2_hidden(D,A) <-> r2_hidden(D,C))) <-> k4_xboole_0(A,B) = C)) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 29 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 30 (all A all B all C ((all D ((r2_hidden(D,B) <-> r2_hidden(D,C)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 31 (all A all B all C (-(r2_hidden(A,B) <-> r2_hidden(A,C)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 32 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) & r2_hidden(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 33 (all A all B (r1_xboole_0(A,B) <-> k3_xboole_0(A,B) = k1_xboole_0)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 34 (all A all B all C ((all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))) <-> C = k2_xboole_0(A,B))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 35 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 36 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 37 (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]. 3.87/4.35 38 (all A all B (r3_xboole_0(A,B) <-> r1_tarski(B,A) | r1_tarski(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 39 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 40 (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]. 3.87/4.35 41 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 42 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) -> f2_s2_xboole_0 = f1_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 43 (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]. 3.87/4.35 44 (all A all B (r2_xboole_0(A,B) <-> B != A & r1_tarski(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 45 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 46 (all A all B (-(-r1_xboole_0(A,B) & (all C -r2_hidden(C,k3_xboole_0(A,B)))) & -(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 47 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 48 (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]. 3.87/4.35 49 (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]. 3.87/4.35 50 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 51 (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]. 3.87/4.35 52 (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]. 3.87/4.35 53 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k5_xboole_0(A,B)) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 54 (all A all B k2_xboole_0(B,A) = k2_xboole_0(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 55 (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]. 3.87/4.35 56 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 57 (all A (v1_xboole_0(A) <-> A = k1_xboole_0)) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 58 (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]. 3.87/4.35 59 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 60 (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]. 3.87/4.35 61 (all A all B -(v1_xboole_0(B) & B != A & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 62 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 63 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 64 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 65 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 66 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 67 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 68 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 69 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 70 (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]. 3.87/4.35 71 (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]. 3.87/4.35 72 (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]. 3.87/4.35 73 (all A (r1_tarski(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 74 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 75 (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]. 3.87/4.35 76 (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]. 3.87/4.35 77 (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]. 3.87/4.35 78 (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]. 3.87/4.35 79 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 80 (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]. 3.87/4.35 81 (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]. 3.87/4.35 82 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 83 (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]. 3.87/4.35 84 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 85 (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]. 3.87/4.35 86 (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]. 3.87/4.35 87 (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]. 3.87/4.35 88 (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]. 3.87/4.35 89 (all A all B all C all D (r1_xboole_0(D,B) & r1_xboole_0(C,A) & k2_xboole_0(A,B) = k2_xboole_0(C,D) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 90 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 91 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 92 (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]. 3.87/4.35 93 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 94 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(A,C) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 95 (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]. 3.87/4.35 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]. 3.87/4.35 97 (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]. 3.87/4.35 98 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 99 (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]. 3.87/4.35 100 (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]. 3.87/4.35 101 (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]. 3.87/4.35 102 (all A all B all C (r1_tarski(B,C) & r2_xboole_0(A,B) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 103 (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]. 3.87/4.35 104 (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]. 3.87/4.35 105 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 106 (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]. 3.87/4.35 107 (all A all B all C (-(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) & r1_xboole_0(A,B)) & -(r1_xboole_0(A,k2_xboole_0(B,C)) & -(r1_xboole_0(A,C) & r1_xboole_0(A,B))))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 108 (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]. 3.87/4.35 109 (all A all B k5_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 110 (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]. 3.87/4.35 111 (all A all B k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 112 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 113 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 114 (all A all B (r1_xboole_0(A,B) <-> k4_xboole_0(A,B) = A)) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 115 (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]. 3.87/4.35 116 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 117 (all A all B all C -(-r1_xboole_0(A,B) & r1_tarski(A,C) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 118 (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]. 3.87/4.35 119 (all A all B all C (-v1_xboole_0(C) -> -(r1_xboole_0(A,B) & r1_tarski(C,B) & r1_tarski(C,A)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 120 (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]. 3.87/4.35 121 (all A all B k3_xboole_0(A,B) = k4_xboole_0(A,k4_xboole_0(A,B))) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 122 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(C,D) & r1_xboole_0(B,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 123 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(A,C))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 124 (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]. 3.87/4.35 125 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 126 (all A all B all C (r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) & r1_tarski(A,B) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 127 (all A all B -(r2_xboole_0(A,B) & k1_xboole_0 = k4_xboole_0(B,A))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 128 (all A all B (k4_xboole_0(A,B) = k4_xboole_0(B,A) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 129 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 130 (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]. 3.87/4.35 131 (all A all B all C (r1_tarski(A,B) & r1_tarski(B,C) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 132 (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]. 3.87/4.35 133 (all A all B all C k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A)) = k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 134 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 135 (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]. 3.87/4.35 136 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 137 (all A all B (k2_xboole_0(A,B) = k1_xboole_0 -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 138 (all A (k1_xboole_0 != A -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 139 (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]. 3.87/4.35 140 (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]. 3.87/4.35 141 (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]. 3.87/4.35 142 (all A all B all C all D (r1_tarski(A,B) & r1_xboole_0(B,D) & r1_tarski(C,D) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 143 (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]. 3.87/4.35 144 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 145 (all A (-(A != k1_xboole_0 & r1_xboole_0(A,A)) & -(-r1_xboole_0(A,A) & k1_xboole_0 = A))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 146 (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]. 3.87/4.35 147 (all A all B all C -(r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)) & -r1_xboole_0(A,B))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 148 (all A all B all C (r1_tarski(A,C) & r1_tarski(A,B) & r1_xboole_0(B,C) -> A = k1_xboole_0)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.35 149 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> A = k1_xboole_0)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 150 (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]. 3.87/4.36 151 (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]. 3.87/4.36 152 (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]. 3.87/4.36 153 (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]. 3.87/4.36 154 (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]. 3.87/4.36 155 (all A all B all C k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C)) = k2_xboole_0(A,k3_xboole_0(B,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 156 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 157 (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]. 3.87/4.36 158 (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]. 3.87/4.36 159 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,k4_xboole_0(B,A)) = B)) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 160 (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]. 3.87/4.36 161 (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]. 3.87/4.36 162 (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]. 3.87/4.36 163 (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]. 3.87/4.36 164 (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]. 3.87/4.36 165 (all A all B (-v1_xboole_0(B) -> -(r1_xboole_0(B,A) & r1_tarski(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 166 (all A all B -(r1_xboole_0(k3_xboole_0(A,B),B) & -r1_xboole_0(A,B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 167 (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]. 3.87/4.36 168 (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]. 3.87/4.36 169 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 170 (all A all B all C (r1_tarski(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 171 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 172 (all A all B all C k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C))) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 173 (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]. 3.87/4.36 174 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 175 (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]. 3.87/4.36 176 (all A all B (-(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 177 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 178 (all A all B all C (r1_xboole_0(C,B) & k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(A,B) -> C = A)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 179 (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]. 3.87/4.36 180 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 181 (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]. 3.87/4.36 182 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 183 (all A all B -(k1_xboole_0 != A & k1_tarski(B) != A & k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0)) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 184 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 185 (all A all B (r2_hidden(A,B) -> k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 186 (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]. 3.87/4.36 187 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 188 (all A all B all C -(-(k1_tarski(A) = C & B = k1_xboole_0) & -(B = k1_tarski(A) & k1_xboole_0 = C) & -(B = k1_tarski(A) & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 189 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 190 (all A all B all C (r1_tarski(k2_tarski(A,B),C) <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 191 (all A all B all C -(-r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(A,B) & -r2_hidden(C,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 192 (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]. 3.87/4.36 193 (all A all B all C (k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 194 (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]. 3.87/4.36 195 (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]. 3.87/4.36 196 (all A all B all C (k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k4_xboole_0(A,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 197 (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]. 3.87/4.36 198 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 199 (all A all B (k1_zfmisc_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 200 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 201 (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]. 3.87/4.36 202 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 203 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 204 (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]. 3.87/4.36 205 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 206 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 207 (all A all B all C all D k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D)))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 208 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 209 (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),D) <-> r2_hidden(k4_tarski(G,H),A))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 210 (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]. 3.87/4.36 211 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> k2_zfmisc_1(A,B) = k1_xboole_0 | r1_tarski(A,C) & r1_tarski(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 212 (all A all B (r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 213 (all A all B k2_tarski(A,B) = k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B)))) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 214 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 215 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 216 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 217 (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)) & k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k3_xboole_0(A,B),C))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 218 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 219 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 220 (all A all B (k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 221 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & B = D)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 222 (all A all B k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B)) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 223 (all A exists B ((all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(-r2_tarski(C,B) & r1_tarski(C,B) & -r2_hidden(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 224 (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]. 3.87/4.36 225 (all A all B all C (k1_xboole_0 = k4_xboole_0(k2_tarski(A,B),C) <-> r2_hidden(B,C) & r2_hidden(A,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 226 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> 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]. 3.87/4.36 227 (all A all B all C all D -(A != D & A != C & k2_tarski(A,B) = k2_tarski(C,D))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 228 (all A A = k3_tarski(k1_zfmisc_1(A))) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 229 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 230 (all A all B k2_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k2_xboole_0(A,B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 231 (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]. 3.87/4.36 232 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(k1_tarski(C) != A & A != k1_tarski(B) & A != k1_xboole_0 & k2_tarski(B,C) != A))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 233 (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]. 3.87/4.36 234 (all A all B (A != B -> k5_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 235 (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]. 3.87/4.36 236 (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]. 3.87/4.36 237 (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]. 3.87/4.36 238 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 239 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 240 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & r2_hidden(F,C) & k4_tarski(E,F) = D)) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 241 (all A all B (k1_xboole_0 = A | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 242 (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]. 3.87/4.36 243 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 244 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 245 (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]. 3.87/4.36 246 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 247 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(B,D) & r2_hidden(A,C))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 248 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 249 (all A all B all C (r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) | C != A & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 250 (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]. 3.87/4.36 251 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> r1_xboole_0(C,D) | C = D)) -> k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 252 (all A all B all C (-r2_hidden(A,C) & -r2_hidden(B,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 253 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 254 (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]. 3.87/4.36 255 (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]. 3.87/4.36 256 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 257 (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]. 3.87/4.36 258 (all A all B all C (-(A != k2_tarski(B,C) & A != k1_tarski(C) & k1_tarski(B) != A & A != k1_xboole_0) <-> k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0)) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 259 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 260 (all A all B (k1_tarski(A) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 261 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 262 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(r2_hidden(F,k3_xboole_0(B,D)) & r2_hidden(G,k3_xboole_0(C,E)) & A = k4_tarski(F,G))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 263 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 264 (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]. 3.87/4.36 265 (all A all B all C all D (B = D & r2_hidden(A,C) <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 266 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 267 (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]. 3.87/4.36 268 (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]. 3.87/4.36 269 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 270 (all A all B all C (k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C) <-> (B = A | r2_hidden(B,C)) & -r2_hidden(A,C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 271 (all A all B all C (k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) = k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) & k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 272 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 273 (all A all B -(k1_tarski(B) != A & (all C -(r2_hidden(C,A) & C != B)) & k1_xboole_0 != A)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 274 (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]. 3.87/4.36 275 (all A all B all C k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 276 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 277 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r2_hidden(C,B) <-> r1_tarski(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 278 (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]. 3.87/4.36 279 (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]. 3.87/4.36 280 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> B = A | B = k1_xboole_0 | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 281 (all A all B all C all 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)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 282 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 283 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 284 (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]. 3.87/4.36 285 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> r2_hidden(B,D) & C = A)) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 286 (all A all B (k1_xboole_0 != A -> k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0 & k2_zfmisc_1(A,k1_tarski(B)) != k1_xboole_0)) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 287 (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]. 3.87/4.36 288 (all A all B all C -(A != B & r1_tarski(k1_tarski(A),k2_tarski(B,C)) & A != C)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 289 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 290 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 291 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> D = B & A = C)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 292 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 293 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k2_xboole_0(k2_tarski(A,C),B) = B)) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 294 (all A all B all 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))) & A != k1_xboole_0 & -r1_tarski(B,C))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 295 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 296 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) | k4_xboole_0(k1_tarski(A),B) = k1_xboole_0)) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 297 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 298 (all A all B all C (k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) = k2_zfmisc_1(C,k2_tarski(A,B)) & k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)) = k2_zfmisc_1(k2_tarski(A,B),C))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 299 (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]. 3.87/4.36 300 (all A all B all C -(r1_xboole_0(k2_tarski(A,B),C) & r2_hidden(A,C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 301 (all A all B (r1_tarski(A,k1_tarski(B)) <-> A = k1_tarski(B) | k1_xboole_0 = A)) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 302 (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]. 3.87/4.36 303 (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]. 3.87/4.36 304 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 305 (all A all B -(r1_xboole_0(k1_tarski(A),B) & r2_hidden(A,B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 306 (all A all B (r2_hidden(A,B) <-> r1_tarski(k1_tarski(A),B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 307 (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]. 3.87/4.36 308 (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]. 3.87/4.36 309 (all A k2_tarski(k1_xboole_0,k1_tarski(A)) = k1_zfmisc_1(k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 310 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 311 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 312 (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]. 3.87/4.36 313 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))) <-> C = k2_zfmisc_1(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 314 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) <-> A != B)) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 315 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 316 (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]. 3.87/4.36 317 (all A all B k1_tarski(A) = k3_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 318 (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]. 3.87/4.36 319 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)) -> 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]. 3.87/4.36 320 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & B != C & k1_xboole_0 != B & C != k1_xboole_0)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 321 (all A all B k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 322 (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]. 3.87/4.36 323 (all A all B all C -(r2_hidden(B,C) & k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) & A != B)) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 324 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 325 (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 k4_tarski(D,E) != C))) & (all C -(r2_hidden(C,B) & (all D all E C != k4_tarski(D,E)))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 326 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 327 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 328 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> B = D & C = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 329 (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]. 3.87/4.36 330 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 331 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 332 (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]. 3.87/4.36 333 (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(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 334 (all A (k1_xboole_0 != A -> (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]. 3.87/4.36 335 (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]. 3.87/4.36 336 (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]. 3.87/4.36 337 (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,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 338 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 339 (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(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 340 (all A all B all C all D (-v1_xboole_0(C) & -v1_xboole_0(D) & -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]. 3.87/4.36 341 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 342 (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]. 3.87/4.36 343 (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)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 344 (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]. 3.87/4.36 345 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 346 (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]. 3.87/4.36 347 (all A k3_subset_1(A,k1_subset_1(A)) = k2_subset_1(A)) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 348 (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) -> (k1_xboole_0 != A -> 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]. 3.87/4.36 349 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 350 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 351 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 352 (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]. 3.87/4.36 353 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)) & (all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 354 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 355 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 356 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,k3_subset_1(A,C)) & r2_hidden(B,C)))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 357 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 358 (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]. 3.87/4.36 359 (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]. 3.87/4.36 360 (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]. 3.87/4.36 361 (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]. 3.87/4.36 362 (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]. 3.87/4.36 363 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 364 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k2_xboole_0(B,C) = k4_subset_1(A,B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 365 (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]. 3.87/4.36 366 (all A A = k2_subset_1(A)) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.36 367 (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,C) <-> r2_hidden(E,D))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 368 (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]. 3.87/4.37 369 (all A all B ((-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))) & (v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 370 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 371 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 372 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 373 (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) -> (A != k1_xboole_0 -> 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]. 3.87/4.37 374 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_xboole_0(A,B) <-> r1_subset_1(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 375 (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,C,B) = k4_subset_1(A,B,C))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 376 (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),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 377 (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]. 3.87/4.37 378 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 379 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 380 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 381 (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]. 3.87/4.37 382 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 383 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 384 (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,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 385 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 386 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 387 (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]. 3.87/4.37 388 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & B != k1_xboole_0))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 389 (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) -> (A != k1_xboole_0 -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 390 (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]. 3.87/4.37 391 (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(k3_subset_1(A,B),k3_subset_1(A,C)) & r1_xboole_0(B,C) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 392 (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(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 393 (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]. 3.87/4.37 394 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 395 (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]. 3.87/4.37 396 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 397 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) & r1_tarski(B,C) -> k1_xboole_0 = B))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 398 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 399 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 400 (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]. 3.87/4.37 401 (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]. 3.87/4.37 402 (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]. 3.87/4.37 403 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 404 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 405 (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) -> (k1_xboole_0 != A -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 406 (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)))) -> f3_s4_subset_1 = f2_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 407 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 408 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 409 (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]. 3.87/4.37 410 (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(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 411 (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]. 3.87/4.37 412 (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]. 3.87/4.37 413 (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]. 3.87/4.37 414 (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]. 3.87/4.37 415 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 416 (exists A ((all B (p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1) <-> r2_hidden(B,A))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 417 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 418 (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]. 3.87/4.37 419 (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,D) | r2_hidden(E,C) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 420 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_xboole_0(A,B) = k3_subset_1(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 421 (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]. 3.87/4.37 422 (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]. 3.87/4.37 423 (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]. 3.87/4.37 424 (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]. 3.87/4.37 425 (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]. 3.87/4.37 426 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 427 (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_xboole_0(B,k3_subset_1(A,C))))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 428 (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]. 3.87/4.37 429 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k3_xboole_0(B,C) = k5_subset_1(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 430 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 431 (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,B) = B)) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 432 (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]. 3.87/4.37 433 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 434 (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) = k5_xboole_0(B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 435 (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]. 3.87/4.37 436 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 437 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (B = k1_subset_1(A) <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 438 (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]. 3.87/4.37 439 (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]. 3.87/4.37 440 (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]. 3.87/4.37 441 (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]. 3.87/4.37 442 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 443 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 444 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 445 (all A all B all C -(v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 446 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 447 (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]. 3.87/4.37 448 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 449 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 450 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v3_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 451 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 452 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 453 (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]. 3.87/4.37 454 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 455 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & A != k1_xboole_0))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 456 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 457 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 458 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 459 (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]. 3.87/4.37 460 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 461 (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]. 3.87/4.37 462 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 463 (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]. 3.87/4.37 464 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E ((exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))) <-> r2_hidden(k4_tarski(D,E),C))) <-> k5_relat_1(A,B) = C))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 465 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C -r2_hidden(C,k1_relat_1(B)))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 466 (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]. 3.87/4.37 467 (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)) -> k1_relat_1(E) = k2_tarski(A,C) & k2_tarski(B,D) = k2_relat_1(E)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 468 (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]. 3.87/4.37 469 (all A (v1_relat_1(A) -> (k1_relat_1(A) = k1_xboole_0 <-> k1_xboole_0 = k2_relat_1(A)))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 470 (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]. 3.87/4.37 471 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 472 (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]. 3.87/4.37 473 (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]. 3.87/4.37 474 (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]. 3.87/4.37 475 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 476 (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]. 3.87/4.37 477 (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]. 3.87/4.37 478 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 479 (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]. 3.87/4.37 480 (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]. 3.87/4.37 481 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 482 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 483 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 3.87/4.37 484 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 485 (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]. 4.29/4.37 486 (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]. 4.29/4.37 487 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 488 (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]. 4.29/4.37 489 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 490 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_relat_1(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 491 (all A (v1_relat_1(A) -> k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 492 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 493 (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]. 4.29/4.37 494 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 495 (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]. 4.29/4.37 496 (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]. 4.29/4.37 497 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 498 (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]. 4.29/4.37 499 (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]. 4.29/4.37 500 (all A (v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B))) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 501 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,B) = k1_xboole_0))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 502 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 503 (all A all B all C (v1_relat_1(C) -> k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 504 (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]. 4.29/4.37 505 (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]. 4.29/4.37 506 (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]. 4.29/4.37 507 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 508 (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]. 4.29/4.37 509 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k2_relat_1(k8_relat_1(A,B)) = A))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 510 (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]. 4.29/4.37 511 (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]. 4.29/4.37 512 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 513 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 514 (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]. 4.29/4.37 515 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 516 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 517 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 518 (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]. 4.29/4.37 519 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 520 (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]. 4.29/4.37 521 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 522 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 523 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 524 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(B,C) & r2_hidden(k4_tarski(A,B),D) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 525 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 526 (all A (v1_relat_1(A) <-> (all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 527 (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]. 4.29/4.37 528 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k5_relat_1(B,k6_relat_1(A))))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 529 (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]. 4.29/4.37 530 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 531 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,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]. 4.29/4.37 532 (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]. 4.29/4.37 533 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 534 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 535 (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]. 4.29/4.37 536 (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]. 4.29/4.37 537 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 538 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 539 (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]. 4.29/4.37 540 (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]. 4.29/4.37 541 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 542 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 543 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 544 (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]. 4.29/4.37 545 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 546 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(k4_tarski(D,A),C) & r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 547 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 548 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D)) <-> B = k6_relat_1(A)))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 549 (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]. 4.29/4.37 550 (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]. 4.29/4.37 551 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 552 (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]. 4.29/4.37 553 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 554 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 555 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 556 (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]. 4.29/4.37 557 (all A (v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 558 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 559 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k4_xboole_0(A,B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 560 (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]. 4.29/4.37 561 (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]. 4.29/4.37 562 (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]. 4.29/4.37 563 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 564 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 565 (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]. 4.29/4.37 566 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 567 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 568 (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]. 4.29/4.37 569 (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]. 4.29/4.37 570 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 571 (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]. 4.29/4.37 572 (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]. 4.29/4.37 573 (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]. 4.29/4.37 574 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 575 (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]. 4.29/4.37 576 (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(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 577 (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]. 4.29/4.37 578 (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(A,B) & r1_tarski(C,D) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 579 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 580 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B) <-> r2_hidden(k4_tarski(D,E),C))) <-> k8_relat_1(A,B) = C))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 581 (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]. 4.29/4.37 582 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k5_relat_1(k4_relat_1(B),k4_relat_1(A)) = k4_relat_1(k5_relat_1(A,B)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 583 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 584 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = A <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A)))))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 585 (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]. 4.29/4.37 586 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 587 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_relat_1(C)) & r2_hidden(A,k1_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 588 (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]. 4.29/4.37 589 (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]. 4.29/4.37 590 (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]. 4.29/4.37 591 (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]. 4.29/4.37 592 (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]. 4.29/4.37 593 (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]. 4.29/4.37 594 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 595 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 596 (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]. 4.29/4.37 597 (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]. 4.29/4.37 598 (all A all B (v1_relat_1(B) -> (k9_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 599 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 600 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.37 601 (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]. 4.29/4.37 602 (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]. 4.29/4.37 603 (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]. 4.29/4.38 604 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 605 (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]. 4.29/4.38 606 (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(A) = k2_relat_1(k5_relat_1(B,A))))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 607 (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]. 4.29/4.38 608 (all A all B (v1_relat_1(B) -> -(k10_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 609 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 610 (all A (v1_relat_1(A) -> (r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) <-> v3_relat_1(A)))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 611 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_xboole_0 = A))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 612 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 613 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 614 (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]. 4.29/4.38 615 (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 & k5_relat_1(B,D) = k6_relat_1(A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & r1_tarski(k2_relat_1(C),A) -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 616 (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]. 4.29/4.38 617 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 618 (all A (v1_relat_1(A) -> k4_relat_1(k4_relat_1(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 619 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 620 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 621 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 622 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k5_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 623 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (C = k7_relat_1(A,B) <-> (all D all E (r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 624 (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]. 4.29/4.38 625 (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]. 4.29/4.38 626 (all A (A = k1_relat_1(k6_relat_1(A)) & A = k2_relat_1(k6_relat_1(A)))) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 627 (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]. 4.29/4.38 628 (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]. 4.29/4.38 629 (all A (v1_relat_1(A) -> (all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> k1_relat_1(A) = B)))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 630 (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]. 4.29/4.38 631 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 632 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 633 (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]. 4.29/4.38 634 (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]. 4.29/4.38 635 (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]. 4.29/4.38 636 (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]. 4.29/4.38 637 (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]. 4.29/4.38 638 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 639 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k2_xboole_0(A,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 640 (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(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 641 (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]. 4.29/4.38 642 (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]. 4.29/4.38 643 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(D,C),A))) <-> B = k4_relat_1(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 644 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 645 (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(D,B) & r2_hidden(k4_tarski(A,D),C)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 646 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k1_relat_1(B)) & (all C -r2_hidden(C,k2_relat_1(B)))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 647 (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,A),B)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 648 (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]. 4.29/4.38 649 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 650 (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]. 4.29/4.38 651 (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(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 652 (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]. 4.29/4.38 653 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 654 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 655 (all A (v1_relat_1(A) -> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A)) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 656 (all 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(k4_tarski(E,D),A) & r2_hidden(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 657 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_xboole_0 = k1_relat_1(A) -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 658 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 659 (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]. 4.29/4.38 660 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 661 (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]. 4.29/4.38 662 (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]. 4.29/4.38 663 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 664 (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]. 4.29/4.38 665 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 666 (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]. 4.29/4.38 667 (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]. 4.29/4.38 668 (all A (v1_relat_1(A) -> k1_xboole_0 = k9_relat_1(A,k1_xboole_0))) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 669 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 670 (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]. 4.29/4.38 671 (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]. 4.29/4.38 672 (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]. 4.29/4.38 673 (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]. 4.29/4.38 674 (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]. 4.29/4.38 675 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_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]. 4.29/4.38 676 (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]. 4.29/4.38 677 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 678 (all A (v2_relat_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 679 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 680 (exists A ((all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s4_funct_1)) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 681 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 682 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 683 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 684 (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,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 685 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k1_xboole_0 != k10_relat_1(B,k1_tarski(A))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 686 (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]. 4.29/4.38 687 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.29/4.38 688 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 689 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 690 (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]. 4.29/4.38 691 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A) & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 692 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 693 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 694 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 695 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = 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]. 4.29/4.38 696 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 697 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k1_relat_1(k2_funct_1(A)) = k2_relat_1(A) & k1_relat_1(A) = k2_relat_1(k2_funct_1(A))))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 698 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 699 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 700 (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]. 4.29/4.38 701 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 702 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 703 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k3_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 704 (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]. 4.29/4.38 705 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 706 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 707 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(B,k2_relat_1(C)) & k10_relat_1(C,B) = k10_relat_1(C,A) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 708 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 709 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 710 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 711 (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 (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & k5_relat_1(C,A) = k5_relat_1(B,A) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(B) = k1_relat_1(C) -> C = B)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 712 (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]. 4.29/4.38 713 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 714 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & k1_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (C = k1_funct_1(B,D) <-> k1_funct_1(A,C) = D))) -> B = k2_funct_1(A)))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 715 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A))) & k2_relat_1(k5_relat_1(A,k2_funct_1(A))) = k1_relat_1(A)))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 716 (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]. 4.29/4.38 717 (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]. 4.29/4.38 718 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k9_relat_1(B,k10_relat_1(B,A))))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 719 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 720 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 721 (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 (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> 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)))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 722 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(A,k9_relat_1(C,B)) = k9_relat_1(k8_relat_1(A,C),B))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 723 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 724 (all A all B -((all C (v1_funct_1(C) & v1_relat_1(C) -> -(r1_tarski(k2_relat_1(C),A) & k1_relat_1(C) = B))) & -(B != k1_xboole_0 & A = k1_xboole_0))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 725 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 726 (all A (v2_funct_1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 727 (all A k6_relat_1(A) = k2_funct_1(k6_relat_1(A))) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 728 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 729 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 730 (all A (v1_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 731 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k6_relat_1(A) <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 732 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 733 (all A (v1_funct_1(A) & v1_relat_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]. 4.29/4.38 734 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 735 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(B) & k1_relat_1(B) = A & B = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(C) -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 736 (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]. 4.29/4.38 737 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(r2_hidden(B,k1_relat_1(A)) & v1_xboole_0(k1_funct_1(A,B)))) <-> v2_relat_1(A)))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 738 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 739 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 740 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 741 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 742 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 743 (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,B) = C <-> r2_hidden(k4_tarski(B,C),A))) & (-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> C = k1_funct_1(A,B))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 744 (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,k1_relat_1(k5_relat_1(C,B))) <-> r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 745 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.29/4.38 746 (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]. 4.29/4.38 747 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.29/4.38 748 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 749 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 750 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 751 (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,B),A) = k7_relat_1(C,A) & k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 752 (all A all B (v1_relat_1(A) & v1_funct_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]. 4.29/4.38 753 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k9_relat_1(B,k10_relat_1(B,A)) = k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 754 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) & k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 755 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) & (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 756 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A)))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 757 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k7_relat_1(C,A) = B <-> k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)))))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 758 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(A) & v2_funct_1(B)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 759 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 760 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 761 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 762 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 763 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 764 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 765 (all 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) -> (A = k1_relat_1(D) & k1_relat_1(C) = A & k5_relat_1(B,C) = k5_relat_1(B,D) -> C = D))))) & r1_tarski(k2_relat_1(B),A) -> k2_relat_1(B) = A))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 766 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 767 (all A all B (r2_hidden(B,A) -> k1_funct_1(k6_relat_1(A),B) = B)) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 768 (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]. 4.29/4.38 769 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 770 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 771 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 772 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 773 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(k9_relat_1(C,A),B) = k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 774 (all A (k1_xboole_0 != A -> (all B exists C (v1_relat_1(C) & v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 775 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 776 (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(k5_relat_1(k2_funct_1(B),B),A) & k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) = A))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 777 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C))))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 778 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 779 (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]. 4.29/4.38 780 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 781 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_tarski(k1_funct_1(B,A)) = k9_relat_1(B,k1_tarski(A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 782 (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) -> k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 783 (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) & (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) -> B = C)) -> (exists A (f1_s2_funct_1 = k1_relat_1(A) & v1_relat_1(A) & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 784 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 785 (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]. 4.29/4.38 786 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 787 (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) & k2_relat_1(A) = k1_relat_1(k5_relat_1(k2_funct_1(A),A))))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 788 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C))) <-> v2_funct_1(A)))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 789 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 790 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 791 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 792 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 793 (all A all B (v1_relat_1(B) & v1_funct_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]. 4.29/4.38 794 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 795 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 796 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 797 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 4.29/4.39 798 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 799 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 800 (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]. 4.29/4.39 801 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 802 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 803 (exists A (v1_funct_1(A) & v1_relat_1(A) & v2_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 804 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 805 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 806 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 807 (exists A (f1_s3_funct_1 = k1_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 808 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(B) & k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 809 (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]. 4.29/4.39 810 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k1_relat_1(B) = k2_relat_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 811 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 812 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) & k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 813 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 814 (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]. 4.29/4.39 815 (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]. 4.29/4.39 816 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 817 (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(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 818 (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]. 4.29/4.39 819 (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]. 4.29/4.39 820 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 4.29/4.39 821 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 822 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 823 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_funct_1(A) <-> (all C all D ((r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C) -> k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A))) & (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C)))) & k1_relat_1(B) = k2_relat_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 824 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 825 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 826 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(B,A) = k9_relat_1(k2_funct_1(B),A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 827 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 828 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 829 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (C = k9_relat_1(A,B) <-> (all D ((exists E (D = k1_funct_1(A,E) & r2_hidden(E,B) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 830 (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]. 4.29/4.39 831 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_funct_1(B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 832 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 833 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 834 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 835 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 836 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 837 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (B = k8_relat_1(A,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(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C))))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 838 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & B = k1_funct_1(C,A) <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 839 (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]. 4.29/4.39 840 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 841 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(r2_hidden(B,k2_relat_1(A)) & (all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 842 (all A all B (v1_relat_1(B) -> ((all C -(k1_xboole_0 = k10_relat_1(B,k1_tarski(C)) & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 843 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k5_relat_1(A,B) = A & k2_relat_1(A) = k1_relat_1(B) -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 844 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,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]. 4.29/4.39 845 (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]. 4.29/4.39 846 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 847 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 848 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 849 (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,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]. 4.29/4.39 850 (all A (v1_funct_1(A) & v1_relat_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]. 4.29/4.39 851 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 852 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 853 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 854 (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]. 4.29/4.39 855 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 856 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 857 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 858 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 859 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 860 (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]. 4.29/4.39 861 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 862 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C)))) <-> B = k2_relat_1(A))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 863 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 864 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 865 (all 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) -> (A = k1_relat_1(C) & k2_relat_1(B) = A & k1_relat_1(D) = A & k5_relat_1(B,D) = k5_relat_1(B,C) -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 866 (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)) & v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 867 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A)) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 868 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.39 869 (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]. 4.29/4.39 870 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,k1_relat_1(B)) & C = k1_funct_1(B,D))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 871 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r4_relat_2(A,k3_relat_1(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 872 (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]. 4.31/4.39 873 (all A (v1_relat_1(A) -> (r8_relat_2(A,k3_relat_1(A)) <-> v8_relat_2(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 874 (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]. 4.31/4.39 875 (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]. 4.31/4.39 876 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 877 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 878 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(k4_tarski(D,C),A) & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) -> D = C)) <-> r4_relat_2(A,B))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 879 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v3_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 880 (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]. 4.31/4.39 881 (all A (v1_relat_1(A) -> (r7_relat_2(A,k3_relat_1(A)) <-> v7_relat_2(A)))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 882 (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))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 883 (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]. 4.31/4.39 884 (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]. 4.31/4.39 885 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v2_relat_2(A) & v4_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 886 (all A (v1_relat_1(A) -> (r5_relat_2(A,k3_relat_1(A)) <-> v5_relat_2(A)))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 887 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 888 (all A (v1_relat_1(A) -> (r1_tarski(k5_relat_1(A,A),A) <-> v8_relat_2(A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 889 (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]. 4.31/4.39 890 (all A (v1_relat_1(A) -> (all B (r2_relat_2(A,B) <-> (all C -(r2_hidden(C,B) & r2_hidden(k4_tarski(C,C),A))))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 891 (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]. 4.31/4.39 892 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 893 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 894 (all A (v1_relat_1(A) -> (k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) <-> v7_relat_2(A)))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 895 (all A (v1_relat_1(A) -> (r6_relat_2(A,k3_relat_1(A)) <-> v6_relat_2(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 896 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 897 (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]. 4.31/4.39 898 (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]. 4.31/4.39 899 (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]. 4.31/4.39 900 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 901 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 902 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v1_relat_2(A) & v6_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 903 (all A (v1_relat_1(A) -> (all B ((all C all D all E (r2_hidden(E,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) -> r2_hidden(k4_tarski(C,E),A))) <-> r8_relat_2(A,B))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 904 (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]. 4.31/4.39 905 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> k4_relat_1(A) = A))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 906 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 907 (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]. 4.31/4.39 908 (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]. 4.31/4.39 909 (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]. 4.31/4.39 910 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B)) & v3_relat_2(k2_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 911 (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]. 4.31/4.39 912 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 913 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 914 (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]. 4.31/4.39 915 (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]. 4.31/4.39 916 (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]. 4.31/4.39 917 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 918 (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]. 4.31/4.39 919 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 920 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r1_xboole_0(k6_relat_1(k3_relat_1(A)),A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 921 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r2_relat_2(A,k3_relat_1(A))))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 922 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 923 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 924 (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]. 4.31/4.39 925 (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]. 4.31/4.39 926 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 927 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))) <-> r1_relat_2(A,B))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 928 (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]. 4.31/4.39 929 (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]. 4.31/4.39 930 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(k4_relat_1(A)) = k2_relat_1(A) & k1_relat_1(A) = k1_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 931 (all A (v1_relat_1(A) -> (all B ((all C all D -(-r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 932 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 933 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 934 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 935 (all A all B (v1_funct_1(A) & v3_ordinal1(B) & v1_relat_1(A) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 936 (all A all B all C all D all E all F -(r2_hidden(C,D) & r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(F,A) & r2_hidden(E,F))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 937 (all A A != k1_ordinal1(A)) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 938 (all A (v3_ordinal1(A) -> (all B ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = f3_s5_ordinal1(k2_ordinal1(C,D))))) & f3_s5_ordinal1(C) = B & v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(C) = A)) <-> B = f2_s5_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_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]. 4.31/4.39 939 (exists A (v1_funct_1(A) & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> k1_funct_1(A,B) = f2_s4_ordinal1(C)))))) & v1_relat_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s4_ordinal1)) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 940 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 941 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(B,A) | r1_ordinal1(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 942 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(B != A & -r2_hidden(B,A) & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 943 (all A all B (r2_hidden(A,B) | A = B <-> r2_hidden(A,k1_ordinal1(B)))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 944 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_tarski(A,B) <-> r1_ordinal1(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 945 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 946 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 947 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 948 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 949 (exists A (v3_ordinal1(A) & p1_s1_ordinal1(A))) -> (exists A (p1_s1_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & v3_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 950 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 951 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 952 (all A -((all B (r2_hidden(B,A) -> v3_ordinal1(B))) & (all B (v3_ordinal1(B) -> -r1_tarski(A,B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 953 (exists A (-v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 954 (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]. 4.31/4.39 955 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 956 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 957 (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]. 4.31/4.39 958 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 959 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 960 f1_s3_ordinal1 = k1_relat_1(f3_s3_ordinal1) & 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(f3_s3_ordinal1,A) = B -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (B = k2_ordinal1(f4_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> 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]. 4.31/4.39 961 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 962 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v1_xboole_0(A) & v3_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 963 (all A (v3_ordinal1(A) -> v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 964 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 965 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 966 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 967 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(B,A) & B != A & -r2_xboole_0(A,B)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 968 (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]. 4.31/4.39 969 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 970 (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]. 4.31/4.39 971 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 972 (all A ((all B all C -(r2_hidden(C,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(B,A))) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 973 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 974 (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]. 4.31/4.39 975 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 976 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 977 (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]. 4.31/4.39 978 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(E,A) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(C,D))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 979 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 980 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 981 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 982 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 983 (all A (v4_ordinal1(A) <-> A = k3_tarski(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 984 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 985 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 986 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 987 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 988 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_hidden(B,A) | r1_ordinal1(A,B))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 989 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r1_tarski(A,B) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 990 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 991 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 992 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 993 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 994 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 995 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 996 (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]. 4.31/4.39 997 (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]. 4.31/4.39 998 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 999 (all A all B (m1_ordinal1(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1000 (all A all B (v5_ordinal1(B) & v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_ordinal1(B,A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1001 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1002 (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]. 4.31/4.39 1003 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1004 (all A (v2_ordinal1(A) & v1_ordinal1(A) <-> v3_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1005 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> v1_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1006 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1007 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) & v1_relat_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1008 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1009 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A))))))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1010 (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]. 4.31/4.39 1011 (all A all B all C all D -(r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(A,B) & r2_hidden(C,D))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1012 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1013 (all A (v3_ordinal1(A) -> -(-v4_ordinal1(A) & (all B (v3_ordinal1(B) -> k1_ordinal1(B) != A))) & -((exists B (v3_ordinal1(B) & A = k1_ordinal1(B))) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1014 (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]. 4.31/4.39 1015 (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]. 4.31/4.39 1016 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1017 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1018 (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]. 4.31/4.39 1019 (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) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C)))) & r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1020 (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))) <-> k4_relset_1(B,A,C) = B))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.39 1021 (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]. 4.31/4.39 1022 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1023 (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]. 4.31/4.40 1024 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,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]. 4.31/4.40 1025 (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]. 4.31/4.40 1026 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1027 (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]. 4.31/4.40 1028 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1029 (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]. 4.31/4.40 1030 (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]. 4.31/4.40 1031 (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]. 4.31/4.40 1032 (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]. 4.31/4.40 1033 (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) -> ((exists E (r2_hidden(k4_tarski(D,E),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1034 (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]. 4.31/4.40 1035 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1036 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1037 (all A all B all C (m2_relset_1(C,B,A) -> k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) & k4_relset_1(B,A,C) = k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1038 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> C = k2_relset_1(A,B,C,C))) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1039 (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]. 4.31/4.40 1040 (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]. 4.31/4.40 1041 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> B = k4_relset_1(B,A,C) & r1_tarski(B,k5_relset_1(B,A,C))))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1042 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k4_relset_1(A,B,D)) & r1_tarski(C,k5_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1043 (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]. 4.31/4.40 1044 (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]. 4.31/4.40 1045 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1046 (all A all B (m2_relset_1(B,A,A) -> k5_relat_1(B,k6_relat_1(A)) = B & B = k5_relat_1(k6_relat_1(A),B))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1047 (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) = k3_xboole_0(C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1048 (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]. 4.31/4.40 1049 (all A all B all C (m2_relset_1(C,A,B) <-> m1_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1050 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1051 (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 (r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E) & m1_subset_1(H,B))) <-> 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]. 4.31/4.40 1052 (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]. 4.31/4.40 1053 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1054 (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)) & k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1055 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1056 (all A all B all C all D (m2_relset_1(D,A,B) -> -(r2_hidden(C,D) & (all E all F -(r2_hidden(E,A) & C = k4_tarski(E,F) & r2_hidden(F,B)))))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1057 (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 (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1058 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1059 (all A all B all C (r1_tarski(C,k2_zfmisc_1(A,B)) <-> m1_relset_1(C,A,B))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1060 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1061 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1062 (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]. 4.31/4.40 1063 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1064 (all A all B all C (m2_relset_1(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C)))) <-> B = k5_relset_1(A,B,C)))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1065 (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]. 4.31/4.40 1066 (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]. 4.31/4.40 1067 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> D = k8_relset_1(B,A,D,C)))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1068 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_xboole_0(C,D) = k1_relset_1(A,B,C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1069 (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]. 4.31/4.40 1070 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1071 (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]. 4.31/4.40 1072 (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]. 4.31/4.40 1073 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,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]. 4.31/4.40 1074 (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) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C) & r2_hidden(F,B)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1075 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1076 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1077 (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]. 4.31/4.40 1078 (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]. 4.31/4.40 1079 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1080 (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]. 4.31/4.40 1081 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1082 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1) & r2_hidden(C,f2_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1083 (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]. 4.31/4.40 1084 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1085 (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]. 4.31/4.40 1086 (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]. 4.31/4.40 1087 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1088 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1089 (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]. 4.31/4.40 1090 (all A all B all C all D (m1_relset_1(C,A,B) -> k11_relset_1(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1091 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1092 (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]. 4.31/4.40 1093 (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]. 4.31/4.40 1094 (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]. 4.31/4.40 1095 (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]. 4.31/4.40 1096 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> 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]. 4.31/4.40 1097 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1098 (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,D,C) = k1_relset_1(A,B,C,D))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1099 (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]. 4.31/4.40 1100 (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 (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1101 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1102 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> k5_relat_1(E,F) = k7_relset_1(A,B,C,D,E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1103 (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]. 4.31/4.40 1104 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1105 (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]. 4.31/4.40 1106 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1107 (all A all B all C (k4_partfun1(A,B) = C <-> (all D ((exists E (r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & D = E & r1_tarski(k1_relat_1(E),A) & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1108 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1109 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1110 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1111 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1112 (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]. 4.31/4.40 1113 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1114 (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 (m2_relset_1(F,A,B) & r1_partfun1(C,F) & v1_partfun1(F,A,B) & E = F & v1_funct_1(F))) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1115 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1116 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1117 (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]. 4.31/4.40 1118 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1119 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1120 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1121 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1122 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1123 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1124 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1125 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1126 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)) & (p1_s1_partfun1(B) -> k1_funct_1(A,B) = f2_s1_partfun1(B)))) & f1_s1_partfun1 = k1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1127 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1128 (all A all B all C (m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1129 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1130 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k3_partfun1(C,A,B) = C)) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1131 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1132 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1133 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1134 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1135 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1136 (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]. 4.31/4.40 1137 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1138 (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 (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B)))) & r1_partfun1(C,D) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1139 (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]. 4.31/4.40 1140 (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]. 4.31/4.40 1141 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1142 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1143 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1144 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1145 (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]. 4.31/4.40 1146 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1147 (all A all B all C all D (v1_relat_1(D) & v1_funct_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]. 4.31/4.40 1148 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_tarski(A) = k1_relat_1(D) -> v1_funct_1(D) & m2_relset_1(D,B,C)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1149 (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]. 4.31/4.40 1150 (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]. 4.31/4.40 1151 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1152 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1153 (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]. 4.31/4.40 1154 (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) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & (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 (p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) & r2_hidden(B,f1_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1155 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(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(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1156 (all A exists B (v4_relat_2(B) & v1_relat_1(B) & m1_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1157 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1158 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1159 (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]. 4.31/4.40 1160 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (r1_tarski(B,C) & r1_tarski(A,C) & v1_relat_1(C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1161 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1162 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1163 (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]. 4.31/4.40 1164 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1165 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1166 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1167 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1168 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1169 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1170 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1171 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (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]. 4.31/4.40 1172 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> 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]. 4.31/4.40 1173 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1174 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> D = C)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1175 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1176 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1177 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1178 (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) & v1_partfun1(D,A,B) & r1_partfun1(C,D) -> D = C))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1179 (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]. 4.31/4.40 1180 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1181 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1182 (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]. 4.31/4.40 1183 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1184 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (A != k1_xboole_0 -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1185 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1186 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1187 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> ((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,E) = k1_funct_1(C,D) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1188 (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]. 4.31/4.40 1189 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_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]. 4.31/4.40 1190 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1191 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1192 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1193 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1194 (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) & (all A all B all C (p1_s2_partfun1(A,B) & p1_s2_partfun1(A,C) & r2_hidden(A,f1_s2_partfun1) -> B = C)) -> (exists A (v1_funct_1(A) & (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 (r2_hidden(B,f1_s2_partfun1) & (exists C p1_s2_partfun1(B,C)) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1195 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1196 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1197 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k5_partfun1(A,B,C) = k1_tarski(C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1198 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m2_relset_1(k2_partfun1(A,B,C,D),A,B) & v1_funct_1(k2_partfun1(A,B,C,D)))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1199 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1200 (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) -> -(r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1201 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1202 (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]. 4.31/4.40 1203 (all A (v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1204 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1205 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1206 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1207 (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) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1208 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1209 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1210 (all A all B (v1_funct_1(B) & v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1211 (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]. 4.31/4.40 1212 (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,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1213 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1214 (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]. 4.31/4.40 1215 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1216 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1217 (all A all B exists C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_relat_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1218 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1219 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1220 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1221 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1222 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1223 (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) -> (k4_relset_1(A,B,D) = k4_relset_1(A,B,C) & (all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1224 (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]. 4.31/4.40 1225 (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]. 4.31/4.40 1226 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.40 1227 (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]. 4.31/4.40 1228 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 4.31/4.40 1229 (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(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]. 4.31/4.40 1230 (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]. 4.31/4.41 1231 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1232 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1233 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_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]. 4.31/4.41 1234 (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,k2_relat_1(D))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1235 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1236 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1237 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 = B & v1_partfun1(C,A,B) -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1238 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1239 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1240 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1241 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> C = D)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1242 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 4.31/4.41 1243 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1244 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (k2_xboole_0(A,B) = C & v1_relat_1(C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1245 (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) -> (r1_tarski(A,C) & r1_tarski(B,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1246 (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]. 4.31/4.41 1247 (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]. 4.31/4.41 1248 (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]. 4.31/4.41 1249 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1250 (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]. 4.31/4.41 1251 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k7_relat_1(k8_relat_1(C,A),B) = k3_partfun1(A,B,C)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1252 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> k3_partfun1(C,A,B) = C))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1253 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1254 (all A all B all C (p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,D) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> D = C)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & v1_funct_1(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))))) & (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)) <-> r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1))))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1255 (all A (v3_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1256 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1257 (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)) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1258 (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]. 4.31/4.41 1259 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1260 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1261 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1262 (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]. 4.31/4.41 1263 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1264 (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]. 4.31/4.41 1265 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1266 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1267 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1268 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1269 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1270 (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]. 4.31/4.41 1271 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) & k1_relat_1(A) = k1_relat_1(B) -> A = B))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1272 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1273 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1274 (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]. 4.31/4.41 1275 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1276 (all A all B all C all D (v1_funct_1(D) & v1_relat_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]. 4.31/4.41 1277 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1278 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1279 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1280 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1281 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1282 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1283 (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]. 4.31/4.41 1284 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,C) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1285 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k4_relset_1(A,k1_xboole_0,B) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1286 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> D = C))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1287 (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) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1288 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1289 (all A all B (v1_funct_1(B) & v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1290 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1291 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1292 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k2_funct_1(k3_partfun1(C,A,B)) = k3_partfun1(k2_funct_1(C),B,A)))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1293 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1294 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (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)))) -> E = D))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1295 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1296 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1297 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1298 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (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]. 4.31/4.41 1299 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1300 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1301 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> 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]. 4.31/4.41 1302 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1303 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(k1_xboole_0) = k5_partfun1(k1_xboole_0,A,B))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1304 (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_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1305 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1306 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1307 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1308 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1309 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1310 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1311 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1312 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1313 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 4.31/4.41 1314 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) <-> p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1))) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1315 (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]. 4.31/4.41 1316 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (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]. 4.31/4.41 1317 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1318 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1319 (all A exists B (v1_relat_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1320 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1321 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1322 (all A all B all C (v1_funct_1(k9_funct_2(A,B,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)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1323 (all A all B all C (v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (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]. 4.31/4.41 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]. 4.31/4.41 1325 (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 -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F -(r2_hidden(F,A) & r2_hidden(F,C) & k1_funct_1(D,F) = E)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1326 (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) -> (k5_partfun1(A,B,D) = k5_partfun1(A,B,C) & (all E B != k1_tarski(E)) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1327 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1328 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1329 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1330 (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_partfun1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1331 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1332 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1333 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1334 (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_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1335 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1336 (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) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> A = k2_relat_1(D) & v2_funct_1(C) | B = k1_xboole_0))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1337 (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_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r1_partfun1(C,E) & r1_partfun1(D,E) -> r1_partfun1(C,D) | k1_xboole_0 = B & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1338 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1339 (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(k2_relat_1(D),C) -> k1_xboole_0 = B & A != k1_xboole_0 | m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1340 (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,B) & (all E -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & k2_relat_1(D) = B))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1341 (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_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1342 (all A all B (v3_funct_2(B,A,A) & v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> k6_funct_2(A,B) = C))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1343 (all A all B all C all 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,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> k1_xboole_0 = B) & (k1_xboole_0 = B -> k1_xboole_0 = A) & -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)))))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1344 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,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,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1345 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1346 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1347 (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 (m2_relset_1(E,B,C) & v1_funct_1(E) & v1_funct_2(E,B,C) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | B = k1_xboole_0 | C = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1348 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1349 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1350 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & v1_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & 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]. 4.31/4.41 1351 (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 (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | k1_xboole_0 = C))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1352 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (r1_tarski(k2_relat_1(E),B) & D = E & v1_funct_1(E) & k1_relat_1(E) = A & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1353 (all A all B all C all D all E (v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> 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]. 4.31/4.41 1354 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1355 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1356 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1357 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1358 (all A all B all C (v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (v2_funct_1(C) <-> (all D all E (k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,A) & r2_hidden(D,A) -> D = E)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1359 (all A all B all C all D all E all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | k1_xboole_0 = C))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1360 (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(C,A) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1361 (all A all B all C (v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_tarski(B,A) -> B = k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) & k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1362 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E (r2_hidden(k1_funct_1(D,E),C) & r2_hidden(E,A) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1363 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1364 (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_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_xboole_0 = B | k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C)))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1365 f3_s11_funct_2 != f4_s11_funct_2 -> (exists A (v1_funct_1(A) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & 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) -> -(B != f4_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f3_s11_funct_2 != B))))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1366 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1367 (all A all B exists C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1368 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1369 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((B = k1_xboole_0 -> 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]. 4.31/4.41 1370 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (p1_s7_funct_2(A,B,C) & m1_subset_1(C,f3_s7_funct_2))))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_2(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))))))))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1371 (all A all B all C (v3_funct_2(B,A,A) & v1_funct_2(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1372 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1373 (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) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k4_funct_2(A,B,C) = B & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1374 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.41 1375 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.31/4.41 1376 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C)) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C) | B = k1_xboole_0))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1377 (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) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1378 (all A all B all C all D (v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(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)) -> A != k1_xboole_0 & B = k1_xboole_0 | v2_funct_1(D) | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1379 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1380 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & k1_funct_1(C,E) = D)))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1381 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1382 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1383 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1384 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1385 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-((all D all E (m2_relset_1(E,D,A) & v1_funct_1(E) & 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) -> F = E))))) <-> v2_funct_1(C)) & B != k1_xboole_0 & A != k1_xboole_0))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1386 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1387 (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) -> (-(B = k1_xboole_0 & C != k1_xboole_0 & A != k1_xboole_0) -> v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_1(k1_partfun1(A,B,B,C,D,E))))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1388 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1389 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1390 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1391 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1392 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1393 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1394 (all A all B all C (m1_relset_1(C,A,B) -> (v2_funct_2(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v2_funct_1(C) -> v3_funct_2(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1395 (all A all B (r2_hidden(B,f2_s6_funct_2) & r2_hidden(A,f1_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (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))) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1396 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1397 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1398 (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 (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(D) = B & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> C = k1_xboole_0 & B != k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1399 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1400 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1401 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1402 (all A (r2_hidden(A,f1_s9_funct_2) -> (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)) & (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & 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) -> k1_funct_1(A,B) = f3_s9_funct_2(B)))))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1403 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1404 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1405 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) -> (r2_hidden(C,A) -> k1_funct_1(D,C) = B))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1406 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1407 (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]. 4.31/4.42 1408 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (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]. 4.31/4.42 1409 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1410 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1411 (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) -> (r1_partfun1(C,D) -> r2_hidden(D,k5_partfun1(A,B,C)) | k1_xboole_0 = B & A != k1_xboole_0))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1412 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | k1_xboole_0 = B))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1413 (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(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]. 4.31/4.42 1414 (all A all B (m2_relset_1(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) -> ((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]. 4.31/4.42 1415 (all A all B all C all D all E (v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(D) & -v1_xboole_0(B) -> k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1416 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) & 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]. 4.31/4.42 1417 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1418 (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,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & (all E all F ((k1_funct_1(C,F) = E & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (F = k1_funct_1(D,E) & r2_hidden(E,B) -> E = k1_funct_1(C,F) & r2_hidden(F,A)))) & k2_relat_1(C) = B -> k2_funct_1(C) = D | k1_xboole_0 = B | k1_xboole_0 = A))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1419 (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_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((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]. 4.31/4.42 1420 (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(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1421 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> B = k1_xboole_0 & A != k1_xboole_0 | v1_partfun1(C,A,B)))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1422 (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]. 4.31/4.42 1423 (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) -> (B != k1_xboole_0 -> k2_relat_1(C) = k1_tarski(k1_funct_1(C,A))))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1424 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1425 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1426 (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) & v2_funct_1(C) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1427 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1428 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1429 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v3_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v2_funct_2(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1430 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1431 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1432 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1433 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,D) = k2_funct_2(A,B,C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1434 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1435 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (k2_relat_1(B) = A & v2_funct_1(B) -> m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1436 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1437 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1438 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> ((all C all D (k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1439 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1440 (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 (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1441 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1442 (all A all B all C (m2_relset_1(C,A,B) -> (k1_xboole_0 = B -> (k1_xboole_0 = C <-> v1_funct_2(C,A,B)) | A = k1_xboole_0) & ((k1_xboole_0 = B -> k1_xboole_0 = A) -> (A = k4_relset_1(A,B,C) <-> v1_funct_2(C,A,B))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1443 (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) -> B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),B)))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1444 (all A all B all C all D (m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1445 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1446 (all 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,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (v2_funct_1(B) & k4_funct_2(A,C,B) = B -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1447 (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) & v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1448 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1449 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1450 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1451 (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 (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))))) -> D = E))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1452 (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A) & v1_funct_2(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) -> f4_s8_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))))))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1453 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(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) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1454 (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) -> 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]. 4.31/4.42 1455 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1456 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) -> v1_funct_1(k6_funct_2(A,B)) & v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1457 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1458 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1459 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (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(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> E = D))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1460 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1461 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1462 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1463 (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) -> A = k3_funct_2(A,B,C,B)))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1464 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & 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]. 4.31/4.42 1465 (all A all B (v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A) & k6_partfun1(A) = k5_funct_2(A,k6_funct_2(A,B),B))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1466 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k2_relat_1(B) = A & A = k2_relat_1(C) -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1467 (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 -> 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]. 4.31/4.42 1468 (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 k1_tarski(E) != B) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1469 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1470 (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) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(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]. 4.31/4.42 1471 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1472 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> D = C | k1_xboole_0 = B & k1_xboole_0 != A))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1473 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & r2_hidden(C,A) & k1_funct_1(B,D) = k1_funct_1(B,C) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1474 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1475 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1476 (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(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D) & v1_funct_2(D,A,C) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1477 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_funct_2) -> f3_s4_funct_2(B) = k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1478 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1479 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A ((all B (m1_subset_1(B,f1_s12_funct_2) -> f3_s12_funct_2(B) = k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_1(A))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1480 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(B) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_1(k4_funct_2(A,B,C)))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1481 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1482 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k4_relset_1(A,A,B) & r1_tarski(k2_relat_1(B),A))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1483 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A (m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & 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)))) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1484 (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) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D)))) <-> k2_relat_1(C) = B))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1485 (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 -> ((all D (k1_xboole_0 != D -> (all E (m2_relset_1(E,B,D) & v1_funct_2(E,B,D) & v1_funct_1(E) -> (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) -> F = E))))))) <-> k2_relat_1(C) = B)))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1486 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1487 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1488 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1489 (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]. 4.31/4.42 1490 (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]. 4.31/4.42 1491 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1492 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1493 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1494 (all A all B all C (v1_funct_1(B) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) -> m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1495 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1496 (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]. 4.31/4.42 1497 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1498 (all A all B all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_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]. 4.31/4.42 1499 (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) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1500 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1501 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1502 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) -> v1_funct_2(C,A,B) & v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1503 (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]. 4.31/4.42 1504 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1505 (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]. 4.31/4.42 1506 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k3_funct_2(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1507 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k2_relat_1(C) = B & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> A = k1_xboole_0 | k2_funct_1(C) = D | B = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1508 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1509 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1510 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_1(C) & m2_relset_1(C,A,A) & r1_partfun1(B,C) & v1_funct_2(C,A,A))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1511 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) -> k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0)) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1512 (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,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(E = k1_funct_1(D,F) & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1513 (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) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1514 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1515 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1516 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1517 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1518 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1519 (all A all B (m2_relset_1(B,A,A) -> B = k7_relset_1(A,A,A,A,k6_partfun1(A),B) & k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B)) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1520 (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 & (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))) & -v2_funct_1(C)))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1521 (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(C,A) -> k1_xboole_0 != A & k1_xboole_0 = B | m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1522 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (C = k5_funct_2(A,B,C) -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1523 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1524 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (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) | B = k1_xboole_0))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1525 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1526 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) & 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]. 4.31/4.42 1527 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1528 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1529 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (p1_s3_funct_2(A,B) & m1_subset_1(B,f2_s3_funct_2))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A) & (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)))))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1530 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1531 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (v2_funct_1(D) & r2_hidden(C,A) -> B = k1_xboole_0 | C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C))))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1532 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & -v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1533 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1534 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (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]. 4.31/4.42 1535 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1536 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & 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]. 4.31/4.42 1537 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1538 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 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 (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,B,C) <-> r5_binop_1(A,B,C) & r4_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1540 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & v1_funct_1(D) & -v1_xboole_0(A) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1541 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1542 (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) -> (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]. 4.31/4.42 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) -> (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]. 4.31/4.42 1544 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & -v1_xboole_0(A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) -> 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]. 4.31/4.42 1545 (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) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1546 (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_xboole_0(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_funct_1(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1547 (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_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((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]. 4.31/4.42 1548 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(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) -> (r7_binop_1(A,B,C) <-> (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))))))))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1549 (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) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1550 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)) = k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E))))))))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1551 (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) & 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) -> ((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)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1552 (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]. 4.31/4.42 1553 (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) -> (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) -> 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))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1554 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1555 (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) -> ((exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A))) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> k3_binop_1(A,B) = C)))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1556 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (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) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) = k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E))))))))))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.42 1557 (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 (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) -> 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]. 4.31/4.42 1558 (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) -> (v1_binop_1(B,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)))))))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1559 (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) -> (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]. 4.31/4.43 1560 (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]. 4.31/4.43 1561 (exists A (m2_relset_1(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))))) & v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 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) -> (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,C,D) = k2_binop_1(A,A,A,B,D,C)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1563 (all 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) -> (r3_binop_1(A,B,C) <-> r1_binop_1(A,B,C) & r2_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1564 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & 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) -> (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]. 4.31/4.43 1565 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (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]. 4.31/4.43 1566 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1567 (all A (-v1_xboole_0(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) -> k2_binop_1(A,A,A,C,B,D) = D)) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 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) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k1_binop_1(B,C,C)))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1569 (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) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D) & k1_binop_1(B,D,C) = D))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1570 (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) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))) <-> r3_binop_1(A,C,B))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1571 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & 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) -> (v1_binop_1(C,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,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)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1572 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1573 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1574 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (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) -> k1_binop_1(B,D,C) = D)))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1575 (all A all B (m1_subset_1(B,A) -> (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) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,D,B)))))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1576 (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]. 4.31/4.43 1577 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1578 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1579 (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 ((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_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1580 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (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) -> (r4_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1581 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1582 (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_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) -> (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)))))))) <-> r5_binop_1(A,B,C)))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1583 (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) -> (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]. 4.31/4.43 1584 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1585 (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 (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) -> (all F (m1_subset_1(F,A) -> 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) & 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)))))))) <-> r6_binop_1(A,B,C)))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1586 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1587 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1588 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C))))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1589 (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) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k1_relat_1(k3_funcop_1(A,B,C)) = k3_xboole_0(k1_relat_1(B),k1_relat_1(C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1590 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & m2_relset_1(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,k7_funcop_1(B,A,C,D,F)) = k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F)))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1591 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1592 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) = k5_funcop_1(A,B,C))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1593 (exists A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1594 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1595 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 4.31/4.43 1596 (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) -> (all D k4_funcop_1(k5_relat_1(C,A),B,D) = k5_relat_1(k4_funcop_1(C,B,D),A)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1597 (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_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) -> k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D) = k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D))))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1598 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k2_funcop_1(k10_relat_1(A,B),C) = k5_relat_1(A,k2_funcop_1(B,C))))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1599 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k13_funct_3(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1600 (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) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & v1_funct_2(E,B,A) & m1_relset_1(D,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k6_funcop_1(A,B,C,D,E)))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1601 (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]. 4.31/4.43 1602 (all A (v1_funct_1(A) & v1_relat_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]. 4.31/4.43 1603 (all A k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A))) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1604 (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_1(D) & v1_funct_2(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]. 4.31/4.43 1605 (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,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1606 (all A (v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1607 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1608 (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_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,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E))))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1609 (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 (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]. 4.31/4.43 1610 (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) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & v1_funct_1(k3_funcop_1(C,D,E)))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1611 (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]. 4.31/4.43 1612 (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 k4_funcop_1(C,k5_relat_1(B,A),D) = k5_relat_1(B,k4_funcop_1(C,A,D))))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1613 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> B = k1_funct_1(A,C))) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1614 (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) -> 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]. 4.31/4.43 1615 (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_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,B) & v1_funct_2(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]. 4.31/4.43 1616 (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]. 4.31/4.43 1617 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(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) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1618 (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]. 4.31/4.43 1619 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (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]. 4.31/4.43 1620 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(A) & v1_funct_1(B) -> v1_relat_1(k4_funcop_1(A,B,C)) & v1_funct_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1621 (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_1(C) & 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 (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]. 4.31/4.43 1622 (all A (k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1623 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1624 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1625 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1626 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_1(C) & -v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & v1_funct_2(E,B,A) -> k5_funcop_1(C,D,E) = k8_funcop_1(A,B,C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1627 (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_1(D) & v1_funct_2(D,A,B) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1628 (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) -> 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]. 4.31/4.43 1629 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funcop_1(A)) & v1_funct_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1630 (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 (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1631 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1632 (all A all B A = k10_relat_1(k2_funcop_1(A,B),k1_tarski(B))) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1633 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1634 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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(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]. 4.31/4.43 1635 (all A (v1_funct_1(A) & v1_relat_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]. 4.31/4.43 1636 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(C) -> 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]. 4.31/4.43 1637 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1638 (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) & v1_funct_1(D) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) = k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1639 (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_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1640 (all A all B all C all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1641 (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(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,B),D) = k7_relat_1(k3_funcop_1(E,C,A),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1642 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(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]. 4.31/4.43 1643 (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_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,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]. 4.31/4.43 1644 (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_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1645 (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_2(D,A,B) & v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1646 (all A all B all C (r2_hidden(B,A) -> C = k1_funct_1(k2_funcop_1(A,C),B))) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1647 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1648 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1649 (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_1(D) & v1_funct_2(D,A,B) -> (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,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F))))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1650 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) = k4_funcop_1(B,A,C)))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1651 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(D) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(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]. 4.31/4.43 1652 (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 (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]. 4.31/4.43 1653 (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_funcop_1(C,D,k5_relat_1(B,A)) = k5_relat_1(B,k5_funcop_1(C,D,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1654 (all A all B all C all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> 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]. 4.31/4.43 1655 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1656 (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]. 4.31/4.43 1657 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,B,A) & v1_funct_1(E) & m1_relset_1(E,B,A) & -v1_xboole_0(B) & -v1_xboole_0(A) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) -> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.31/4.43 1658 (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]. 4.31/4.43 1659 (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]. 4.35/4.43 1660 (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 (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]. 4.35/4.43 1661 (all A all B (v1_funcop_1(A) & v1_relat_1(A) & v1_funct_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]. 4.35/4.43 1662 (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)) -> k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1663 (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_1(C) & v1_funct_2(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) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1664 (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]. 4.35/4.43 1665 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1666 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1667 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m2_relset_1(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,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1668 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1669 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1670 (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_1(D) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,B) & v1_funct_1(F) & v1_funct_2(F,A,B) -> ((all G (m1_subset_1(G,A) -> k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) = k8_funct_2(A,B,F,G))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1671 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_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]. 4.35/4.43 1672 (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)) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1673 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1674 (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_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) & v1_funct_2(D,A,B) -> (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]. 4.35/4.43 1675 (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 (v1_relat_1(D) & v1_funct_1(D) -> k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)) = k5_relat_1(C,k3_funcop_1(D,A,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1676 (all A all B (v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1677 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1678 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(A) & k1_relat_1(B) = k1_xboole_0 -> A = B))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1679 (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(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1680 (all A all B all C (r2_hidden(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(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1681 (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) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,B) & v1_funct_2(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]. 4.35/4.43 1682 (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]. 4.35/4.43 1683 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(r2_hidden(C,k1_relat_1(A)) & k1_xboole_0 != B & k1_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)))))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1684 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1685 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1686 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funcop_1(A,B,C)) & v1_relat_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1687 (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,k1_relat_1(A)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k1_funct_1(B,C) = k4_tarski(E,D))) & -(k1_funct_1(B,C) != k1_funct_1(A,C) & (all D all E k4_tarski(D,E) != k1_funct_1(A,C))))) & k1_relat_1(B) = k1_relat_1(A) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1688 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k3_funcop_1(A,B,C)) & v1_funct_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1689 (all A all B all C all D (m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1690 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> k1_relat_1(A) = B & k2_relat_1(A) = C | C = k1_xboole_0 | B = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1691 (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]. 4.35/4.43 1692 (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) -> (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]. 4.35/4.43 1693 (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) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1694 (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,k2_zfmisc_1(B,C)) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> 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))) = k1_funct_1(k1_funcop_1(D),E))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1695 (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) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & v1_funct_1(E) & m2_relset_1(E,A,B) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,E,D) = k6_funcop_1(B,A,C,D,E)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1696 (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_binop_1(B,k1_funct_1(A,C),D) = k1_funct_1(k4_funcop_1(B,A,D),C))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1697 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & 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 (m2_relset_1(E,B,A) & v1_funct_1(E) & v1_funct_2(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]. 4.35/4.43 1698 (all A all B (v1_xboole_0(B) -> v1_xboole_0(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1699 (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 (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]. 4.35/4.43 1700 (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 (m1_subset_1(C,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_1(D) & v1_funct_2(D,A,A) -> k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.35/4.43 1701 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k4_funcop_1(C,k7_relat_1(A,B),D) = k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D))))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.36/4.46 1702 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(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) -> (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,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))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.36/4.46 1703 (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]. 4.36/4.46 1704 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & -v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,B,A) -> 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]. 4.36/4.46 1705 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.46 1706 (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]. 4.36/4.46 1707 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & f4_s16_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f6_s16_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_ordinal2(C) = B & v1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & v5_ordinal1(C))) <-> B = f3_s16_ordinal2(A)))))) & v4_ordinal1(f2_s16_ordinal2) & f2_s16_ordinal2 = k1_relat_1(f1_s16_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) & f2_s16_ordinal2 != k1_xboole_0 -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.46 1708 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = A & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & v1_ordinal2(C))) & B != A & (exists C (f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D))))) & B = k1_ordinal2(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (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))))) & v1_relat_1(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.36/4.46 1709 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v1_funct_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)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & A = k1_ordinal2(B) & v1_ordinal2(B) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> C = k1_xboole_0 | f4_s13_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & k1_relat_1(B) = k1_ordinal1(f1_s13_ordinal2) & v5_ordinal1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1710 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1711 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1712 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k1_funct_1(A,B) & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> k1_xboole_0 = B | r1_ordinal2(C,k2_ordinal1(A,B)))))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1713 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & B = k1_ordinal2(C) & v1_relat_1(C) & v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s8_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & k1_relat_1(C) = k1_ordinal1(A))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1714 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1715 (all A (v3_ordinal1(A) -> A = k2_ordinal2(A))) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1716 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_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]. 4.36/4.49 1717 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1718 (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]. 4.36/4.49 1719 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1720 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1721 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f6_s4_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A)) = f3_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(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f6_s4_ordinal2) = f1_s4_ordinal2 & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) -> f5_s4_ordinal2 = f6_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1722 (all A all B -((exists C (v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,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))) & v1_funct_1(C) & v1_relat_1(C) & B = k1_ordinal2(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2)) & A != B & (exists C (k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = D | f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1723 (exists A exists B (v1_funct_1(B) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> C = k1_xboole_0 | f4_s7_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & v5_ordinal1(B) & k1_ordinal2(B) = A & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & (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))))) & v1_relat_1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1724 (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]. 4.36/4.49 1725 (all A (v4_ordinal2(A) <-> r2_hidden(A,k5_ordinal2))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1726 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1727 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1728 (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]. 4.36/4.49 1729 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1730 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1731 (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]. 4.36/4.49 1732 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1733 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1734 (exists A (v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> f2_s2_ordinal2(B) = k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v1_funct_1(A) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1735 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1736 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1737 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1738 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1739 (all A all B (k2_ordinal2(A) = B <-> (all C (v3_ordinal1(C) & r2_hidden(C,A) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.49 1740 (all A (v3_ordinal1(A) -> (all B (f4_s9_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s9_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f1_s9_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & v5_ordinal1(C) & v1_relat_1(C))))))) -> (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]. 4.36/4.50 1741 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1742 (all A all B (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1743 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k4_ordinal2 = k16_ordinal2(k4_ordinal2,A))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1744 k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & k1_xboole_0 != f2_s10_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (all B (B = f3_s10_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & (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)))) & f4_s10_ordinal2 = k1_funct_1(C,k1_xboole_0) & (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))))) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f3_s10_ordinal2(f2_s10_ordinal2) = f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1745 (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]. 4.36/4.50 1746 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1747 (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]. 4.36/4.50 1748 (all A all B (B = k3_ordinal2(A) <-> (all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (v3_ordinal1(D) & C = D & v4_ordinal1(D))))))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1749 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k1_xboole_0) = A)) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1750 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_ordinal1(k14_ordinal2(A,B)) = k14_ordinal2(A,k1_ordinal1(B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1751 (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]. 4.36/4.50 1752 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v5_ordinal1(C) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (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))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_relat_1(C) & v1_ordinal2(C))) <-> f1_s14_ordinal2(A) = B))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1753 (all A (v3_ordinal1(A) -> (exists B ((exists C (v4_ordinal1(B) & A = k14_ordinal2(B,C) & v3_ordinal1(C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1754 (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]. 4.36/4.50 1755 (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]. 4.36/4.50 1756 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1757 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1758 (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]. 4.36/4.50 1759 (exists A ((r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s11_ordinal2) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s11_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B)) | k1_xboole_0 = B))) & k1_relat_1(A) = f1_s11_ordinal2 & v5_ordinal1(A) & v1_ordinal2(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1760 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1761 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (r1_ordinal2(B,A) <-> B = k12_ordinal2(A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1762 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1763 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1764 (all A all B (v3_ordinal1(B) -> (B = k7_ordinal2(A) <-> (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1765 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1766 (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]. 4.36/4.50 1767 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(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]. 4.36/4.50 1768 (exists A (v1_relat_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s5_ordinal2 & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s5_ordinal2) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | k1_xboole_0 = B))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1769 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> k2_ordinal2(B) = k1_xboole_0 | r1_ordinal1(A,k6_ordinal2(B)))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1770 (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]. 4.36/4.50 1771 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_funct_1(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) = k1_funct_1(D,E) | k1_xboole_0 = E))) & k1_relat_1(D) = k1_ordinal1(A) & v5_ordinal1(D) & v1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k1_funct_1(D,k1_ordinal1(E)) = k14_ordinal2(k1_funct_1(D,E),B)))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0) & k1_ordinal2(D) = C & v1_ordinal2(D))) <-> k15_ordinal2(A,B) = C))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1772 (all A (v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_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))))))) & B = k9_ordinal2(C) & v1_relat_1(C) & v1_ordinal2(C) & k1_relat_1(A) = k1_relat_1(C) & v5_ordinal1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1773 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1774 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> (r1_ordinal2(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(A,D) & r2_hidden(C,A) & (all E (v3_ordinal1(E) -> -(r2_hidden(E,k1_relat_1(B)) & (all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(C,k1_funct_1(B,F)) & r2_hidden(k1_funct_1(B,F),D)))))))))))))) & (k1_xboole_0 = A -> (r1_ordinal2(A,B) <-> (exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1775 (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]. 4.36/4.50 1776 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1777 (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]. 4.36/4.50 1778 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1779 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) & v1_relat_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1780 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1781 p1_s1_ordinal2(k1_xboole_0) & (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)))) -> p1_s1_ordinal2(A) | A = k1_xboole_0))) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1782 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1783 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1784 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1785 (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]. 4.36/4.50 1786 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1787 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1788 (exists A (v4_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A) & v3_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1789 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v3_ordinal1(B) & v4_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1790 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.36/4.50 1791 (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]. 4.43/4.55 1792 (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s6_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (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))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C ((all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_relat_1(C) = k1_ordinal1(A) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0) & (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))))) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) -> (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]. 4.43/4.55 1793 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1794 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) & v1_funct_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1795 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1796 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & k8_ordinal2(C) = B & (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)))) & k1_relat_1(A) = k1_relat_1(C) & v1_relat_1(C))) <-> k11_ordinal2(A) = B))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1797 (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]. 4.43/4.55 1798 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1799 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1800 (all A all B (v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) & v5_ordinal1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) & v1_ordinal2(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1801 (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]. 4.43/4.55 1802 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1803 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1804 (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]. 4.43/4.55 1805 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> f2_s3_ordinal2(B) = k1_funct_1(A,B)))) & f1_s3_ordinal2 = k1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.43/4.55 1806 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v1_relat_1(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & B = k1_ordinal2(C) & v5_ordinal1(C))) <-> B = f4_s15_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1807 (all A (k5_ordinal2 = 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) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1808 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k14_ordinal2(B,A) = k8_ordinal2(C)))) | A = k1_xboole_0))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1809 (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]. 4.48/4.62 1810 (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]. 4.48/4.62 1811 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)) & k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1812 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B))) <-> v1_ordinal2(A)))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1813 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1814 (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]. 4.48/4.62 1815 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1816 k1_relat_1(f1_s12_ordinal2) = f3_s12_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s12_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A)) = f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A))))) & (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) -> (all B (v3_ordinal1(B) -> (f2_s12_ordinal2(A) = B <-> (exists C (v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & (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))))) & v1_relat_1(C)))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1817 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k14_ordinal2(A,B) <-> (exists D (A = 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)) = k1_ordinal1(k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k8_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & v1_ordinal2(D) & v1_relat_1(D) & v1_funct_1(D) & k1_relat_1(D) = k1_ordinal1(B) & C = k1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1818 (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) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B)))) | k1_xboole_0 = A))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1819 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1820 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (C = k1_ordinal2(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)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & v1_funct_1(D) & v1_relat_1(D) & v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & v1_ordinal2(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1821 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k4_ordinal2) = A & k15_ordinal2(k4_ordinal2,A) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1822 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1823 (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]. 4.48/4.62 1824 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1825 (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]. 4.48/4.62 1826 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1827 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1828 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1829 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (B = A & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)) & k1_funct_1(B,k13_arytm_3) = np__0)))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1830 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1831 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1832 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1833 (exists A (-v1_xboole_0(A) & v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v2_xreal_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1834 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) <-> v2_xreal_0(A)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1835 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(B,A)) & -v2_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]. 4.48/4.62 1836 (all A all B (-v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v3_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)) & -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(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1837 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1838 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1839 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1840 (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]. 4.48/4.62 1841 (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]. 4.48/4.62 1842 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1843 (exists A (v1_xcmplx_0(A) & -v2_xreal_0(A) & v1_xboole_0(A) & -v3_xreal_0(A) & v1_xreal_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1844 (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]. 4.48/4.62 1845 (all A all B (-v2_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> 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]. 4.48/4.62 1846 (all A all B (-v3_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1847 (all A all B (-v2_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_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]. 4.48/4.62 1848 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_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]. 4.48/4.62 1849 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1850 (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]. 4.48/4.62 1851 (all A (-v1_xboole_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1852 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1853 (exists A (-v3_xreal_0(A) & v2_xreal_0(A) & -v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1854 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(A) & -v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1855 (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]. 4.48/4.62 1856 (all A all B (v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) & -v2_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1857 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> 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]. 4.48/4.62 1858 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1859 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1860 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (A = C & m1_subset_1(D,k2_arytm_2) & r1_arytm_2(C,D) & B = D)))))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (k4_tarski(np__0,C) = A & r1_arytm_2(D,C) & B = k4_tarski(np__0,D) & m1_subset_1(D,k2_arytm_2))))))) & -(-(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r1_xreal_0(A,B) <-> r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1861 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1862 (all A all B (-v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1863 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1864 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(B) -> -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1865 (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]. 4.48/4.62 1866 (all A all B (v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1867 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1868 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & v3_xreal_0(A) & -v2_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1869 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1870 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1871 (all A all B (-v3_xreal_0(A) & v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1872 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1873 (all A (v3_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) & v1_xcmplx_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1874 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & v1_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]. 4.48/4.62 1875 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(B,A) | r1_xreal_0(A,B))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1876 (all A all B (-v3_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1877 (all A all B (-v3_xreal_0(B) & v1_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)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1878 (all A all B (-v2_xreal_0(B) & v1_xreal_0(A) & -v2_xreal_0(A) & 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(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1879 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1880 (all A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1881 (all A all B (v1_int_1(A) & v1_int_1(B) -> v4_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1882 (all A all B (v5_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1883 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1884 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1885 (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]. 4.48/4.62 1886 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k5_xboole_0(A,B)))) # label(fc42_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1887 (all A all B (v5_membered(A) & v5_membered(B) -> v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1888 (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_xboole_0(A,B)))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1889 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1890 (all A all B all C (v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1891 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B) & v4_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1892 (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]. 4.48/4.62 1893 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1894 (all A all B (v4_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1895 (exists A (v5_membered(A) & -v1_xboole_0(A) & v2_membered(A) & v4_membered(A) & v3_membered(A) & v1_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1896 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1897 (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]. 4.48/4.62 1898 (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]. 4.48/4.62 1899 (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]. 4.48/4.62 1900 (all A (v1_xreal_0(A) -> v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1901 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1902 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1903 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> A = B))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1904 (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]. 4.48/4.62 1905 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1906 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1907 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1908 (all A (v5_membered(A) -> ((all B (v4_ordinal2(B) -> r2_hidden(B,A))) -> A = k5_numbers))) # label(t15_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1909 (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]. 4.48/4.62 1910 (all A (v5_membered(A) <-> (all B (r2_hidden(B,A) -> v4_ordinal2(B))))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1911 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> A = k3_numbers))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1912 (all A all B (v4_membered(B) & v4_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1913 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1914 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1915 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1916 (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]. 4.48/4.62 1917 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1918 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xreal_0(B) & r2_hidden(B,A))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1919 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1920 (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]. 4.48/4.62 1921 (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_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1922 (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]. 4.48/4.62 1923 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1924 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v1_membered(A) & v2_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1925 (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]. 4.48/4.62 1926 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1927 (all A all B (v3_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1928 (all A all B all C (v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1929 (exists A (v3_membered(A) & (all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1930 (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]. 4.48/4.62 1931 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v3_membered(B) & v2_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1932 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1933 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1934 (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]. 4.48/4.62 1935 (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]. 4.48/4.62 1936 (all A all B (v4_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1937 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v2_membered(A) & v1_membered(A) & v3_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1938 (all A all B (v2_membered(B) & v2_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1939 (all A all B (v3_membered(A) & v3_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1940 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1941 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1942 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1943 (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]. 4.48/4.62 1944 (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]. 4.48/4.62 1945 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 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]. 4.48/4.62 1947 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v4_ordinal2(B) & v1_rat_1(B) & v1_xcmplx_0(B) & v1_int_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1948 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) -> v4_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1949 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1950 (all A all B (r2_hidden(B,A) & v3_membered(B) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1951 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1952 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1953 (all A all B (v5_membered(A) -> v5_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)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1954 (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]. 4.48/4.62 1955 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v4_membered(A) & v1_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1956 (all A (-v1_xboole_0(A) & v5_membered(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1957 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v2_membered(A) & v3_membered(A) & v1_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1958 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1959 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_int_1(B) & v1_rat_1(B) & v1_xcmplx_0(B) & v1_xreal_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1960 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1961 (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]. 4.48/4.62 1962 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1963 (all A (v1_rat_1(A) -> v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1964 (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]. 4.48/4.62 1965 (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]. 4.48/4.62 1966 (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]. 4.48/4.62 1967 (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]. 4.48/4.62 1968 (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]. 4.48/4.62 1969 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1970 (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]. 4.48/4.62 1971 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1972 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1973 (all A all B (v2_membered(B) & v2_membered(A) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1974 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1975 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s4_membered(B)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1976 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1977 (all A all B (v4_membered(B) & v4_membered(A) -> v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1978 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (A = B <-> (all C (v1_int_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1979 (all A all B all C (v1_int_1(A) & v1_int_1(B) & v1_int_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1980 (all A (-v1_xboole_0(A) & v4_membered(A) -> (exists B (r2_hidden(B,A) & v1_int_1(B))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1981 (all A (v4_membered(A) <-> (all B (r2_hidden(B,A) -> v1_int_1(B))))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1982 (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]. 4.48/4.62 1983 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1984 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (B = A <-> (all C (v1_xcmplx_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1985 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1986 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1987 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1988 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1989 (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]. 4.48/4.62 1990 (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]. 4.48/4.62 1991 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v3_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]. 4.48/4.62 1992 (all A (v4_ordinal2(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1993 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1994 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1995 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1996 (all A all B all C (v1_rat_1(B) & v1_rat_1(C) & v1_rat_1(A) -> v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1997 (all A all B (m1_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) -> k8_eqrel_1(A,B) = k7_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1998 (all A all B (m2_relset_1(B,A,A) -> (exists C (v3_relat_2(C) & v1_partfun1(C,A,A) & (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & v8_relat_2(D) & m2_relset_1(D,A,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & m2_relset_1(C,A,A) & r1_tarski(B,C) & v8_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.62 1999 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2000 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> -((exists C r2_hidden(C,A)) & k1_xboole_0 = B))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2001 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2002 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2003 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v8_relat_2(B) & v1_partfun1(B,A,A) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(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) -> (D = k3_eqrel_1(A,B,C) -> (all E -(k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,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]. 4.48/4.63 2004 (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]. 4.48/4.63 2005 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2006 (all A all B (m2_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) & v1_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]. 4.48/4.63 2007 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2008 (all A all B all C (m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & v1_partfun1(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,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2009 (all A all B (v8_relat_2(B) & v3_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]. 4.48/4.63 2010 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2011 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2012 (all A (m2_relset_1(k6_partfun1(A),A,A) & v3_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & v8_relat_2(k6_partfun1(A)))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2013 (all A all B all C all D (v1_partfun1(D,A,A) & m2_relset_1(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]. 4.48/4.63 2014 (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]. 4.48/4.63 2015 (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 -(-r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & r2_hidden(D,A) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2016 (all A all B all C all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) -> (all E (v8_relat_2(E) & v1_partfun1(E,B,B) & m2_relset_1(E,B,B) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (k1_funct_1(F,np__1) = A & r1_xreal_0(np__1,k3_finseq_1(F)) & v1_funct_1(F) & v1_relat_1(F) & v1_finseq_1(F) & 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)))))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2017 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (k1_xboole_0 = A -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2018 (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]. 4.48/4.63 2019 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2020 (all A all B all C (v3_relat_2(C) & v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(B,A,A) & v8_relat_2(B) -> v1_partfun1(k4_eqrel_1(A,B,C),A,A) & m2_relset_1(k4_eqrel_1(A,B,C),A,A) & v3_relat_2(k4_eqrel_1(A,B,C)) & v8_relat_2(k4_eqrel_1(A,B,C)))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2021 (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]. 4.48/4.63 2022 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C k6_eqrel_1(A,B,C) = k10_relset_1(A,A,B,k1_tarski(C))))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2023 (all A all B all C (v3_relat_2(B) & v3_relat_2(C) & v8_relat_2(C) & v8_relat_2(B) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2024 (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 (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (D = k6_eqrel_1(A,B,E) & r2_hidden(E,A)))))) <-> C = k7_eqrel_1(A,B)))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2025 (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 (v8_relat_2(C) & v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v3_relat_2(D) -> (r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v8_relat_2(E) & v1_partfun1(E,A,A) & v3_relat_2(E) & m2_relset_1(E,A,A) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E)))) <-> k5_eqrel_1(A,B,C) = D))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2026 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2027 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & m2_relset_1(B,A,A) -> (all C -((all D -r2_hidden(C,k6_eqrel_1(A,B,D))) & r2_hidden(C,A))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2028 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2029 (all A all B (m1_eqrel_1(B,A) -> (exists C (m2_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(C,A,A) & k7_eqrel_1(A,C) = B & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2030 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2031 (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]. 4.48/4.63 2032 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & v3_relat_2(B) -> k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2033 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2034 (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 (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> B = k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)))))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2035 (all A (v1_partfun1(k1_eqrel_1(A),A,A) & v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2036 (all A all B all C (v1_partfun1(C,A,A) & v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) -> (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]. 4.48/4.63 2037 (all A all B all C all D (v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v1_relat_2(D) & v3_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]. 4.48/4.63 2038 (all A all B (m2_relset_1(B,A,A) -> (v3_relat_2(B) & k3_relat_1(B) = A & v1_relat_2(B) & v8_relat_2(B) <-> v1_partfun1(B,A,A) & v8_relat_2(B) & m2_relset_1(B,A,A) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2039 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2040 (all A all B (m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2041 (all A all B (m1_relset_1(B,A,A) & v8_relat_2(B) & v1_partfun1(B,A,A) & v3_relat_2(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2042 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != A -> (m1_eqrel_1(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) & C != D & -r1_xboole_0(C,D))))))) & k5_setfam_1(A,B) = A)) & (k1_xboole_0 = A -> (B = k1_xboole_0 <-> m1_eqrel_1(B,A))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2043 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2044 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_relat_2(B) & v3_relat_2(B) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2045 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & v1_partfun1(C,A,A) -> B = k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)))))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2046 (all A all B all C all D all E (m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) -> (r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2047 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2048 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2049 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & 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) & v1_partfun1(B,A,A) -> k5_eqrel_1(A,B,B) = B)) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2050 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & -v1_xboole_0(A) & m1_relset_1(B,A,A) & v3_relat_2(B) -> 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]. 4.48/4.63 2051 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2052 (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]. 4.48/4.63 2053 (all A all B (m2_relset_1(B,A,A) -> B = k2_eqrel_1(A,k1_eqrel_1(A),B))) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2054 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(B) & v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(B,A,A) & v8_relat_2(B) -> m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & v3_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2055 (all A all B all C (m2_relset_1(C,A,A) & v1_relat_2(C) & v1_partfun1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2056 (all A all B all C all D all E (m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) & v3_relat_2(E) & v1_relat_2(E) -> (r2_hidden(D,k6_eqrel_1(A,E,C)) & r2_hidden(B,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2057 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> B = k2_eqrel_1(A,B,B))) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2058 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2059 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2060 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2061 (all A all B (v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) -> B = k5_eqrel_1(A,B,B))) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2062 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2063 (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) -> -(k1_eqrel_1(A) = k3_eqrel_1(A,B,C) & k1_eqrel_1(A) != B & C != k1_eqrel_1(A)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2064 (all A all B (m1_relset_1(B,A,A) & v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2065 (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) -> v1_partfun1(C,A,A) & v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A))) -> k1_xboole_0 = B | v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B))))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2066 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,C,B) = k2_eqrel_1(A,B,C))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2067 (all A all B all C (v8_relat_2(B) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v1_partfun1(B,A,A) & v3_relat_2(B) & m1_relset_1(B,A,A) & v3_relat_2(C) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2068 (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 (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_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]. 4.48/4.63 2069 (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) & (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(A,B) & p1_s1_eqrel_1(B,C) -> p1_s1_eqrel_1(A,C))) -> (exists A (m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A) & (all B all C (r2_hidden(B,f1_s1_eqrel_1) & r2_hidden(C,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v3_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2070 (all A all B (v1_partfun1(B,A,A) & v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) -> ((exists C k6_eqrel_1(A,B,C) = A) -> B = k1_eqrel_1(A)))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2071 (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]. 4.48/4.63 2072 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> B = k3_eqrel_1(A,B,B))) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2073 (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]. 4.48/4.63 2074 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2075 (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]. 4.48/4.63 2076 (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]. 4.48/4.63 2077 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> A = g1_struct_0(u1_struct_0(A))))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2078 (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]. 4.48/4.63 2079 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_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]. 4.48/4.63 2080 (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]. 4.48/4.63 2081 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2082 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k1_struct_0(A,B) = k1_tarski(B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2083 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2084 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_struct_0(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,B) <-> m1_struct_0(C,A,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2085 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2086 (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]. 4.48/4.63 2087 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2088 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2089 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2090 (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]. 4.48/4.63 2091 (exists A (v1_struct_0(A) & l1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2092 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_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]. 4.48/4.63 2093 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2094 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) & -v3_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]. 4.48/4.63 2095 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2096 (all A all B (m1_subset_1(B,A) -> l2_struct_0(g2_struct_0(A,B)) & v2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2097 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2098 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k2_struct_0(A,B,C) = k2_struct_0(A,C,B))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2099 (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]. 4.48/4.63 2100 (all A all B (-v1_xboole_0(B) & -v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2101 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2102 (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]. 4.48/4.63 2103 (exists A (l2_struct_0(A) & -v3_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2104 (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]. 4.48/4.63 2105 (all A all B all C all D (l1_struct_0(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> 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]. 4.48/4.63 2106 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> l1_pre_topc(g1_pre_topc(A,B)) & v1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2107 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 4.48/4.63 2108 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2109 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2110 (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)) -> ((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)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2111 (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]. 4.48/4.63 2112 (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) & (B = k6_pre_topc(A,B) & v2_pre_topc(A) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2113 (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(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2114 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2115 (all A (l1_struct_0(A) -> v3_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2116 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2117 (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 -> k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2118 (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]. 4.48/4.63 2119 (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) -> D = B & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2120 (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]. 4.48/4.63 2121 (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))) -> 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]. 4.48/4.63 2122 (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)) & v4_pre_topc(D,A))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2123 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2124 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2125 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2126 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2127 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2128 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2129 (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,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & (v2_pre_topc(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)) -> v3_pre_topc(B,A)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2130 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2131 (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) != k1_xboole_0 & k2_pre_topc(A) = B) & -(k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) & B != k2_pre_topc(A)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2132 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2133 (all A (v2_pre_topc(A) & l1_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]. 4.48/4.63 2134 (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,k6_pre_topc(A,B)) <-> -v3_struct_0(A) & (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(B,D))))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2135 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2136 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(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]. 4.48/4.63 2137 (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)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) <-> r2_hidden(D,C)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2138 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2139 (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]. 4.48/4.63 2140 (all A all B all C all D (l1_struct_0(B) & l1_struct_0(A) & m1_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) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2141 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2142 (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]. 4.48/4.63 2143 (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) -> (k2_pre_topc(C) = B <-> C = k3_pre_topc(A,B)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2144 (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]. 4.48/4.63 2145 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2146 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2147 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k1_xboole_0)) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2148 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(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]. 4.48/4.63 2149 (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]. 4.48/4.63 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]. 4.48/4.63 2151 (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]. 4.48/4.63 2152 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2153 (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]. 4.48/4.63 2154 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2155 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v4_pre_topc(B,A))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2156 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2157 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2158 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2159 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2160 (all A (-v3_struct_0(A) & l1_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]. 4.48/4.63 2161 (all A all B (l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_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]. 4.48/4.63 2162 (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]. 4.48/4.63 2163 (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]. 4.48/4.63 2164 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2165 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2166 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)) = k2_pre_topc(A))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2167 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2168 (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]. 4.48/4.63 2169 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2170 (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]. 4.48/4.63 2171 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2172 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((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))) & k3_xboole_0(D,k2_pre_topc(B)) = C & r2_hidden(D,u1_pre_topc(A)))) <-> r2_hidden(C,u1_pre_topc(B))))) & r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) <-> m1_pre_topc(B,A)))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2173 (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]. 4.48/4.63 2174 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2175 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2176 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2177 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2178 (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]. 4.48/4.63 2179 (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]. 4.48/4.63 2180 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2181 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2182 (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]. 4.48/4.63 2183 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2184 (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]. 4.48/4.63 2185 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2186 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = B)))) # label(t15_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2187 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2188 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2189 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2190 (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]. 4.48/4.63 2191 (all A (l1_struct_0(A) -> k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),k1_pre_topc(A)))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2192 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2193 (all A all B all C all D (l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2194 (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))) -> (k6_pre_topc(A,B) = C <-> (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))))))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2195 (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]. 4.48/4.63 2196 (all A all B all C all D (l1_struct_0(B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_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]. 4.48/4.63 2197 (all A (l1_pre_topc(A) -> (r2_hidden(u1_struct_0(A),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(C,u1_pre_topc(A)) & r2_hidden(B,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_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))))) <-> v2_pre_topc(A)))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2198 (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]. 4.48/4.63 2199 (all A (l1_pre_topc(A) -> (all 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))) -> (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]. 4.48/4.63 2200 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) <-> B = k6_pre_topc(A,k1_tops_1(A,B))))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2201 (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))) -> (v4_tops_1(D,B) & v4_pre_topc(D,B) -> v5_tops_1(D,B)) & (v5_tops_1(C,A) -> v4_tops_1(C,A) & v4_pre_topc(C,A)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2202 (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(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]. 4.48/4.63 2203 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2204 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2205 (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]. 4.48/4.63 2206 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2207 (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))) -> (C = k1_tops_1(A,C) -> v3_pre_topc(C,A)) & (v3_pre_topc(D,B) -> D = k1_tops_1(B,D)))))))))) # label(t55_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2208 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2209 (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]. 4.48/4.63 2210 (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(C,A) & v3_tops_1(B,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2211 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2212 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2213 (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,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,D) & v3_pre_topc(D,A) -> -r1_xboole_0(B,D) & -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D)))) <-> r2_hidden(C,k2_tops_1(A,B))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2214 (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(B,A) & v4_pre_topc(C,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2215 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2216 (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]. 4.48/4.63 2217 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> k1_tops_1(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t43_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2218 (all 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_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.63 2219 (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]. 4.48/4.63 2220 (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))) -> 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))) = k4_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]. 4.48/4.64 2221 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2222 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 4.48/4.64 2223 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v2_tops_1(B,A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2224 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2225 (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]. 4.48/4.64 2226 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 4.48/4.64 2227 (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]. 4.48/4.64 2228 (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]. 4.48/4.64 2229 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2230 (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]. 4.48/4.64 2231 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2232 (all A all B (l1_pre_topc(A) & v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v1_xboole_0(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2233 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2234 (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]. 4.48/4.64 2235 (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]. 4.48/4.64 2236 (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]. 4.48/4.64 2237 (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) -> 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]. 4.48/4.64 2238 (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]. 4.48/4.64 2239 (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]. 4.48/4.64 2240 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k6_pre_topc(A,k6_pre_topc(A,B)))))) # label(t26_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2241 (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]. 4.48/4.64 2242 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2243 (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))) -> k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2244 (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,k6_pre_topc(A,B)),B) & r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) <-> v4_tops_1(B,A)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2245 (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]. 4.48/4.64 2246 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2247 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2248 (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]. 4.48/4.64 2249 (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))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,C) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)))))))))) # label(t81_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2250 (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))) -> (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)) & (v3_pre_topc(D,B) & v4_tops_1(D,B) -> v6_tops_1(D,B)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2251 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2252 (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]. 4.48/4.64 2253 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2254 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2255 (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]. 4.48/4.64 2256 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = 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)))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2257 (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) & v1_tops_1(C,A) & v1_tops_1(B,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2258 (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]. 4.48/4.64 2259 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & v1_membered(B) & v3_pre_topc(B,A) & v2_membered(B) & v4_membered(B) & v5_membered(B) & v3_tops_1(B,A) & v2_tops_1(B,A) & v3_membered(B) & v1_xboole_0(B))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 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_xboole_0(B) -> v3_tops_1(B,A)))))) # label(cc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2261 (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(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]. 4.48/4.64 2262 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2263 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v2_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A) & v1_xboole_0(k1_pre_topc(A)))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2264 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2265 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v3_pre_topc(B,A) & v2_pre_topc(A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2266 (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]. 4.48/4.64 2267 (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(C,A) & v5_tops_1(B,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2268 (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]. 4.48/4.64 2269 (all A all B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 4.48/4.64 2270 (all 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) <-> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B))))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2271 (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]. 4.48/4.64 2272 (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]. 4.48/4.64 2273 (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]. 4.48/4.64 2274 (all A all B (l1_pre_topc(A) & v2_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]. 4.48/4.64 2275 (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]. 4.48/4.64 2276 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)) & v3_pre_topc(k1_pre_topc(A),A) & v2_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2277 (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]. 4.48/4.64 2278 (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]. 4.48/4.64 2279 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2280 (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]. 4.48/4.64 2281 (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) & v2_tops_1(C,A) & v2_tops_1(B,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2282 (all A (l1_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) -> v3_tops_1(B,A)))))) # label(t93_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2283 (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) & r1_tarski(C,B) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2284 (all A all B (l1_pre_topc(A) & v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2285 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k2_tops_1(A,B)) <-> v2_tops_1(B,A)))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2286 (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]. 4.48/4.64 2287 (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]. 4.48/4.64 2288 (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(k6_pre_topc(A,B),A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2289 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (r1_tarski(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r2_hidden(B,D))) <-> r2_hidden(B,k1_tops_1(A,C))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2290 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2291 (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]. 4.48/4.64 2292 (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) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2293 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A))))) # label(t2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2294 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2295 (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(B,A) -> (v5_tops_1(B,A) <-> v6_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2296 (all A (l1_pre_topc(A) -> (exists B (v1_membered(B) & v3_membered(B) & v5_membered(B) & v1_xboole_0(B) & v4_membered(B) & v2_tops_1(B,A) & v2_membered(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2297 (all 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) & v3_pre_topc(B,A) -> k1_xboole_0 = B))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2298 (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) & v1_tops_1(B,A) -> v1_tops_1(C,A)))))))) # label(t79_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2299 (all A (l1_pre_topc(A) -> v1_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v3_membered(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2300 (all 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) -> v2_tops_1(B,A)))))) # label(cc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2301 (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))) -> (v3_pre_topc(C,A) & r1_tarski(C,B) -> k1_xboole_0 = C)))))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2302 (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]. 4.48/4.64 2303 (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]. 4.48/4.64 2304 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2305 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) = k2_tops_1(A,B))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2306 (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]. 4.48/4.64 2307 (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]. 4.48/4.64 2308 (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) & v4_pre_topc(B,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2309 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (exists B (-v1_xboole_0(B) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2310 (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) & v3_pre_topc(D,A) & r1_xboole_0(B,D))))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2311 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),k2_pre_topc(A)))) # label(t8_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2312 (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,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t58_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2313 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2314 (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]. 4.48/4.64 2315 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 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_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]. 4.48/4.64 2317 (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) & C != k1_xboole_0 & r1_xboole_0(B,C)))) <-> v1_tops_1(B,A)))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2318 (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]. 4.48/4.64 2319 (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]. 4.48/4.64 2320 (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]. 4.48/4.64 2321 (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]. 4.48/4.64 2322 (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))) -> (v6_tops_1(B,A) & v6_tops_1(C,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2323 (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),B) = k3_subset_1(u1_struct_0(A),C) -> B = C))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2324 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2325 (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) & v4_pre_topc(B,A) -> v3_tops_1(B,A) & v2_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2326 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2327 (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]. 4.48/4.64 2328 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2329 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2330 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2331 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (B = k2_tops_1(A,B) <-> v3_tops_1(B,A))))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2332 (all 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) & v3_pre_topc(B,A) -> v3_pre_topc(B,A) & v4_membered(B) & v2_tops_1(B,A) & v5_membered(B) & v4_pre_topc(B,A) & v2_membered(B) & v3_tops_1(B,A) & v3_membered(B) & v1_membered(B) & v1_xboole_0(B)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2333 (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)) & k2_tops_1(A,k6_pre_topc(A,B)) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2334 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2335 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2336 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2337 (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))) -> -(v3_pre_topc(C,A) & C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_xboole_0(B,D) & r1_tarski(D,C) & v3_pre_topc(D,A) & k1_xboole_0 != D)))))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2338 (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(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]. 4.48/4.64 2339 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v3_tops_1(B,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]. 4.48/4.64 2340 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2341 (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 ((exists D (r2_hidden(C,D) & r1_tarski(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A))) <-> r2_hidden(C,B)))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2342 (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]. 4.48/4.64 2343 (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]. 4.48/4.64 2344 (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]. 4.48/4.64 2345 $T # label(t15_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2346 (all A all B all C (l1_pre_topc(A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,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]. 4.48/4.64 2347 (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)))) -> -(v1_tops_2(D,A) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (E = k2_pre_topc(B) -> C = k1_tops_2(A,E,D))))))) & v1_tops_2(C,B)))))))) # label(t49_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2348 $T # label(t2_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2349 (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)) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> k5_pre_topc(A,B,C,k2_pre_topc(B)) = k2_pre_topc(A))))))) # label(t52_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2350 (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_finset_1(B) & v1_tops_2(B,A) -> v3_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t27_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2351 $T # label(t7_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2352 (all 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 (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))) -> 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]. 4.48/4.64 2353 (all A (-v3_struct_0(A) & l1_pre_topc(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)) -> (k2_pre_topc(A) = k1_relat_1(C) & k2_pre_topc(B) = k2_relat_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)))) & v2_funct_1(C) <-> v3_tops_2(C,A,B)))))))) # label(t73_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2354 $T # label(t4_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2355 $T # label(t9_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2356 (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) -> (v3_tops_2(C,A,B) <-> k2_pre_topc(A) = k1_relat_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) <-> v4_pre_topc(k4_pre_topc(A,B,C,D),B)))) & v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C)))))))) # label(t72_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2357 (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]. 4.48/4.64 2358 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_pre_topc(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) -> (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]. 4.48/4.64 2359 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(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_1(C) & 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))) -> k4_pre_topc(A,B,C,k6_pre_topc(A,D)) = k6_pre_topc(B,k4_pre_topc(A,B,C,D)))) & v2_funct_1(C) & k2_pre_topc(B) = k2_relat_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]. 4.48/4.64 2360 (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]. 4.48/4.64 2361 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_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(B))) -> (v3_pre_topc(D,B) -> v3_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(t55_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2362 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) -> (all 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)) & v1_funct_1(E) -> (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]. 4.48/4.64 2363 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_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(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]. 4.48/4.64 2364 (all A (l1_pre_topc(A) -> (all 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)) -> (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)))) -> (E = k9_relat_1(k3_funct_3(C),D) -> v2_tops_2(E,A))))))))))))) # label(t60_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2365 (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) <-> v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t16_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2366 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(B = k1_xboole_0 & r1_pre_topc(A,B)))))) # label(t5_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2367 $T # label(t53_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2368 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (l1_struct_0(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_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (v2_funct_1(E) & v2_funct_1(D) & k1_relat_1(D) = k2_pre_topc(A) & k2_relat_1(D) = k2_pre_topc(B) & k1_relat_1(E) = k2_pre_topc(B) & k2_pre_topc(C) = k2_relat_1(E) -> 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]. 4.48/4.64 2369 (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]. 4.48/4.64 2370 (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)))) -> (B = D -> v2_tops_2(D,C))))))))))) # label(t36_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2371 (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]. 4.48/4.64 2372 (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]. 4.48/4.64 2373 $T # label(t39_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2374 (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(C,A) & v2_tops_2(B,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]. 4.48/4.64 2375 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & m2_relset_1(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)))) -> (v1_tops_2(D,B) & v5_pre_topc(C,A,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]. 4.48/4.64 2376 (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 (k2_relat_1(D) = k1_tops_2(A,B,C) & k1_relat_1(D) = C & v1_relat_1(D) & (all E (r2_hidden(E,C) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (F = E -> k1_funct_1(D,E) = k5_subset_1(u1_struct_0(A),F,B)))))) & v1_funct_1(D))))))))) # label(t50_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2377 (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]. 4.48/4.64 2378 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> v2_funct_1(k2_tops_2(A,B,C))))))))) # label(t63_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2379 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & k7_setfam_1(A,B) = k1_xboole_0) & -(B = k1_xboole_0 & k7_setfam_1(A,B) != k1_xboole_0))) # label(t10_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2380 (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]. 4.48/4.64 2381 (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]. 4.48/4.64 2382 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> 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]. 4.48/4.64 2383 (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]. 4.48/4.64 2384 (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]. 4.48/4.64 2385 (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) -> v4_pre_topc(C,A)))) <-> v2_tops_2(B,A)))))) # label(d2_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2386 (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]. 4.48/4.64 2387 (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]. 4.48/4.64 2388 $T # label(t37_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2389 (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]. 4.48/4.64 2390 (all A (l1_struct_0(A) -> (all B (l1_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)) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k6_relat_1(k2_relat_1(C)) = k5_relat_1(k2_tops_2(A,B,C),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]. 4.48/4.64 2391 (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]. 4.48/4.64 2392 (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) & v1_tops_2(C,A) -> v1_tops_2(B,A)))))))) # label(t18_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2393 (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]. 4.48/4.64 2394 (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]. 4.48/4.64 2395 (all A all B all C (l1_struct_0(A) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & v1_funct_1(C) -> v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(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]. 4.48/4.64 2396 $T # label(t8_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 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(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]. 4.48/4.64 2398 $T # label(t30_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2399 (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]. 4.48/4.64 2400 (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) -> (v3_tops_2(C,A,B) <-> k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & v5_pre_topc(k2_tops_2(A,B,C),B,A) & k2_pre_topc(A) = k1_relat_1(C) & v5_pre_topc(C,A,B)))))))) # label(d5_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2401 (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))) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> 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]. 4.48/4.64 2402 (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]. 4.48/4.64 2403 (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]. 4.48/4.64 2404 $T # label(t69_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2405 (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]. 4.48/4.64 2406 $T # label(t14_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2407 (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]. 4.48/4.64 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 (k5_subset_1(u1_struct_0(A),F,B) = E & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(F,C))) <-> r2_hidden(E,D))))))))))))) # label(d3_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2409 $T # label(t61_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.64 2410 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_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,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]. 4.48/4.64 2411 (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]. 4.48/4.64 2412 (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))) -> (B = D -> v4_pre_topc(D,C))))))))))) # label(t34_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2413 (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]. 4.48/4.65 2414 (all A (l1_struct_0(A) -> (all 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) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> 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]. 4.48/4.65 2415 (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))) -> (D = B -> v3_pre_topc(D,C))))))))))) # label(t33_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2416 (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]. 4.48/4.65 2417 (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(B,A) <-> v2_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t17_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 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(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]. 4.48/4.65 2419 (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 (v3_pre_topc(D,A) & C = k3_xboole_0(D,k2_pre_topc(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v3_pre_topc(C,B)))))))) # label(t32_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2420 (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]. 4.48/4.65 2421 (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(C,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]. 4.48/4.65 2422 (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) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t29_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2423 (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_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k2_pre_topc(A) = k2_relat_1(k2_tops_2(A,B,C)) & k1_relat_1(k2_tops_2(A,B,C)) = k2_pre_topc(B)))))))) # label(t62_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2424 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_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_tops_2(B,A,k2_tops_2(A,B,C)) = C))))))) # label(t64_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2425 (all A (l1_struct_0(A) -> (all B (l1_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)) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> k2_funct_1(C) = k2_tops_2(A,B,C)))))))) # label(d4_tops_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2426 (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)) -> r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))))))))) <-> v9_metric_1(A)))) # label(t4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2427 (exists A (v1_metric_1(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & -v3_struct_0(A) & l1_metric_1(A) & v7_metric_1(A))) # label(rc3_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2428 (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]. 4.48/4.65 2429 (all A (l1_metric_1(A) -> (v8_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)))))))) # label(t3_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2430 (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]. 4.48/4.65 2431 (all A (v1_metric_1(k6_metric_1(A)) & v8_metric_1(k6_metric_1(A)) & v6_metric_1(k6_metric_1(A)) & v7_metric_1(k6_metric_1(A)) & v9_metric_1(k6_metric_1(A)))) # label(fc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2432 (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]. 4.48/4.65 2433 (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)) -> (B = C -> k2_metric_1(A,B,C) = np__0) & (k2_metric_1(A,B,C) = np__0 -> C = B) & k2_metric_1(A,C,B) = k2_metric_1(A,B,C) & r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))))))))) -> l1_metric_1(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & v7_metric_1(A)))) # label(t6_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2434 (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]. 4.48/4.65 2435 (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]. 4.48/4.65 2436 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(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]. 4.48/4.65 2437 (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]. 4.48/4.65 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)) -> a_3_1_metric_1(A,B,C) = k10_metric_1(B,C,A))))))) # label(t19_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2439 (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) & (exists F (B = F & E = A & a_3_0_metric_1(C,E,F) = D & m1_subset_1(F,u1_struct_0(E)))) & l1_metric_1(E))) <-> k9_metric_1(A,B,C) = D)))))))))) # label(d15_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2440 (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,k9_metric_1(B,C,A)) <-> -r1_xreal_0(A,k2_metric_1(B,C,D)) & -v3_struct_0(B)))))))))) # label(t12_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2441 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (A = B <-> np__0 = k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B)))))) # label(t9_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2442 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> ((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))))) <-> A = k7_metric_1))) # label(d13_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2443 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> (all C all D (g1_metric_1(A,B) = g1_metric_1(C,D) -> D = B & C = A)))) # label(free_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2444 (exists A (v1_metric_1(A) & l1_metric_1(A) & -v3_struct_0(A))) # label(rc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2445 (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) -> (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))))))))) <-> v5_metric_1(B,A)))) # label(d6_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2446 (all A (l1_metric_1(A) -> (v2_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v6_metric_1(A)))) # label(d7_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 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]. 4.48/4.65 2448 (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 (l1_metric_1(E) & -v3_struct_0(E) & (exists F (m1_subset_1(F,u1_struct_0(E)) & D = a_3_2_metric_1(C,E,F) & F = B & A = E)))) <-> D = k11_metric_1(A,B,C))) & (v3_struct_0(A) -> (v1_xboole_0(D) <-> D = k11_metric_1(A,B,C))))))))))) # label(d17_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2449 (all A (-v1_xboole_0(A) -> v1_metric_1(k6_metric_1(A)) & -v3_struct_0(k6_metric_1(A)))) # label(fc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2450 (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]. 4.48/4.65 2451 (all A (l1_metric_1(A) -> (v7_metric_1(A) <-> v3_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d8_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2452 (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]. 4.48/4.65 2453 (all A (l1_metric_1(A) -> (v9_metric_1(A) <-> v5_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d10_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2454 (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(k2_metric_1(B,C,D),A) <-> r2_hidden(D,k10_metric_1(B,C,A))))))))))) # label(t13_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2455 (all A all B all C all D (v1_xreal_0(B) & -v3_struct_0(C) & m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) -> (r2_hidden(A,a_3_2_metric_1(B,C,D)) <-> (exists E (A = E & k2_metric_1(C,D,E) = B & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2456 (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]. 4.48/4.65 2457 (all A all B all C all D all E (m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(E,B) & 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]. 4.48/4.65 2458 (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]. 4.48/4.65 2459 (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) & v1_funct_1(u1_metric_1(A)) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers))) # label(dt_u1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2460 (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]. 4.48/4.65 2461 (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) -> (all D (m1_subset_1(D,A) -> k1_metric_1(A,A,B,C,D) = k1_metric_1(A,A,B,D,C))))) <-> v4_metric_1(B,A)))) # label(d5_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2462 (all A (v9_metric_1(A) & v6_metric_1(A) & v8_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]. 4.48/4.65 2463 $T # label(t8_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2464 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) & l1_metric_1(A) -> 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]. 4.48/4.65 2465 (exists A l1_metric_1(A)) # label(existence_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2466 $T # label(t7_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2467 (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]. 4.48/4.65 2468 (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)) -> k9_metric_1(B,C,A) = a_3_0_metric_1(A,B,C))))))) # label(t18_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2469 (all A all B all C all D (-v3_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) & v1_xreal_0(B) -> (r2_hidden(A,a_3_1_metric_1(B,C,D)) <-> (exists E (A = E & m1_subset_1(E,u1_struct_0(C)) & r1_xreal_0(k2_metric_1(C,D,E),B)))))) # label(fraenkel_a_3_1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2470 (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]. 4.48/4.65 2471 (all A (l1_metric_1(A) -> (v1_metric_1(A) -> A = g1_metric_1(u1_struct_0(A),u1_metric_1(A))))) # label(abstractness_v1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2472 (all A g1_metric_1(A,k5_metric_1(A)) = k6_metric_1(A)) # label(d12_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2473 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (D != C -> k1_metric_1(A,A,B,C,D) = np__1) & k1_metric_1(A,A,B,C,C) = np__0)))) <-> B = k5_metric_1(A)))) # label(d11_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2474 (all A (l1_metric_1(A) -> l1_struct_0(A))) # label(dt_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2475 (exists A (v1_metric_1(A) & l1_metric_1(A))) # label(rc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2476 (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) -> (np__0 = k1_metric_1(A,A,B,C,D) -> C = D)))))))) # label(d4_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2477 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k4_subset_1(u1_struct_0(B),k11_metric_1(B,C,A),k9_metric_1(B,C,A)) = k10_metric_1(B,C,A))))))) # label(t17_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2478 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (v2_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> np__0 = k1_metric_1(A,A,B,C,C)))))) # label(d3_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2479 (all A all B all C all D (l1_metric_1(C) & v1_xreal_0(B) & -v3_struct_0(C) & m1_subset_1(D,u1_struct_0(C)) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & A = E & -r1_xreal_0(B,k2_metric_1(C,D,E)))) <-> r2_hidden(A,a_3_0_metric_1(B,C,D))))) # label(fraenkel_a_3_0_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2480 (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]. 4.48/4.65 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) -> (k10_metric_1(A,B,C) = D <-> (exists E (l1_metric_1(E) & (exists F (B = F & E = A & a_3_1_metric_1(C,E,F) = D & m1_subset_1(F,u1_struct_0(E)))) & -v3_struct_0(E))))) & (v3_struct_0(A) -> (v1_xboole_0(D) <-> D = k10_metric_1(A,B,C))))))))))) # label(d16_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2482 (all A all B all C (l1_metric_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v8_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]. 4.48/4.65 2483 (all A (m2_relset_1(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(k5_metric_1(A)) & 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]. 4.48/4.65 2484 (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) = np__0 -> C = B))))) <-> v7_metric_1(A)))) # label(t2_metric_1) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2485 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> 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]. 4.48/4.65 2486 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v2_connsp_2(B,A) <-> v1_connsp_2(k3_pre_topc(A,B))))))) # label(d6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2487 (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]. 4.48/4.65 2488 (all A (v2_pre_topc(A) & l1_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]. 4.48/4.65 2489 (all A (l1_pre_topc(A) & -v3_struct_0(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))) -> (m2_connsp_2(C,A,k1_struct_0(A,B)) <-> m1_connsp_2(C,A,B)))))))) # label(t10_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2490 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_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) -> (r2_hidden(B,C) & v3_pre_topc(C,A) -> r2_connsp_2(A,C,B))))))))) # label(t22_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2491 (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))) -> (v4_pre_topc(C,A) & r1_tarski(C,k1_connsp_2(A,B)) & v3_pre_topc(C,A) & r2_hidden(B,C) -> k1_connsp_2(A,B) = C))))))) # label(t31_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2492 $T # label(t17_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2493 (all A (v2_pre_topc(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) & v3_pre_topc(B,A) -> m1_connsp_2(B,A,C)))))))) # label(t5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2494 (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 (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(B = D & (all E (m1_subset_1(E,u1_struct_0(k3_pre_topc(A,D))) -> -(C = E & r1_connsp_2(k3_pre_topc(A,D),E))))))) <-> r2_connsp_2(A,B,C)))))))) # label(d5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2495 $T # label(t15_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2496 (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))) & -v1_xboole_0(D) -> -(m1_connsp_2(D,A,B) & r1_tarski(D,C) & v3_pre_topc(D,A)))) & m1_connsp_2(C,A,B)))))))) # label(t7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2497 (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) & m1_connsp_2(D,k3_pre_topc(A,B),C) & F = C & D = E -> m1_connsp_2(E,A,F)))))))))))))) # label(t11_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2498 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> (exists C m2_connsp_2(C,A,B)))) # label(existence_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2499 (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) & r3_connsp_1(A,B) -> r4_connsp_1(A,C,B)))))))) # label(t13_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2500 (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) & 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]. 4.48/4.65 2501 (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))) -> (r4_connsp_1(A,C,D) & r2_hidden(B,D) & m1_connsp_2(C,A,B) -> m1_connsp_2(D,A,B)))))) <-> r1_connsp_2(A,B)))))) # label(t19_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2502 (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) & 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]. 4.48/4.65 2503 (all A (v2_pre_topc(A) & l1_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]. 4.48/4.65 2504 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(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)) -> (C = D -> r1_tarski(k1_connsp_1(B,D),k1_connsp_1(A,C))))))))))) # label(t14_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2505 (all A (v2_pre_topc(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))) -> (v3_pre_topc(B,A) & r4_connsp_1(A,B,C) -> v3_pre_topc(C,A)))))) <-> v1_connsp_2(A)))) # label(t24_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2506 (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) -> -(v3_pre_topc(C,A) & r2_hidden(B,C) & (all D (m1_subset_1(D,u1_struct_0(k3_pre_topc(A,C))) -> -(D = B & r2_hidden(B,k1_tops_1(k3_pre_topc(A,C),k1_connsp_1(k3_pre_topc(A,C),D))))))))) <-> r1_connsp_2(A,B)))))) # label(t20_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2507 $T # label(t18_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2508 (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))) & -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) -> -((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 & v2_connsp_1(D,A)))) & v3_pre_topc(C,k3_pre_topc(A,B)) & v2_connsp_1(C,k3_pre_topc(A,B)))))))))) # label(t25_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2509 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (v1_connsp_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_connsp_2(A,B)))))) # label(d4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2510 (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)))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) & v4_pre_topc(D,A) & r2_hidden(B,D) <-> r2_hidden(D,C)))) & C = k1_xboole_0))))))) # label(t28_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2511 (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,u1_struct_0(A)) -> (m1_connsp_2(B,A,C) -> r2_hidden(C,B)))))))) # label(t6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2512 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(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]. 4.48/4.65 2513 $T # label(t2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2514 (all A all B (l1_pre_topc(A) & v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 4.48/4.65 2515 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v5_compts_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))) -> -(k2_pre_topc(A) != C & r1_tarski(B,C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k6_pre_topc(A,D),C) & r1_tarski(B,D) & v3_pre_topc(D,A)))) & v3_pre_topc(C,A) & v4_pre_topc(B,A) & B != k1_xboole_0)))))))) # label(t26_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2516 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists C m1_connsp_2(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2517 $T # label(t16_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2518 (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,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(D,A,C) & r1_tarski(D,B))))))) <-> v3_pre_topc(B,A)))))) # label(t9_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2519 (all A all B (m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(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]. 4.48/4.65 2520 $T # label(t29_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2521 $T # label(t1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2522 (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]. 4.48/4.65 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)) -> (D = E & C = F & 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]. 4.48/4.65 2524 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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]. 4.48/4.65 2525 (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))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> m1_connsp_2(C,A,B)))))))) # label(d1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2526 (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))) -> ((exists D (v3_pre_topc(D,A) & r2_hidden(B,D) & r1_tarski(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> m1_connsp_2(C,A,B)))))))) # label(t8_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2527 (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(k1_zfmisc_1(u1_struct_0(A)))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(E,D) <-> r2_hidden(B,E) & v4_pre_topc(E,A) & v3_pre_topc(E,A)))) & C = k6_setfam_1(u1_struct_0(A),D))) <-> C = k1_connsp_2(A,B)))))))) # label(d7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.48/4.65 2528 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) & v5_compts_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))) -> -(v4_pre_topc(C,A) & v4_pre_topc(B,A) & B != k1_xboole_0 & k1_xboole_0 != C & r1_xboole_0(B,C) & v2_connsp_1(B,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))) -> -(v3_pre_topc(D,A) & r1_tarski(C,E) & r1_tarski(B,D) & v2_connsp_1(D,A) & v3_pre_topc(E,A) & r1_xboole_0(D,E) & v2_connsp_1(E,A)))))) & v2_connsp_1(C,A))))))))) # label(t27_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2529 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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]. 4.58/4.65 2530 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_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))) -> -(m1_connsp_2(C,A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(D,A,B) & r1_tarski(D,C) & v2_connsp_1(D,A)))))))))))) # label(d3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2531 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_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]. 4.58/4.65 2532 (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]. 4.58/4.65 2533 (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)))) -> (r2_hidden(A,a_3_0_pcomps_1(B,C,D)) <-> (exists E (E = A & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & -r1_xboole_0(E,D) & r2_hidden(E,C)))))) # label(fraenkel_a_3_0_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2534 (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)))) -> (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]. 4.58/4.65 2535 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (v2_compts_1(A) -> v2_pcomps_1(A)))) # label(t25_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2536 (all A (-v1_xboole_0(A) -> -v3_struct_0(k2_pcomps_1(A)) & v2_pre_topc(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)))) # label(fc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2537 (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]. 4.58/4.65 2538 (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]. 4.58/4.65 2539 (all A k2_pcomps_1(A) = g1_pre_topc(A,k1_pcomps_1(A))) # label(d1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2540 (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]. 4.58/4.65 2541 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> (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]. 4.58/4.65 2542 (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]. 4.58/4.65 2543 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_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]. 4.58/4.65 2544 (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 (r2_hidden(D,B) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2545 (all A u1_struct_0(k2_pcomps_1(A)) = A) # label(t8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2546 (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]. 4.58/4.65 2547 (all A v2_compts_1(k2_pcomps_1(k1_tarski(A)))) # label(t9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2548 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (v3_pcomps_1(A) <-> (exists B (m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & k4_pcomps_1(k6_pcomps_1(u1_struct_0(A),B)) = u1_pre_topc(A) & r1_pcomps_1(u1_struct_0(A),B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_1(B)))))) # label(d9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2549 (all A (v2_pre_topc(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)))) -> 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]. 4.58/4.65 2550 (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 (m2_relset_1(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)))) & v1_funct_2(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & v1_funct_1(A))) # label(s1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2551 $T # label(t4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2552 (exists A (-v3_struct_0(A) & v3_compts_1(A) & v2_pre_topc(A) & v1_pre_topc(A) & l1_pre_topc(A))) # label(rc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2553 (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]. 4.58/4.65 2554 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k4_pcomps_1(A) = B <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (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(C,B))))))))) # label(d5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2555 (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)) -> -((all G (m1_subset_1(G,k1_numbers) -> -(r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,F,C)) & r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,E,B))))) & v9_metric_1(A) & 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]. 4.58/4.65 2556 (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))) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & k6_pre_topc(A,E) = D & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))) <-> k3_pcomps_1(A,B) = C))))))) # label(d3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2557 (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]. 4.58/4.65 2558 (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]. 4.58/4.65 2559 (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) -> -(r2_hidden(B,k9_metric_1(A,C,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)))) & v9_metric_1(A)))))))))) # label(t30_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2560 (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)))) -> r1_setfam_1(B,k3_pcomps_1(A,B)))))) # label(t20_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2561 (all A (l1_metric_1(A) -> l1_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))))) # label(t37_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2562 (all A k1_pcomps_1(A) = k1_zfmisc_1(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2563 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(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]. 4.58/4.65 2564 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,k1_numbers) & r1_tarski(k9_metric_1(A,B,C),u1_struct_0(A)) & -r1_xreal_0(C,np__0))))))) # label(t29_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2565 (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_compts_1(A) -> v4_pre_topc(k1_struct_0(A,B),A)))))) # label(t10_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2566 (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) -> (np__0 = k1_metric_1(A,A,B,C,D) -> C = D) & k1_metric_1(A,A,B,D,C) = k1_metric_1(A,A,B,C,D) & 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))) & (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]. 4.58/4.65 2567 (all A (l1_pre_topc(A) & -v3_struct_0(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_xboole_0(B,C) & v4_pre_topc(C,A) & v4_pre_topc(B,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))) -> -(v3_pre_topc(D,A) & r1_xboole_0(D,E) & r1_tarski(B,D) & r1_tarski(C,E) & v3_pre_topc(E,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(F,A) & r1_xboole_0(E,F) & r1_tarski(B,E) & r2_hidden(D,F) & v3_pre_topc(E,A)))))) & r2_hidden(D,C))))))))))) # label(t26_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2568 (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 & k6_pre_topc(A,B) != k1_xboole_0) & -(k6_pre_topc(A,B) = k1_xboole_0 & B != k1_xboole_0))))) # label(t2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2569 (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]. 4.58/4.65 2570 (all A all B all C all D (v2_pre_topc(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))) & -v3_struct_0(B) & l1_pre_topc(B) -> (r2_hidden(A,a_3_1_pcomps_1(B,C,D)) <-> (exists E (r2_hidden(E,C) & A = E & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & -r1_xboole_0(E,D)))))) # label(fraenkel_a_3_1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.65 2571 (all A (l1_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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_setfam_1(C,B) & r1_pre_topc(A,C) & v1_pcomps_1(C,A) & v1_tops_2(C,A)))) & v1_tops_2(B,A)))) <-> v2_pcomps_1(A)))) # label(d4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2572 (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)))) -> k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C)) = k3_pcomps_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)))))))) # label(t18_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2573 (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]. 4.58/4.66 2574 (all A (l1_pre_topc(A) & -v3_struct_0(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) -> r1_tarski(k3_pcomps_1(A,B),k3_pcomps_1(A,C))))))))) # label(t17_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2575 (all A l1_pre_topc(k2_pcomps_1(A))) # label(dt_k2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2576 (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)))) -> (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]. 4.58/4.66 2577 (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]. 4.58/4.66 2578 $T # label(t32_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2579 $T # label(t6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2580 (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(k3_pcomps_1(A,B),A))))) # label(t14_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2581 (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]. 4.58/4.66 2582 (all A (l1_metric_1(A) -> l1_pre_topc(k5_pcomps_1(A)))) # label(dt_k5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2583 (all A (l1_pre_topc(A) & -v3_struct_0(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(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]. 4.58/4.66 2584 (all A k1_pcomps_1(A) = u1_pre_topc(k2_pcomps_1(A))) # label(t7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2585 (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)))) -> (r1_tarski(B,C) & v1_pcomps_1(C,A) -> v1_pcomps_1(B,A)))))))) # label(t12_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2586 (all A all B (-v1_xboole_0(A) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) -> v9_metric_1(k6_pcomps_1(A,B)) & v7_metric_1(k6_pcomps_1(A,B)) & l1_metric_1(k6_pcomps_1(A,B)) & v8_metric_1(k6_pcomps_1(A,B)) & v6_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]. 4.58/4.66 2587 (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)))) -> (k1_xboole_0 = B -> k3_pcomps_1(A,B) = k1_xboole_0))))) # label(t15_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2588 (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(C,k4_pcomps_1(A)) & r2_hidden(B,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]. 4.58/4.66 2589 (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) -> v1_pcomps_1(k3_pcomps_1(A,B),A)))))) # label(t21_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2590 (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) -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t23_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2591 (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) -> (r1_pcomps_1(A,B) <-> l1_metric_1(g1_metric_1(A,B)) & v8_metric_1(g1_metric_1(A,B)) & v9_metric_1(g1_metric_1(A,B)) & v7_metric_1(g1_metric_1(A,B)) & v6_metric_1(g1_metric_1(A,B))))) # label(t39_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2592 (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,u1_struct_0(A)) -> (exists D (r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & v1_finset_1(a_3_0_pcomps_1(A,B,D)))))) <-> v1_pcomps_1(B,A)))))) # label(d2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2593 (all A (v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & -v3_struct_0(A) & l1_metric_1(A) & v9_metric_1(A) -> v3_compts_1(k5_pcomps_1(A)))) # label(t38_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2594 $T # label(t3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2595 (exists A (-v3_struct_0(A) & v2_pcomps_1(A) & v2_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2596 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) & v2_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 -((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]. 4.58/4.66 2597 (all A all B all C all D (-v3_struct_0(A) & v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(B) -> 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]. 4.58/4.66 2598 (all A all B all C all D all E (-v3_struct_0(C) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & l1_pre_topc(B) & -v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & v5_pre_topc(E,B,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)) & l1_pre_topc(C) & v2_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(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]. 4.58/4.66 2599 (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)) -> C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C))))))))) # label(t54_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2600 (all A all B all C all D all E all F (-v3_struct_0(B) & v2_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & v2_pre_topc(A) & -v3_struct_0(A) & m1_connsp_2(F,B,D) & m1_connsp_2(E,A,C) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(B) & l1_pre_topc(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]. 4.58/4.66 2601 (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]. 4.58/4.66 2602 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & -v3_struct_0(B) & l1_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]. 4.58/4.66 2603 (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))))) -> (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 != 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)) & (E != k1_xboole_0 -> 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))))))))))))) # label(t62_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2604 (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]. 4.58/4.66 2605 (all A all B all C all D all E (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(C,u1_struct_0(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) & v2_pre_topc(A) -> k5_borsuk_1(A,B,C,D,E) = k10_relat_1(D,E))) # label(redefinition_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2606 (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)))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) & C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D) & (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))) -> -(k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G) = E & v3_pre_topc(F,A) & v3_pre_topc(G,B)))))) & r2_hidden(E,D))))) <-> v3_pre_topc(C,k6_borsuk_1(A,B))))))))) # label(t45_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2607 (all A all B all C all D all E all F (-v3_struct_0(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_connsp_2(F,B,D) & v2_pre_topc(A) & v2_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m2_connsp_2(E,A,C) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) -> k10_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F))) # label(redefinition_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2608 (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)) -> B != k1_struct_0(A,C))) & r2_hidden(B,k15_borsuk_1(A))))))) # label(t68_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2609 (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_tarski(C) = k3_funct_2(A,B,k2_borsuk_1(A,B),C))))))) # label(t31_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2610 (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) -> (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_struct_0(A,D)))))))))) # label(t77_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2611 (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) -> ((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 (r1_tarski(E,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(E,A) & r1_tarski(C,E) & (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_borsuk_1(B,A)))))) # label(d13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2612 (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))) -> (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]. 4.58/4.66 2613 (all A all B all C all D (v2_pre_topc(B) & l1_pre_topc(C) & l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,C)))) & v2_pre_topc(C) -> ((exists E exists F (r1_tarski(k7_borsuk_1(B,C,E,F),D) & 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))) & v3_pre_topc(E,B))) <-> r2_hidden(A,a_3_1_borsuk_1(B,C,D))))) # label(fraenkel_a_3_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2614 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & -v3_struct_0(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(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(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))))) -> -(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),E) = C & v1_finset_1(E) & r1_tarski(E,D)))) & v1_finset_1(C)))))))))) # label(t64_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2615 (all A all B all C (-v3_struct_0(B) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & v1_borsuk_1(B,A) & v2_pre_topc(A) & -v3_struct_0(A) & m1_pre_topc(B,A) & l1_pre_topc(A) -> k21_borsuk_1(A,B,C) = k16_borsuk_1(B,C))) # label(redefinition_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2616 (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 -> C = k1_funct_1(k1_funct_3(k9_funct_3(A,B)),k12_mcart_1(A,B,C,D)) & D = k1_funct_1(k1_funct_3(k10_funct_3(A,B)),k12_mcart_1(A,B,C,D))))))) # label(t13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2617 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 4.58/4.66 2618 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & m1_pre_topc(C,B) & l1_pre_topc(B) & -v3_struct_0(C) -> (r2_hidden(A,a_2_3_borsuk_1(B,C)) <-> (exists D (-r2_hidden(D,u1_struct_0(C)) & k1_struct_0(B,D) = A & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2619 (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)))) -> 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]. 4.58/4.66 2620 (all A (-v1_xboole_0(A) -> (exists B (v1_setfam_1(B) & -v1_xboole_0(B) & m1_eqrel_1(B,A))))) # label(rc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2621 (all A all B all C (v2_pre_topc(A) & v1_borsuk_1(B,A) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_borsuk_1(C,B) & -v3_struct_0(B) -> v1_pre_topc(k21_borsuk_1(A,B,C)) & v1_borsuk_1(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & m1_pre_topc(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))))) # label(dt_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2622 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k1_funct_1(k1_funct_3(k10_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),C,k10_funct_3(B,C),A))) # label(t10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2623 (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) -> k12_mcart_1(A,C,k3_funct_2(A,B,D,k6_domain_1(B,E)),k6_domain_1(C,F)) = 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))))))))))))))) # label(t24_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2624 (all A (l1_struct_0(A) -> k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))) = k15_borsuk_1(A))) # label(d9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2625 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(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]. 4.58/4.66 2626 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_pre_topc(B) & v1_pre_topc(B) & v1_borsuk_1(B,A))))) # label(rc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2627 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (l1_pre_topc(C) & v1_pre_topc(C) & v2_pre_topc(C) -> (a_3_0_borsuk_1(A,B,C) = u1_pre_topc(C) & k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) = u1_struct_0(C) <-> C = k6_borsuk_1(A,B)))))))) # label(d5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2628 (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 (m2_relset_1(E,A,B) & v1_funct_1(E) & v1_funct_2(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(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]. 4.58/4.66 2629 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_setfam_1(B) & v2_borsuk_1(B,A) & -v1_xboole_0(B) & m1_borsuk_1(B,A))))) # label(rc5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2630 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) & v1_funct_1(C) & 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]. 4.58/4.66 2631 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & -v3_struct_0(A) & v2_pre_topc(B) & l1_pre_topc(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))) & v1_funct_1(k12_borsuk_1(A,B)) & 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]. 4.58/4.66 2632 (all A (l1_struct_0(A) & -v3_struct_0(A) -> v1_setfam_1(k15_borsuk_1(A)) & -v1_xboole_0(k15_borsuk_1(A)))) # label(fc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2633 (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]. 4.58/4.66 2634 (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)) -> (k3_tarski(C) = D -> k3_tarski(k3_subset_1(B,C)) = k3_subset_1(A,D)))))))))) # label(t27_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2635 (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) -> A = k3_pre_topc(k5_pcomps_1(k8_metric_1),B)))) <-> k22_borsuk_1 = A))) # label(d16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2636 $T # label(t40_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2637 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(A) -> v1_pre_topc(k6_borsuk_1(A,B)) & -v3_struct_0(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)))) # label(fc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2638 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (k2_borsuk_1(A,B) = C <-> (all D (m1_subset_1(D,A) -> r2_hidden(D,k8_funct_2(A,B,C,D))))))))))) # label(d1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2639 (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))) -> (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)) & 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)) = D))))))))) # label(t65_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2640 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> (exists D (k8_funct_2(A,B,k2_borsuk_1(A,B),D) = C & m1_subset_1(D,A))))))))) # label(t32_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2641 (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)))) -> 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]. 4.58/4.66 2642 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> (r2_hidden(A,a_2_0_borsuk_1(B,C)) <-> (exists D (A = k3_tarski(D) & r2_hidden(D,C) & m1_subset_1(D,k1_zfmisc_1(B))))))) # label(fraenkel_a_2_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2643 (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) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (exists D (k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D) = C & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t71_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2644 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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]. 4.58/4.66 2645 (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,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,C) -> k1_domain_1(B,C,k8_funct_2(A,B,D,E),F) = 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)))))))))))))) # label(t21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2646 $T # label(t22_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2647 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(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))) = k12_borsuk_1(A,B))))) # label(d7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2648 (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) -> (r2_borsuk_1(A,B) <-> (exists C (v1_funct_2(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))) & 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 & 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)))) & v1_funct_1(C) & v5_pre_topc(C,k6_borsuk_1(A,k22_borsuk_1),A) & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A))))))))) # label(d21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2649 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_borsuk_1(B,A) -> (v2_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))))))))) # label(d15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2650 (all A (v2_pre_topc(A) & -v3_struct_0(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 (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]. 4.58/4.66 2651 (all A all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) & -v1_xboole_0(A) -> m2_relset_1(k2_borsuk_1(A,B),A,B) & v1_funct_2(k2_borsuk_1(A,B),A,B) & v1_funct_1(k2_borsuk_1(A,B)))) # label(dt_k2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2652 (all A all B all C all D (-v3_struct_0(A) & l1_pre_topc(A) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) -> k8_borsuk_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2653 (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,u1_struct_0(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v5_pre_topc(D,B,A) & m2_relset_1(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]. 4.58/4.66 2654 (all A all B (l1_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) & v2_pre_topc(A) -> v2_pre_topc(k16_borsuk_1(A,B)) & v1_pre_topc(k16_borsuk_1(A,B)) & l1_pre_topc(k16_borsuk_1(A,B)))) # label(dt_k16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2655 (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,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]. 4.58/4.66 2656 (all A all B all C (v2_pre_topc(A) & v1_borsuk_1(B,A) & v2_borsuk_1(C,B) & -v3_struct_0(B) & -v3_struct_0(A) & l1_pre_topc(A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) -> 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]. 4.58/4.66 2657 $T # label(t11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2658 $T # label(t2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2659 (all A all B all C all D (v1_pre_topc(D) & l1_pre_topc(C) & l1_pre_topc(B) & v2_pre_topc(D) & l1_pre_topc(D) & v2_pre_topc(C) & v2_pre_topc(B) -> (r2_hidden(A,a_3_0_borsuk_1(B,C,D)) <-> (exists E (r1_tarski(E,a_2_1_borsuk_1(B,C)) & A = k5_setfam_1(u1_struct_0(D),E) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D))))))))) # label(fraenkel_a_3_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2660 (all A all B (l1_pre_topc(A) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) -> l1_pre_topc(k6_borsuk_1(A,B)) & v1_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]. 4.58/4.66 2661 (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))))) -> (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]. 4.58/4.66 2662 (all A all B (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> v2_pre_topc(k16_borsuk_1(A,B)) & v1_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]. 4.58/4.66 2663 (all A all B all C (l1_struct_0(A) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> v1_funct_1(k3_borsuk_1(A,B,C)) & 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)))) # label(dt_k3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2664 (all A (v2_pre_topc(A) & -v3_struct_0(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)) -> k18_borsuk_1(A,B,C) = k2_xboole_0(C,a_2_3_borsuk_1(A,B)))))))) # label(d12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2665 (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_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,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))) <-> v3_borsuk_1(C,A,B)))))))) # label(d19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2666 (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(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(k1_zfmisc_1(u1_struct_0(A)))) -> -((all F -(r1_xboole_0(F,D) & r2_hidden(F,E))) & r1_compts_1(A,E,D) & r1_tarski(E,C)))) & r1_compts_1(A,C,D)))))))))) # label(t63_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2667 (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]. 4.58/4.66 2668 (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(C,A) <-> v6_compts_1(D,B))))))))))) # label(t42_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2669 $T # label(t8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2670 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(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]. 4.58/4.66 2671 (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 (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]. 4.58/4.66 2672 (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 ((exists G (k12_mcart_1(A,B,F,G) = E & m1_subset_1(G,k1_zfmisc_1(B)))) & m1_subset_1(F,k1_zfmisc_1(A)))) & 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]. 4.58/4.66 2673 (all A all B (-v3_struct_0(A) & m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) & v2_pre_topc(A) & l1_pre_topc(A) -> v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v1_funct_1(k17_borsuk_1(A,B)) & v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B)) & m2_relset_1(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]. 4.58/4.66 2674 (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]. 4.58/4.66 2675 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k5_setfam_1(A,B) = A -> (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]. 4.58/4.66 2676 (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]. 4.58/4.66 2677 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(B) -> k1_funct_1(k13_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0 & k1_funct_1(k12_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0)))) # label(t66_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2678 (all A all B all C all D (l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v2_pre_topc(B) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k7_borsuk_1(A,B,C,D) = k2_zfmisc_1(C,D))) # label(redefinition_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2679 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_partfun1(B,A,A) -> -v1_xboole_0(k8_eqrel_1(A,B)))))) # label(t28_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2680 (all A all B all C all D all E (v2_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & 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_2(D,u1_struct_0(A),u1_struct_0(B)) & l1_pre_topc(A) & v2_pre_topc(B) & -v3_struct_0(B) & -v3_struct_0(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]. 4.58/4.66 2681 (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]. 4.58/4.66 2682 (all A all B all C (m1_eqrel_1(C,u1_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(C)) & r2_hidden(k3_tarski(D),u1_pre_topc(B)) & A = D)) <-> r2_hidden(A,a_2_2_borsuk_1(B,C))))) # label(fraenkel_a_2_2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2683 (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]. 4.58/4.66 2684 $T # label(t7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2685 $T # label(t3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2686 $T # label(t43_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2687 (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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C) = k1_xboole_0 | k1_xboole_0 = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C) -> C = k1_xboole_0))))))) # label(t61_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2688 (all A all B all C (v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> 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]. 4.58/4.66 2689 $T # label(d4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2690 (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))) -> (u1_struct_0(B) = C -> v4_pre_topc(C,A))))))))) # label(d14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2691 (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]. 4.58/4.66 2692 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(B) -> k13_borsuk_1(A,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))))))) # label(d8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2693 (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]. 4.58/4.66 2694 (all A all B all C all D all E (-v3_struct_0(C) & v2_pre_topc(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)) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) & l1_pre_topc(C) & v5_pre_topc(D,A,B) & v5_pre_topc(E,B,C) & v1_funct_1(E) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_funct_1(k4_borsuk_1(A,B,C,D,E)) & v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C) & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)))) # label(dt_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2695 (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_tarski(D,C) | r1_xboole_0(D,C)))) -> k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C)) = C))))))) # label(t33_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2696 (all A all B (-v3_struct_0(A) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) & v2_pre_topc(B) -> (exists C (v1_relat_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & -v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)))))) # label(rc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2697 (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]. 4.58/4.66 2698 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(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))) -> (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]. 4.58/4.66 2699 (all A all B all C (l1_pre_topc(C) & v2_pre_topc(C) & v2_pre_topc(B) & l1_pre_topc(B) -> (r2_hidden(A,a_2_1_borsuk_1(B,C)) <-> (exists D exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & r2_hidden(E,u1_pre_topc(C)) & A = k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(D,u1_pre_topc(B))))))) # label(fraenkel_a_2_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2700 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(a_2_0_borsuk_1(A,B)) = k3_tarski(k5_setfam_1(A,B)))) # label(t17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2701 (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))) -> 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]. 4.58/4.66 2702 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & v1_borsuk_1(B,A))))) # label(rc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2703 (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_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]. 4.58/4.66 2704 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) -> (all C (l1_pre_topc(C) & v1_pre_topc(C) & v2_pre_topc(C) -> (C = k16_borsuk_1(A,B) <-> u1_struct_0(C) = B & u1_pre_topc(C) = a_2_2_borsuk_1(A,B)))))))) # label(d10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2705 (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]. 4.58/4.66 2706 (all A (v2_pre_topc(A) & -v3_struct_0(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,u1_struct_0(k6_borsuk_1(A,B))) -> (exists D ((exists E (m1_subset_1(E,u1_struct_0(B)) & C = k8_borsuk_1(A,B,D,E))) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t50_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.66 2707 (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]. 4.58/4.66 2708 (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(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) -> (exists F ((exists G (E = k7_borsuk_1(A,B,F,G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))) & r1_tarski(E,C))) -> 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]. 4.58/4.67 2709 $T # label(t1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2710 (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]. 4.58/4.67 2711 $T # label(t34_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2712 (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,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,C) & v1_funct_1(E) & m2_relset_1(E,A,C) -> -((all F (v1_funct_1(F) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> k7_funct_2(A,B,C,D,F) != E)) & (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k8_funct_2(A,B,D,F) = k8_funct_2(A,B,D,G) -> k8_funct_2(A,C,E,G) = k8_funct_2(A,C,E,F))))))))))))))))) # label(t19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2713 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) -> k14_borsuk_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2714 (all A (l1_pre_topc(A) & -v3_struct_0(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 (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]. 4.58/4.67 2715 (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)))) -> v1_tops_2(k11_borsuk_1(A,B,C),k6_borsuk_1(A,B)))))))) # label(t51_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2716 (all A all B all C (v2_pre_topc(A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & v1_borsuk_1(B,A) & -v3_struct_0(B) & l1_pre_topc(A) & -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]. 4.58/4.67 2717 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(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]. 4.58/4.67 2718 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B m1_borsuk_1(B,A)))) # label(existence_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2719 (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 (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)) -> (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]. 4.58/4.67 2720 (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)) -> k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C) = k3_borsuk_1(A,B,C))))))) # label(d3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2721 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v2_borsuk_1(C,B) & m1_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]. 4.58/4.67 2722 (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,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))) -> (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)),C) -> 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]. 4.58/4.67 2723 (all A (v2_pre_topc(A) & -v3_struct_0(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 (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) -> r2_hidden(D,u1_struct_0(B)) | D = E))))))))))) # label(t78_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2724 (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]. 4.58/4.67 2725 (all A all B all C (m1_subset_1(C,A) & -v1_xboole_0(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]. 4.58/4.67 2726 (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]. 4.58/4.67 2727 (all A all B all C (l1_pre_topc(A) & m1_borsuk_1(C,B) & v2_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(A) & -v3_struct_0(B) & v2_pre_topc(A) -> k20_borsuk_1(A,B,C) = k18_borsuk_1(A,B,C))) # label(redefinition_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2728 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & -v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) & m1_pre_topc(B,A) & -v3_struct_0(B) & v2_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]. 4.58/4.67 2729 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(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,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]. 4.58/4.67 2730 $T # label(t44_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2731 (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_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)) -> r2_hidden(k1_struct_0(A,D),k18_borsuk_1(A,B,C))))))))))) # label(t75_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2732 (all A all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(B) -> v1_funct_1(k13_borsuk_1(A,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))) & 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))))) # label(dt_k13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2733 (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) -> (r1_borsuk_1(A,B) <-> (exists C (v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B)))))))) # label(d20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2734 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(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]. 4.58/4.67 2735 (all A all B all C all D (v2_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & 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]. 4.58/4.67 2736 (all A all B all C (v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) & -v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> -v1_xboole_0(k3_borsuk_1(A,B,C)) & v1_relat_1(k3_borsuk_1(A,B,C)) & v5_pre_topc(k3_borsuk_1(A,B,C),A,B) & 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)) & 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]. 4.58/4.67 2737 (all A all B all C all D all E all F (v2_pre_topc(B) & m1_connsp_2(F,B,D) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(B) & v2_pre_topc(A) & -v3_struct_0(A) & m1_subset_1(D,u1_struct_0(B)) & m2_connsp_2(E,A,C) & l1_pre_topc(B) & l1_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]. 4.58/4.67 2738 (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 -> k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) = 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]. 4.58/4.67 2739 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_borsuk_1(B,A) -> -v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)))))) # label(dt_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2740 (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 (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]. 4.58/4.67 2741 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> C = k3_funct_2(A,B,k2_borsuk_1(A,B),k6_domain_1(B,C)))))))) # label(t30_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2742 (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) -> D = k8_funct_2(A,B,k2_borsuk_1(A,B),C)))))))))) # label(t29_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2743 (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 -(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)))) -> -(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) = D & r2_hidden(E,C)))))))))))) # label(t57_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2744 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(k3_tarski(C),u1_pre_topc(A)) <-> r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B)))))))))) # label(t69_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2745 (all A all B all C all D all E all F (v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(B) & m1_connsp_2(E,A,C) & m1_connsp_2(F,B,D) -> k9_borsuk_1(A,B,C,D,E,F) = k2_zfmisc_1(E,F))) # label(redefinition_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2746 (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,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(-r2_hidden(E,k2_pre_topc(B)) & D = k1_struct_0(A,E)))) & r2_hidden(D,k18_borsuk_1(A,B,C))))))))))) # label(t74_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2747 (all A all B all C (-v3_struct_0(B) & m1_borsuk_1(C,B) & v1_borsuk_1(B,A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_pre_topc(B,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]. 4.58/4.67 2748 (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]. 4.58/4.67 2749 (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) -> (m1_pre_topc(B,A) & v1_borsuk_1(B,A) <-> v4_pre_topc(C,A))))))))) # label(t11_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2750 (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 (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> u1_struct_0(C) != B)) & v3_pre_topc(B,A)))))) # label(t20_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2751 (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) -> ((exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) & (exists E (m1_pre_topc(C,E) & v1_borsuk_1(E,A) & -v3_struct_0(E) & (r1_tsep_1(A,D,E) | r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C))) & m1_pre_topc(B,D) & m1_pre_topc(E,A))))) <-> r3_tsep_1(A,B,C)))))))) # label(t81_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2752 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(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]. 4.58/4.67 2753 (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))) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(C,E) & r1_tarski(B,D) & r2_tsep_1(A,D,E))) & 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]. 4.58/4.67 2754 (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) -> (all C (m1_pre_topc(C,A) & v1_tsep_1(C,A) -> r4_tsep_1(A,B,C))))))) # label(t88_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2755 (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(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]. 4.58/4.67 2756 (all A (l1_pre_topc(A) & -v3_struct_0(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) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),B) & m1_pre_topc(k2_tsep_1(A,B,C),C)))))))) # label(t30_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2757 (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(B,C) -> r2_tsep_1(A,B,C)))))))) # label(t52_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2758 (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 ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(D,A) & v4_pre_topc(E,A) & r1_tarski(C,E))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t47_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2759 (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,C,D) & r1_connsp_1(A,B,D) <-> r1_connsp_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t45_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2760 (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) -> (m1_pre_topc(B,C) <-> k1_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))))) # label(t23_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2761 (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 ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & 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)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r1_connsp_1(A,B,C)))))))) # label(t49_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2762 (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))) -> (r2_tsep_1(A,C,B) & r1_tarski(E,C) & r1_tarski(D,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]. 4.58/4.67 2763 (all A all B all C (m1_pre_topc(C,A) & l1_pre_topc(A) & m1_pre_topc(B,A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,C,B)))) # label(symmetry_r4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2764 (all A all B all C (l1_pre_topc(A) & -v3_struct_0(B) & -v3_struct_0(A) & m1_pre_topc(B,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> -v3_struct_0(k1_tsep_1(A,B,C)) & v1_pre_topc(k1_tsep_1(A,B,C)) & m1_pre_topc(k1_tsep_1(A,B,C),A))) # label(dt_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2765 (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]. 4.58/4.67 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 (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,C) & -r1_tsep_1(A,k2_tsep_1(A,B,C),D) | -r1_tsep_1(A,C,D) & -r1_tsep_1(A,B,k2_tsep_1(A,C,D)) -> k2_tsep_1(A,B,k2_tsep_1(A,C,D)) = k2_tsep_1(A,k2_tsep_1(A,B,C),D)) & (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,B,C) = k2_tsep_1(A,C,B)))))))))) # label(t29_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2767 (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))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(E,A) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & 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(D,B) & r1_tarski(E,C) & v3_pre_topc(F,A) & v4_pre_topc(D,A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_tsep_1(A,B,C))))))))) # label(t61_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2768 (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) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (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]. 4.58/4.67 2769 (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]. 4.58/4.67 2770 $T # label(t50_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2771 (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) & v1_tsep_1(B,A) -> (all C (-v3_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_tsep_1(k2_tsep_1(A,B,C),A)))))))) # label(t33_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2772 (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) -> (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]. 4.58/4.67 2773 (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))) -> -(-r1_tarski(B,C) & -r1_tarski(C,B) & r2_tsep_1(A,B,C) & (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(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & v3_pre_topc(D,A) & v3_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))) -> -(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)))) & -r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E))))))))))))))) # label(t64_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2774 (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) -> (r3_tsep_1(A,B,C) -> r1_tsep_1(A,B,C)))))))) # label(t68_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2775 (all A (v2_pre_topc(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) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) & (exists E (m1_pre_topc(E,A) & (r1_tsep_1(A,D,E) | r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C))) & m1_pre_topc(C,E) & -v3_struct_0(E) & m1_pre_topc(B,D) & v1_tsep_1(E,A)))))))))))) # label(t83_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2776 (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) -> (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]. 4.58/4.67 2777 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(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]. 4.58/4.67 2778 (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(B,C) & (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) -> -(v4_pre_topc(D,A) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(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)) & v3_pre_topc(F,A) & 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(E,A)))))) & -r1_tarski(C,B)))))))) # label(t60_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2779 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t70_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2780 (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))) -> -(v4_pre_topc(B,A) & (all C (v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> u1_struct_0(C) != B))))))) # label(t15_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2781 (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) & v1_borsuk_1(B,A) -> (all C (-v3_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> (-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]. 4.58/4.67 2782 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_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 (-v3_struct_0(D) & m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) & -v3_struct_0(E) -> (m1_pre_topc(E,C) & r4_tsep_1(A,C,B) & m1_pre_topc(D,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]. 4.58/4.67 2783 $T # label(t69_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2784 (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]. 4.58/4.67 2785 (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))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (r1_tarski(D,B) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A) & v3_pre_topc(E,A) & 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(D,A) & m1_subset_1(F,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(t65_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2786 $T # label(t28_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2787 $T # label(d6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2788 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_borsuk_1(k1_tsep_1(A,B,C),A))))))) # label(t24_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2789 (all A (v2_pre_topc(A) & -v3_struct_0(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) -> (all D (m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) -> (m1_pre_topc(D,B) & m1_pre_topc(E,C) & r3_tsep_1(A,B,C) -> r3_tsep_1(A,D,E)))))))))))) # label(t77_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2790 (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 (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r3_tsep_1(A,C,D) -> r1_tsep_1(A,D,B) | r3_tsep_1(A,k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) & r3_tsep_1(A,k2_tsep_1(A,C,B),k2_tsep_1(A,D,B)) | r1_tsep_1(A,C,B)))))))))) # label(t76_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2791 (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) -> (-r1_tsep_1(A,B,C) -> k1_tsep_1(A,k2_tsep_1(A,B,C),D) = k2_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D)) & k2_tsep_1(A,k1_tsep_1(A,D,B),k1_tsep_1(A,D,C)) = k1_tsep_1(A,D,k2_tsep_1(A,B,C))))))))))) # label(t36_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2792 (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) <-> (exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & (exists E ((r1_tsep_1(A,D,E) | r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C))) & m1_pre_topc(B,D) & r4_tsep_1(A,D,E) & -v3_struct_0(E) & m1_pre_topc(C,E) & m1_pre_topc(E,A)))))))))))) # label(t99_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2793 (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(B,C) & (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) & -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A) & 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)))) & k4_subset_1(u1_struct_0(A),D,E) != k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(E,C) & v3_pre_topc(D,A) & v3_pre_topc(E,A)))))) & -r1_tarski(C,B) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t66_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2794 $T # label(t84_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2795 (all A (v2_pre_topc(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) & A = k1_tsep_1(A,B,C) -> (v1_borsuk_1(C,A) & v1_borsuk_1(B,A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) <-> r4_tsep_1(A,B,C))))))))) # label(t95_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2796 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all 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 -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))))))) # label(t17_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 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(B,A) & v3_pre_topc(C,A) -> (r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C))))))))) # label(t41_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2798 (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(k4_subset_1(u1_struct_0(A),B,C),A) & r1_connsp_1(A,B,C) -> v4_pre_topc(C,A) & v4_pre_topc(B,A)))))))) # label(t39_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2799 (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,C,D) & r2_tsep_1(A,B,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]. 4.58/4.67 2800 (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 (v1_tsep_1(C,A) & 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))))))) # label(t25_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2801 (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))) -> (C = u1_struct_0(B) -> v3_pre_topc(C,A)))) <-> v1_tsep_1(B,A)))))) # label(d1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2802 (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(k2_tsep_1(A,B,C),k1_tsep_1(A,B,C))))))))) # label(t34_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2803 (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(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))))) # label(t5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2804 (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(k4_subset_1(u1_struct_0(A),B,C),A) & r1_connsp_1(A,B,C) -> v3_pre_topc(B,A) & v3_pre_topc(C,A)))))))) # label(t42_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2805 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v2_pre_topc(B) & m1_pre_topc(B,A) & v1_pre_topc(B) & v1_tsep_1(B,A))))) # label(rc1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2806 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (v1_borsuk_1(C,B) & m1_pre_topc(C,B) -> m1_pre_topc(C,A) & v1_borsuk_1(C,A))))))) # label(t13_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2807 (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(D,C) & v3_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) & E = D -> (v3_pre_topc(D,A) <-> v3_pre_topc(E,B))))))))))))) # label(t9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2808 (all A (-v3_struct_0(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) -> (all D (v1_pre_topc(D) & -v3_struct_0(D) & m1_pre_topc(D,A) -> (D = k1_tsep_1(A,B,C) <-> k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D)))))))))) # label(d2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2809 (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]. 4.58/4.67 2810 (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]. 4.58/4.67 2811 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,C,B)))) # label(symmetry_r2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2812 (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]. 4.58/4.67 2813 (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) -> (m1_pre_topc(B,C) -> r4_tsep_1(A,B,C)))))))) # label(t86_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2814 (all A (v2_pre_topc(A) & l1_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]. 4.58/4.67 2815 (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))) -> (r2_tsep_1(A,B,C) <-> r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,C),k6_subset_1(u1_struct_0(A),C,B))))))))) # label(d7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2816 (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) -> r2_tsep_1(A,B,C)))))))) # label(t54_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2817 (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) -> (k1_tsep_1(A,B,C) = A -> r1_tsep_1(A,B,C) | (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(C,B) & -m1_pre_topc(B,C) & (all D (v1_borsuk_1(D,A) & -v3_struct_0(D) & m1_pre_topc(D,A) -> (all E (v1_borsuk_1(E,A) & -v3_struct_0(E) & m1_pre_topc(E,A) -> -(m1_pre_topc(D,B) & m1_pre_topc(E,C) & -((all F (-v3_struct_0(F) & m1_pre_topc(F,A) & v1_tsep_1(F,A) -> -(k1_tsep_1(A,k1_tsep_1(A,D,E),F) = A & m1_pre_topc(F,k2_tsep_1(A,B,C))))) & k1_tsep_1(A,D,E) != A))))))))))))))) # label(t94_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2818 (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) -> ((exists D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) & (exists E (m1_pre_topc(B,D) & r1_tsep_1(A,D,C) & m1_pre_topc(C,E) & -v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) & r1_tsep_1(A,E,B))))) <-> r3_tsep_1(A,B,C)))))))) # label(t80_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2819 (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) -> r2_tsep_1(A,B,C)))))))) # label(t53_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2820 (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) -> (r1_tsep_1(A,B,C) & A = k1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> v1_tsep_1(C,A) & v1_tsep_1(B,A) & m1_pre_topc(B,A) & m1_pre_topc(C,A))))))))) # label(t98_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2821 (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) -> (-r1_tsep_1(A,B,C) -> (-((all D (v1_tsep_1(D,A) & -v3_struct_0(D) & m1_pre_topc(D,A) -> (all E (v1_tsep_1(E,A) & -v3_struct_0(E) & 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 (-v3_struct_0(F) & m1_pre_topc(F,A) & v1_borsuk_1(F,A) -> -(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(C,B) & -m1_pre_topc(B,C)) <-> r4_tsep_1(A,B,C))))))))) # label(t96_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2822 (all A all B all C (-v3_struct_0(B) & -v3_struct_0(C) & -v3_struct_0(A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) & l1_pre_topc(A) -> k1_tsep_1(A,C,B) = k1_tsep_1(A,B,C))) # label(commutativity_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2823 (all A (l1_pre_topc(A) & -v3_struct_0(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 -> (r4_tsep_1(A,B,C) <-> -((all D (v1_tsep_1(D,A) & m1_pre_topc(D,A) & -v3_struct_0(D) -> (all E (v1_tsep_1(E,A) & -v3_struct_0(E) & m1_pre_topc(E,A) -> -(-(A != k1_tsep_1(A,D,E) & (all F (v1_borsuk_1(F,A) & -v3_struct_0(F) & 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(C,B) & -m1_pre_topc(B,C))) | r1_tsep_1(A,B,C)))))))) # label(t97_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2824 (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 (v3_pre_topc(D,A) & r1_tarski(C,E) & r1_tarski(B,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_xboole_0(D,C) & v3_pre_topc(E,A) & r1_xboole_0(E,B)))))))))))) # label(t48_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2825 (all A all B all C (l1_pre_topc(A) & -v3_struct_0(C) & m1_pre_topc(C,A) & -v3_struct_0(A) & -v3_struct_0(B) & m1_pre_topc(B,A) -> -v3_struct_0(k2_tsep_1(A,B,C)) & v1_pre_topc(k2_tsep_1(A,B,C)) & m1_pre_topc(k2_tsep_1(A,B,C),A))) # label(dt_k2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2826 (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))) -> (r2_tsep_1(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) = u1_struct_0(A) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & v4_pre_topc(E,A) & v3_pre_topc(F,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)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))))))))) # label(t59_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2827 $T # label(t26_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2828 (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_1(A,B,C) <-> (exists D ((exists E ((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) & 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),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))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t63_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2829 (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) -> (-r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(B,C) & (all D (-v3_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) & v1_borsuk_1(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C) & m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B) & -((all F (v1_tsep_1(F,A) & -v3_struct_0(F) & m1_pre_topc(F,A) -> -(k1_tsep_1(A,k1_tsep_1(A,D,E),F) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & 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)))))))))) # label(t93_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2830 (all 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) -> (-r1_tsep_1(A,B,C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_pre_topc(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]. 4.58/4.68 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,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]. 4.58/4.68 2832 $T # label(t27_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2833 (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) -> (r3_tsep_1(A,B,C) & m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_tsep_1(k1_tsep_1(A,B,C),A) -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t75_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2834 (all A (v2_pre_topc(A) & -v3_struct_0(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 (-v3_struct_0(D) & m1_pre_topc(D,A) -> (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]. 4.58/4.68 2835 (all A (v2_pre_topc(A) & l1_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(D,B) <-> v4_pre_topc(C,A))))))))))) # label(t12_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2836 (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) -> (-r1_tsep_1(A,C,D) -> (r4_tsep_1(A,D,B) & r4_tsep_1(A,C,B) -> r4_tsep_1(A,k2_tsep_1(A,C,D),B)) & (r4_tsep_1(A,B,D) & r4_tsep_1(A,B,C) -> r4_tsep_1(A,B,k2_tsep_1(A,C,D)))))))))))) # label(t91_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2837 (all A (v2_pre_topc(A) & l1_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 (v1_tsep_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t73_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2838 (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) <-> (exists D ((exists E (r1_tarski(C,E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_xboole_0(D,C) & r1_xboole_0(E,B) & v4_pre_topc(E,A) & v4_pre_topc(D,A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t46_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2839 (all A (v2_pre_topc(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) -> m1_pre_topc(B,k1_tsep_1(A,B,C)))))))) # label(t22_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2840 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_pre_topc(B) & v1_pre_topc(B) & v1_tsep_1(B,A))))) # label(rc2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2841 (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]. 4.58/4.68 2842 (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]. 4.58/4.68 2843 (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) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> -(-r1_tsep_1(A,B,D) & -(k1_tsep_1(A,k2_tsep_1(A,D,B),k2_tsep_1(A,D,C)) = k2_tsep_1(A,D,k1_tsep_1(A,B,C)) & k2_tsep_1(A,k1_tsep_1(A,B,C),D) = k1_tsep_1(A,k2_tsep_1(A,B,D),k2_tsep_1(A,C,D))) & -r1_tsep_1(A,D,C)))))))))) # label(t35_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2844 (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) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & v1_tsep_1(D,A) & (exists E (m1_pre_topc(B,D) & r1_tsep_1(A,E,B) & r1_tsep_1(A,D,C) & m1_pre_topc(E,A) & -v3_struct_0(E) & m1_pre_topc(C,E) & v1_tsep_1(E,A))) & m1_pre_topc(D,A)))))))))) # label(t82_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2845 (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]. 4.58/4.68 2846 (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_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> -v3_struct_0(B) & m1_pre_topc(B,C) & v1_borsuk_1(B,C)))))))) # label(t14_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2847 $T # label(d4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2848 (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]. 4.58/4.68 2849 (all A (v2_pre_topc(A) & -v3_struct_0(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) -> (m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_borsuk_1(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t72_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2850 (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) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r4_tsep_1(A,B,D) & r4_tsep_1(A,C,D) -> r4_tsep_1(A,k1_tsep_1(A,B,C),D)) & (r4_tsep_1(A,D,C) & r4_tsep_1(A,D,B) -> r4_tsep_1(A,D,k1_tsep_1(A,B,C))))))))))) # label(t92_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2851 (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) & k1_tsep_1(A,B,C) = A -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t71_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2852 (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))) -> (D = E & r1_tarski(D,C) & v4_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) -> (v4_pre_topc(D,A) <-> v4_pre_topc(E,B))))))))))))) # label(t8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2853 (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(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(B),u1_pre_topc(B)) = k2_tsep_1(A,B,C) -> m1_pre_topc(B,C)) & (g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_tsep_1(A,B,C) -> m1_pre_topc(C,B)) & (m1_pre_topc(B,C) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = k2_tsep_1(A,B,C))))))))) # label(t31_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2854 (all A (l1_pre_topc(A) -> m1_pre_topc(A,A))) # label(t2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 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))) -> (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]. 4.58/4.68 2856 (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))) -> (u1_struct_0(B) = C -> (v3_pre_topc(C,A) <-> m1_pre_topc(B,A) & v1_tsep_1(B,A))))))))) # label(t16_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2857 (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) -> 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]. 4.58/4.68 2858 (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) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) & (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))) -> -(r1_tarski(E,C) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_tarski(D,B) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(F,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & 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)))) & k4_subset_1(u1_struct_0(A),B,C) != k4_subset_1(u1_struct_0(A),D,E))))))) & -r1_tarski(B,C)))))))) # label(t62_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2859 $T # label(t37_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2860 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(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))) -> (E = u1_struct_0(C) & u1_struct_0(B) = D -> r1_connsp_1(A,D,E)))))) <-> r3_tsep_1(A,B,C)))))))) # label(d8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2861 (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) -> (exists C (v1_pre_topc(C) & m1_pre_topc(C,A) & -v3_struct_0(C) & u1_struct_0(C) = B)))))) # label(t10_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2862 (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) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (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]. 4.58/4.68 2863 (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) & r4_tsep_1(A,B,C)))))))) # label(t85_tsep_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2864 (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,C,D) | r1_connsp_1(A,B,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]. 4.58/4.68 2865 (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]. 4.58/4.68 2866 (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))) -> (v1_tops_1(B,A) | v1_tops_1(C,A) -> v1_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t21_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2867 (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_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t39_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2868 (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]. 4.58/4.68 2869 (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 -> k6_pre_topc(B,D) = k6_pre_topc(A,C)))))) & u1_struct_0(B) = u1_struct_0(A) -> 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]. 4.58/4.68 2870 (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) | v2_tops_1(C,A) -> v2_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t15_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2871 (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_tops_1(C,A) & r1_tarski(D,C) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v3_tops_1(D,B)))))))))) # label(t84_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2872 (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_1(B,A) & v3_tops_1(B,A)))))) # label(t25_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2873 (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),B) = k1_xboole_0 -> B = u1_struct_0(A)) & (k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),B) -> k2_pre_topc(A) = B) & (u1_struct_0(A) = B -> k1_xboole_0 = k3_subset_1(u1_struct_0(A),B)) & (k2_pre_topc(A) = B -> k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),B)))))) # label(t2_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2874 (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(B),D) = k3_subset_1(u1_struct_0(A),C) <-> D = C)))))))))) # label(t71_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2875 (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) | v3_tops_1(C,A) -> v3_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2876 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_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))) -> (D = C -> k1_tops_1(B,D) = k1_tops_1(A,C)))))) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))))) # label(t74_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2877 (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) & v1_tops_1(B,A) -> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t46_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2878 (all A (l1_pre_topc(A) & -v3_struct_0(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))) -> -(v4_pre_topc(D,A) & k4_subset_1(u1_struct_0(A),C,k5_subset_1(u1_struct_0(A),B,D)) = B & v2_tops_1(D,A) & v3_pre_topc(C,A) & v1_tops_1(C,A) & r1_xboole_0(C,D) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D))))))))))) # label(t50_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2879 (all A (v2_pre_topc(A) & -v3_struct_0(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))) -> (C = D -> k6_pre_topc(A,C) = k6_pre_topc(B,D)))))))))) # label(t55_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2880 (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))) -> (v3_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)) & D = C -> v3_pre_topc(D,B)))))))))) # label(t76_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2881 (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]. 4.58/4.68 2882 (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))) -> (v1_tops_3(C,A) & r1_tarski(C,D) -> v1_tops_3(D,B)))))))))) # label(t61_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2883 (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))) -> (v1_tops_1(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_1(D,B)))))))))) # label(t83_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2884 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_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]. 4.58/4.68 2885 (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(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(D,C) & v3_pre_topc(C,A) & D = E & v3_tops_1(D,A) & r1_tarski(C,u1_struct_0(B)) -> v3_tops_1(E,B)))))))))))) # label(t69_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2886 (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))) -> (v2_tops_1(C,A) & r1_tarski(D,C) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v2_tops_1(D,B)))))))))) # label(t82_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2887 (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(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]. 4.58/4.68 2888 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) & 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))) -> (u1_struct_0(B) = D & C = E -> (v1_tops_3(C,A) <-> v1_tops_1(D,A) & v1_tops_3(E,B))))))))))))) # label(t63_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2889 (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_pre_topc(D,B) <-> v4_pre_topc(C,A))))))) & 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(t73_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2890 (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(k3_subset_1(u1_struct_0(A),B),A) <-> v3_tops_1(B,A)))))) # label(t40_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 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))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(C,A) & v1_tops_3(D,A) & k4_subset_1(u1_struct_0(A),C,D) = u1_struct_0(A) & v2_tops_1(C,A) & B = k5_subset_1(u1_struct_0(A),C,D)))))) & v3_tops_1(B,A)))))) # label(t51_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2892 (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]. 4.58/4.68 2893 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = k1_xboole_0 -> u1_struct_0(A) = k3_subset_1(u1_struct_0(A),B)) & (k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),B) -> k1_pre_topc(A) = B) & (u1_struct_0(A) = k3_subset_1(u1_struct_0(A),B) -> B = k1_xboole_0) & (B = k1_pre_topc(A) -> k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),B)))))) # label(t1_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2894 (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) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & r1_tarski(B,C) -> u1_struct_0(A) = C)))))))) # label(t19_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2895 (all A (v2_pre_topc(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))) -> (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]. 4.58/4.68 2896 (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)) & D = C -> k1_tops_1(A,C) = k1_tops_1(B,D)))))))))) # label(t77_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2897 (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))) -> (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(k1_tops_1(A,C),k1_tops_1(B,D))))))))))) # label(t78_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2898 (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(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]. 4.58/4.68 2899 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_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))) -> -(B = k5_subset_1(u1_struct_0(A),C,k4_subset_1(u1_struct_0(A),B,D)) & v4_pre_topc(C,A) & v2_tops_1(C,A) & v3_pre_topc(D,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),C,D) & r1_xboole_0(C,D) & v1_tops_1(D,A))))))))))) # label(t52_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2900 (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(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) & D = C -> k6_pre_topc(A,C) = k6_pre_topc(B,D)))))))))) # label(t80_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2901 (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]. 4.58/4.68 2902 (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(C,B) & v2_tops_1(B,A) -> v2_tops_1(C,A)))))))) # label(t11_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2903 (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(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]. 4.58/4.68 2904 (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(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]. 4.58/4.68 2905 (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(d1_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 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))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_3(B,A) & v2_tops_1(C,A) -> v1_tops_1(k6_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t47_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2907 (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))) -> (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]. 4.58/4.68 2908 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,k6_pre_topc(A,k1_tops_1(A,B))) -> k6_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A)))))) # label(t8_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2909 (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))) -> (v4_pre_topc(C,A) & C = D & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) -> v4_pre_topc(D,B)))))))))) # label(t79_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 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) & B = k1_xboole_0))))) # label(t34_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2911 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> k1_xboole_0 = k1_tops_1(A,k6_pre_topc(A,B))))))) # label(d3_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2912 (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 -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))) & 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]. 4.58/4.68 2913 (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) & 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 -> (v2_tops_1(D,B) <-> v2_tops_1(C,A))))))))))) # label(t67_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 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(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]. 4.58/4.68 2915 (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]. 4.58/4.68 2916 (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(B))) -> (r1_tarski(C,D) & v2_tops_1(D,B) -> v2_tops_1(C,A)))))))))) # label(t65_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2917 (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))) -> -(u1_struct_0(A) = B & v3_tops_1(B,A)))))) # label(t23_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2918 (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]. 4.58/4.68 2919 (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))) -> (r1_tarski(D,C) & r1_tarski(C,u1_struct_0(B)) & E = D -> (v1_tops_3(C,A) & v1_tops_3(E,B) <-> v1_tops_3(D,A))))))))))))) # label(t64_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2920 (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) = u1_struct_0(A)))))) # label(d2_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2921 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> v3_tops_1(k1_pre_topc(A),A))) # label(t22_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2922 (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))) -> -(v2_tops_1(B,A) & v1_tops_3(B,A)))))) # label(t37_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2923 (all A (l1_pre_topc(A) & -v3_struct_0(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_3(B,A) & r1_tarski(B,C) -> v1_tops_3(C,A)))))))) # label(t38_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2924 (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(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]. 4.58/4.68 2925 (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_1(k1_tops_1(A,B),A) <-> v1_tops_3(B,A)))))) # label(t35_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2926 (all A (v2_pre_topc(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))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_xboole_0(B,D) & k1_xboole_0 != D & r1_tarski(D,C) & v3_pre_topc(D,A)))) & v3_pre_topc(C,A) & C != k1_xboole_0))) <-> v3_tops_1(B,A)))))) # label(t28_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2927 (all A (l1_pre_topc(A) & -v3_struct_0(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_1(B,A)))))) # label(t33_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 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))) -> -(v2_tops_1(B,A) & u1_struct_0(A) = B))))) # label(t10_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2929 (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_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))) -> (C = D -> k1_tops_1(A,C) = k1_tops_1(B,D)))))))))) # label(t58_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2930 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_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))) -> (v3_tops_1(D,B) & r1_tarski(C,D) -> v3_tops_1(C,A)))))))))) # label(t68_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2931 (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]. 4.58/4.68 2932 (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))) -> (v2_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v1_tops_1(B,A)))))) # label(t18_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2933 (all A (v2_pre_topc(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_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]. 4.58/4.68 2934 (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))) -> ((exists C (r1_tarski(C,B) & v3_pre_topc(C,A) & v1_tops_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))) <-> v1_tops_3(B,A)))))) # label(t41_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 2935 (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_tops_3(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(C != u1_struct_0(A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k4_subset_1(u1_struct_0(A),B,D) = u1_struct_0(A) & r1_tarski(C,D) & D != u1_struct_0(A) & v4_pre_topc(D,A)))) & v4_pre_topc(C,A))))))))) # label(t42_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2936 (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(B,A) & v1_tops_3(C,A) -> v1_tops_3(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t44_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2937 (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(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]. 4.58/4.69 2938 (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(C,B) & v3_tops_1(B,A) -> v3_tops_1(C,A)))))))) # label(t26_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2939 (all A (v2_pre_topc(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))) -> (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) & D = E & r1_tarski(C,u1_struct_0(B)) -> (v1_tops_1(C,A) & v1_tops_3(E,B) <-> v1_tops_3(D,A))))))))))))) # label(t62_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2940 (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))) -> (r1_tarski(D,C) & r1_tarski(C,u1_struct_0(B)) & v3_pre_topc(C,A) & E = D -> k1_tops_1(A,D) = k1_tops_1(B,E)))))))))))) # label(t57_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2941 (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,C) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B))))) <-> v2_tops_1(B,A)))))) # label(t14_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2942 (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))) -> (v4_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) & D = E & r1_tarski(D,C) -> k6_pre_topc(A,D) = k6_pre_topc(B,E)))))))))))) # label(t54_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2943 (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_3(C,A) -> v1_tops_3(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t43_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2944 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(t16_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2945 (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) & (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) & r1_xboole_0(C,D) & v3_pre_topc(C,A) & v3_tops_1(D,A) & B = k4_subset_1(u1_struct_0(A),C,D))))))))))) # label(t49_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2946 (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))) -> (C = D -> (v3_tops_1(D,B) <-> v3_tops_1(C,A))))))))))) # label(t70_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2947 (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) & v1_tops_1(B,A) -> v1_tops_3(B,A)))))) # label(t36_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2948 (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(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]. 4.58/4.69 2949 (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,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]. 4.58/4.69 2950 (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]. 4.58/4.69 2951 (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))) -> (r1_tarski(D,C) & v2_tops_1(D,A) & E = D & v3_pre_topc(C,A) & r1_tarski(C,u1_struct_0(B)) -> v2_tops_1(E,B)))))))))))) # label(t66_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2952 (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))) -> -(r1_xboole_0(k3_subset_1(u1_struct_0(A),B),C) & v3_pre_topc(C,A) & k1_xboole_0 != C)))))))) # label(t13_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2953 (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))) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v2_tops_1(C,A) & r1_tarski(B,C) & v4_pre_topc(C,A))) <-> v3_tops_1(B,A)))))) # label(t27_tops_3) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2954 (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))) -> (r1_tarski(D,C) & D = E & 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]. 4.58/4.69 2955 (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))) -> -(k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C) & v3_pre_topc(D,A)))))))))))) # label(t32_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2956 (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]. 4.58/4.69 2957 (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 -> (v3_tex_2(B,A) <-> v1_tdlat_3(A))))))) # label(t27_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2958 (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) -> (v5_tex_2(B,A) -> v1_tsep_1(B,A) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & -v2_tex_2(B,A)))))) # label(cc39_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2959 (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))) -> (v4_pre_topc(C,A) & v3_tex_2(C,A) & v4_pre_topc(B,A) & v3_tex_2(B,A) -> v3_tex_2(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t39_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2960 (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)) -> v1_xboole_0(B) & v3_membered(B) & v1_tex_2(B,k1_zfmisc_1(A)) & v5_membered(B) & v1_membered(B) & v2_membered(B) & v4_membered(B)))))) # label(cc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2961 (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) -> (v2_tex_2(B,A) -> v3_tdlat_3(B) & v1_tdlat_3(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & -v5_tex_2(B,A) & v1_borsuk_1(B,A)))))) # label(cc40_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2962 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_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]. 4.58/4.69 2963 (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 ((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)) & v1_funct_2(A,f2_s1_tex_2,u1_struct_0(f1_s1_tex_2)) & v1_funct_1(A))) # label(s1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2964 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> (k1_struct_0(A,B) = u1_struct_0(C) <-> k1_tex_2(A,B) = C))))))) # label(d4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2965 (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_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc29_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2966 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v5_tex_2(B,A) & m1_pre_topc(B,A) -> (all C (v5_pre_topc(C,A,B) & 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) -> (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 -> k6_pre_topc(A,k1_struct_0(A,E)) = k5_pre_topc(A,B,C,k1_struct_0(B,D)))))))))))))) # label(t77_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2967 (all A (v1_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & -v3_realset2(A) -> (exists B (v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & m1_pre_topc(B,A) & v2_tex_2(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc17_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2968 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_realset2(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_tex_2(B,A) -> -v3_realset2(B) & -v3_struct_0(B)))))) # label(cc15_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2969 (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_xboole_0(B) & -v1_realset1(B)))))) # label(cc7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 2970 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((all C (v1_tdlat_3(C) & -v3_struct_0(C) & m1_pre_topc(C,A) -> (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]. 4.58/4.69 2971 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(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]. 4.58/4.69 2972 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (exists B (v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_pre_topc(B) & m1_pre_topc(B,A) & v1_tsep_1(B,A))))) # label(rc16_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2973 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) & -v3_struct_0(B) & -v3_realset2(B) -> -v1_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc25_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2974 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) -> -v3_struct_0(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)))) # label(fc2_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2975 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (v3_realset2(A) & u1_struct_0(A) = u1_struct_0(B) -> v3_realset2(B)))))) # label(t4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2976 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(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(cc6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2977 (all A (-v3_realset2(A) & l1_struct_0(A) & -v3_struct_0(A) -> (exists B (v1_realset1(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc8_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2978 (all A (-v1_xboole_0(A) -> ((exists B (m1_subset_1(B,A) & A = k6_domain_1(A,B))) <-> v1_realset1(A)))) # label(d1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2979 (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)) & v1_tdlat_3(k1_tex_2(A,B)) & v3_tdlat_3(k1_tex_2(A,B)) & v5_tdlat_3(k1_tex_2(A,B)) & v2_pre_topc(k1_tex_2(A,B)) & v4_tdlat_3(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)))) # label(fc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2980 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> -v3_struct_0(k1_tex_2(A,B)) & v2_pre_topc(k1_tex_2(A,B)) & v3_tdlat_3(k1_tex_2(A,B)) & v4_tdlat_3(k1_tex_2(A,B)) & v2_tdlat_3(k1_tex_2(A,B)) & v1_pre_topc(k1_tex_2(A,B)) & v5_tdlat_3(k1_tex_2(A,B)) & v3_realset2(k1_tex_2(A,B)) & v1_tdlat_3(k1_tex_2(A,B)))) # label(fc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2981 (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_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]. 4.62/4.69 2982 (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_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> v5_pre_topc(C,B,A))))) -> v2_tdlat_3(A)))) # label(t71_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2983 (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]. 4.62/4.69 2984 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> ((all B (l1_pre_topc(B) & -v3_struct_0(B) & v2_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) -> v5_pre_topc(C,A,B))))) -> v1_tdlat_3(A)))) # label(t69_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2985 (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))) -> -(v4_tex_2(B,A) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & (v4_pre_topc(B,A) | v3_pre_topc(B,A))))))) # label(t61_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2986 (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,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_struct_0(A,C) = k5_subset_1(u1_struct_0(A),B,D))))))) -> v3_tex_2(B,A)))))) # label(t37_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2987 (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) & -v3_struct_0(B) -> (exists C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C))))))) # label(t72_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2988 (all A (-v3_struct_0(A) & l1_pre_topc(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))) <-> v2_tex_2(k1_tex_2(A,B),A)))))) # label(t20_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2989 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tdlat_3(B) & v1_tdlat_3(B) & -v3_struct_0(B) -> v3_realset2(B) & -v3_struct_0(B)))))) # label(cc24_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2990 (all A (v2_pre_topc(A) & v2_tdlat_3(A) & -v3_struct_0(A) & l1_pre_topc(A) & -v3_realset2(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_tex_2(B,A) & v3_tdlat_3(B) & -v1_borsuk_1(B,A) & v2_tdlat_3(B) & -v1_tsep_1(B,A) & v2_pre_topc(B))))) # label(rc18_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2991 (all A (l1_pre_topc(A) & v2_tdlat_3(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & -v3_struct_0(B) -> v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & -v3_struct_0(B) & -v5_tex_2(B,A) & v4_tdlat_3(B)))))) # label(cc44_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2992 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & v1_tdlat_3(B) & -v3_struct_0(B) -> -v3_struct_0(B) & -v2_tdlat_3(B)))))) # label(cc26_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2993 (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]. 4.62/4.69 2994 (all A (v2_pre_topc(A) & -v3_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(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))) <-> v4_tex_2(B,A)))))) # label(t49_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2995 (all A (-v3_struct_0(A) & v2_tdlat_3(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))) -> (v1_realset1(B) <-> v3_tex_2(B,A)))))) # label(t44_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 2996 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(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]. 4.62/4.69 2997 (all A (v1_realset1(A) & -v1_xboole_0(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]. 4.62/4.69 2998 (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]. 4.62/4.69 2999 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) & v3_pre_topc(B,A) -> v1_tops_1(B,A)))))) # label(t47_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3000 (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(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & C = k5_subset_1(u1_struct_0(A),B,D)))) & r1_tarski(C,B)))) <-> v3_tex_2(B,A)))))) # label(d5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3001 (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]. 4.62/4.69 3002 (all A (v3_realset2(A) & -v3_struct_0(A) & l1_struct_0(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_realset1(B) & -v1_xboole_0(B)))))) # label(cc9_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3003 (all A (v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & -v3_realset2(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tex_2(B,A) -> v5_tdlat_3(B) & v2_tex_2(B,A) & v2_tdlat_3(B) & -v1_borsuk_1(B,A) & v2_pre_topc(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & -v1_tsep_1(B,A) & -v3_struct_0(B)))))) # label(cc35_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3004 (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(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = C))) & r1_tarski(C,B)))) <-> v3_tex_2(B,A)))))) # label(d6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3005 (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) -> r1_borsuk_1(A,B))))) # label(t73_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3006 (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(k4_subset_1(u1_struct_0(A),B,C),A) & v4_pre_topc(k5_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(C,A) & v3_tex_2(B,A) & v4_pre_topc(B,A) & v3_tex_2(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]. 4.62/4.69 3007 (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) -> -((all C (v1_pre_topc(C) & v1_tdlat_3(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v3_tex_2(B,A)))))) # label(t34_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3008 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_realset1(B) & -v1_xboole_0(B))))) # label(rc5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3009 (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]. 4.62/4.69 3010 (all A (-v3_struct_0(A) & v2_pre_topc(A) & -v1_tdlat_3(A) & l1_pre_topc(A) & v3_tdlat_3(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) & v4_tdlat_3(B) & v3_tdlat_3(B) & -v3_struct_0(B) & v5_tdlat_3(B)))))) # label(cc47_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3011 (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_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc30_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3012 (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(B,C) & v3_tex_2(C,A) -> B = C))) <-> v4_tex_2(B,A)))))) # label(d7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3013 (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_tex_2(B,A) & v1_tops_1(B,A) -> v4_tex_2(B,A)))))) # label(t48_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3014 (all A (l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v2_tex_2(B,A) & v3_realset2(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc13_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3015 (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) -> v5_tdlat_3(B) & v4_tdlat_3(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v3_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc37_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3016 (all A (v3_realset2(A) & -v3_struct_0(A) & l1_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]. 4.62/4.69 3017 (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_2(C,A) & C = D & 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(D,B)))))))))) # label(t25_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3018 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v2_tex_2(B,A) -> v1_tsep_1(B,A) & v2_pre_topc(B) & v1_borsuk_1(B,A)))))) # label(cc28_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3019 (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]. 4.62/4.69 3020 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & -v3_struct_0(B) & v3_realset2(B) & m1_pre_topc(B,A))))) # label(rc12_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3021 (all A (l1_struct_0(A) & -v3_struct_0(A) & -v3_realset2(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]. 4.62/4.69 3022 (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_tex_2(C,A) & v3_tex_2(B,A) & v3_pre_topc(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]. 4.62/4.69 3023 (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) & v1_tdlat_3(B) & -v3_struct_0(B) -> (exists C (v3_borsuk_1(C,A,B) & 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) & v1_funct_1(C))))))) # label(t78_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3024 $T # label(t11_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3025 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v2_tex_2(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc11_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3026 (all A (v2_pre_topc(A) & l1_pre_topc(A) & v3_tdlat_3(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]. 4.62/4.69 3027 (all A (l1_struct_0(A) & -v3_realset2(A) & -v3_struct_0(A) -> (exists 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))))))) # label(rc10_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3028 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (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)) & r2_hidden(D,B)))))))))) # label(t64_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3029 (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)) & v1_tdlat_3(A) -> v1_tdlat_3(B)))))) # label(t17_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3030 (all A (-v3_struct_0(A) & v2_tdlat_3(A) & -v3_realset2(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v3_tdlat_3(B) & v2_tex_2(B,A) & v3_realset2(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v4_tdlat_3(B) & v5_tdlat_3(B) & v1_tdlat_3(B)))))) # label(cc36_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3031 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (v3_realset2(B) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (g1_pre_topc(u1_struct_0(k1_tex_2(A,C)),u1_pre_topc(k1_tex_2(A,C))) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & m1_subset_1(C,u1_struct_0(A)))))))) # label(t23_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3032 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.69 3033 $T # label(t22_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3034 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.69 3035 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tex_2(B,A) <-> v1_realset1(B)))))) # label(t50_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3036 (all A (v2_pre_topc(A) & -v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (v5_tex_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (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))) -> (D = E -> k6_pre_topc(A,E) = k5_pre_topc(A,B,C,D))))))))))))) # label(t76_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3037 (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))) -> -(v4_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = k1_tarski(C)))))))))))) # label(t33_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3038 (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]. 4.62/4.69 3039 (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) -> -v5_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc38_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3040 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v2_pre_topc(k1_tex_2(A,B)) -> v2_tdlat_3(k1_tex_2(A,B)) & v1_tdlat_3(k1_tex_2(A,B))))))) # label(t24_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3041 (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_tdlat_3(A) -> v2_tdlat_3(B)))))) # label(t18_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3042 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v2_pre_topc(B) & v3_realset2(B) & -v3_struct_0(B) -> v2_pre_topc(B) & v5_tdlat_3(B) & v3_realset2(B) & v3_tdlat_3(B) & -v3_struct_0(B) & v2_tdlat_3(B) & v4_tdlat_3(B) & v1_tdlat_3(B)))))) # label(cc27_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3043 (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_realset2(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v5_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v1_tdlat_3(B) & v5_tex_2(B,A) & v2_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc45_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3044 (all A (v2_pre_topc(A) & -v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v5_tex_2(B,A) -> (exists C (v3_borsuk_1(C,A,B) & 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))))))) # label(t74_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3045 (all A (v2_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tdlat_3(B) & -v3_struct_0(B) -> v1_tdlat_3(B) & v4_tdlat_3(B) & -v3_struct_0(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v3_realset2(B) & v2_pre_topc(B)))))) # label(cc33_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3046 (all A all B (m1_subset_1(B,A) -> (B != k3_tarski(A) <-> v1_tex_2(B,A)))) # label(d2_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3047 $T # label(t10_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3048 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.69 3049 (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))) -> (v4_tex_2(B,A) -> u1_struct_0(A) = k3_tarski(a_2_0_tex_2(A,B))))))) # label(t63_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3050 (all A (-v1_xboole_0(A) -> (all B (v1_realset1(B) & -v1_xboole_0(B) -> (r1_tarski(A,B) -> B = A))))) # label(t1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3051 (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]. 4.62/4.69 3052 (all A (-v2_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v5_tex_2(B,A) & -v3_struct_0(B) -> v3_tdlat_3(B) & v4_tdlat_3(B) & -v3_struct_0(B) & v2_pre_topc(B) & v5_tdlat_3(B) & -v3_realset2(B)))))) # label(cc49_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3053 (all A (v2_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v5_tex_2(B,A) -> v4_tdlat_3(B) & -v5_tex_2(B,A) & -v3_realset2(B) & v3_tdlat_3(B) & v2_tdlat_3(B) & -v3_struct_0(B) & v5_tdlat_3(B) & -v1_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc46_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3054 (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) -> (-v5_tex_2(B,A) -> v1_tsep_1(B,A) & v2_tex_2(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v3_tdlat_3(B) & v1_tdlat_3(B)))))) # label(cc42_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3055 (all A (l1_struct_0(A) & -v3_realset2(A) & -v3_struct_0(A) -> (exists B (-v1_realset1(B) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc9_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3056 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_tex_2(B,k1_zfmisc_1(A)))))) # label(rc3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3057 (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) | v3_tex_2(C,A) -> v3_tex_2(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3058 (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]. 4.62/4.69 3059 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(A)) & v1_realset1(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc6_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3060 (all A all B (m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.69 3061 (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]. 4.62/4.69 3062 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (v2_tex_2(B,A) & g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v2_tex_2(C,A)))))))) # label(t14_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3063 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.69 3064 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v2_pre_topc(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) & v5_tdlat_3(B) & v3_realset2(B) & v2_tdlat_3(B) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc14_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3065 (all 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) -> (v5_tex_2(B,A) <-> v4_tex_2(C,A))))))))) # label(t51_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3066 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v1_tdlat_3(B) & v2_tdlat_3(B) & v3_realset2(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v1_pre_topc(B) & m1_pre_topc(B,A) & v2_pre_topc(B) & v5_tdlat_3(B) & -v3_struct_0(B))))) # label(rc15_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3067 (all A (v2_pre_topc(A) & -v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(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]. 4.62/4.69 3068 (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) -> (v5_tex_2(B,A) & -v3_struct_0(B) -> v1_tdlat_3(B) & v2_tdlat_3(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v3_tdlat_3(B) & v2_pre_topc(B) & v3_realset2(B) & -v3_struct_0(B)))))) # label(cc43_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3069 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v3_realset2(B) -> -v3_struct_0(B) & -v3_realset2(B) & -v2_tdlat_3(B) & v1_tdlat_3(B) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_tsep_1(B,A) & v4_tdlat_3(B) & v5_tdlat_3(B) & v3_tdlat_3(B)))))) # label(cc32_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3070 (all A (-v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (v1_tdlat_3(B) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & m1_pre_topc(C,A) & v5_tex_2(C,A) & v1_pre_topc(C) & m1_pre_topc(B,C))))))) # label(t67_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3071 (all A (l1_pre_topc(A) & -v1_tdlat_3(A) & -v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_tex_2(B,A) -> v2_pre_topc(B) & v5_tdlat_3(B) & -v5_tex_2(B,A) & v4_tdlat_3(B) & -v3_struct_0(B) & v3_tdlat_3(B)))))) # label(cc48_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3072 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc4_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3073 (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) -> (-v2_tex_2(B,A) -> v5_tex_2(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B)))))) # label(cc41_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3074 (all A (-v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.69 3075 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v3_realset2(A) & v1_tex_2(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t8_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3076 (all A (-v3_struct_0(A) & v1_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))))) # label(t43_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3077 (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)) & -v1_xboole_0(B) -> -v1_xboole_0(B) & -v1_tex_2(B,k1_zfmisc_1(A)) & v1_realset1(B)))))) # label(cc5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3078 (all A (v2_tdlat_3(A) & -v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_realset2(B) & -v3_struct_0(B) -> v2_pre_topc(B) & v5_tdlat_3(B) & v3_tdlat_3(B) & v4_tdlat_3(B) & -v3_realset2(B) & v2_tdlat_3(B) & -v1_tdlat_3(B) & -v3_struct_0(B)))))) # label(cc34_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3079 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.69 3080 (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))) -> ((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]. 4.62/4.69 3081 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_realset2(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v2_pre_topc(B) & -v3_struct_0(B) & v4_tdlat_3(B) & v2_tex_2(B,A))))) # label(rc19_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3082 (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]. 4.62/4.69 3083 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3084 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_tex_2(B,k1_zfmisc_1(A)) <-> A != B))) # label(t5_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3085 (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))) -> (v4_tex_2(C,A) & C = D & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v4_tex_2(D,B)))))))))) # label(t45_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3086 (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))) -> -v4_tex_2(B,A))))) # label(t46_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.69 3087 (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_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]. 4.62/4.69 3088 (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]. 4.62/4.69 3089 (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]. 4.62/4.69 3090 (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_struct_0(B) & v2_tdlat_3(B) -> v1_borsuk_1(B,A) & v3_tdlat_3(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v1_tsep_1(B,A) & v2_pre_topc(B) & -v3_struct_0(B) & v3_realset2(B) & v2_tdlat_3(B) & v1_tdlat_3(B)))))) # label(cc31_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3091 (all A (-v1_realset1(A) & -v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & -v1_realset1(B) & -v1_tex_2(B,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc7_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3092 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v3_realset2(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_tex_2(B,A) -> v3_realset2(B) & -v3_struct_0(B)))))) # label(cc13_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3093 (all A (v3_tdlat_3(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_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]. 4.62/4.70 3094 (all A all B all C (-v3_struct_0(B) & l1_pre_topc(B) & v3_tdlat_3(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v2_pre_topc(B) -> (r2_hidden(A,a_2_0_tex_2(B,C)) <-> (exists D (r2_hidden(D,C) & A = k6_pre_topc(B,k1_struct_0(B,D)) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3095 $T # label(t3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3096 (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]. 4.62/4.70 3097 (all A (v2_pre_topc(A) & -v3_struct_0(A) & v3_tdlat_3(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_tex_2(C,A) & r1_tarski(B,C)))) & v3_tex_2(B,A)))))) # label(t65_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3098 (all A (-v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v1_pre_topc(B) & v2_pre_topc(B) & v5_tex_2(B,A) & v4_tdlat_3(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) & -v3_struct_0(B) & v3_tdlat_3(B) & v5_tdlat_3(B))))) # label(rc20_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3099 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_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]. 4.62/4.70 3100 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.70 3101 (all 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))) -> (u1_struct_0(B) = C -> (v1_tdlat_3(B) <-> v3_tex_2(C,A))))))))) # label(t26_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3102 (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))) -> ((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]. 4.62/4.70 3103 (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]. 4.62/4.70 3104 (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(d3_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 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_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) & v3_pre_topc(k5_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]. 4.62/4.70 3106 (all A (v1_realset1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3107 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v2_tex_2(B,A) & m1_pre_topc(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]. 4.62/4.70 3108 (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))) -> (v3_tex_2(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) -> D = C | r1_xboole_0(k6_pre_topc(A,k1_struct_0(A,C)),k6_pre_topc(A,k1_struct_0(A,D))))))))))))) # label(t59_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3109 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_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) -> v5_pre_topc(C,A,B))))))) # label(t68_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3110 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_tex_2(B,A) & (all C (v1_pre_topc(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> -(v5_tex_2(C,A) & u1_struct_0(C) = B)))))))) # label(t53_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3111 (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_tdlat_3(B) & v2_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> v5_pre_topc(C,A,B))))))) # label(t70_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3112 (all A (-v3_realset2(A) & -v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_realset1(B) & -v1_xboole_0(B) -> -v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(cc10_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3113 (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))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -((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)))) & r2_hidden(C,k6_pre_topc(A,B))))) <-> v3_tex_2(B,A)))))) # label(t60_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3114 (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)) & v3_tdlat_3(A) -> v3_tdlat_3(B)))))) # label(t19_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3115 (all A (l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (v3_realset2(B) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_tex_2(B,A)))))) # label(cc14_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3116 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) & v3_tdlat_3(A) & -v2_tdlat_3(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v3_realset2(B) -> v4_tdlat_3(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & -v5_tex_2(B,A) & -v3_struct_0(B)))))) # label(cc50_tex_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3117 (all A (-v3_struct_0(A) & v3_realset2(A) & l1_pre_topc(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]. 4.62/4.70 3118 (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]. 4.62/4.70 3119 (all A (l1_pre_topc(A) & -v3_struct_0(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) -> (v3_tex_3(B,A) & v4_tex_3(C,A) | v3_tex_3(C,A) & v4_tex_3(B,A) -> v3_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t45_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3120 (all A (l1_pre_topc(A) & v3_tdlat_3(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v2_pre_topc(B) & -v1_borsuk_1(B,A) & v3_tdlat_3(B) & v2_tex_2(B,A) & v5_tdlat_3(B) & v4_tdlat_3(B)))))) # label(cc28_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3121 (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) -> (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]. 4.62/4.70 3122 (all A (v3_tdlat_3(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) & v2_tex_2(B,A) -> v2_pre_topc(B) & -v1_tex_3(B,A) & -v2_tex_3(B,A) & v2_tex_2(B,A)))))) # label(cc32_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3123 (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) & v2_tex_3(B,A) -> (all C (v2_tex_3(C,B) & -v3_struct_0(C) & m1_pre_topc(C,B) -> m1_pre_topc(C,A) & v2_tex_3(C,A))))))) # label(t21_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3124 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & -v3_struct_0(A) & l1_pre_topc(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 (v2_tex_2(C,A) & m1_pre_topc(C,A) & v2_tex_3(C,A) & v1_pre_topc(C) -> u1_struct_0(C) != B))))))) # label(t63_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3125 (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) & v1_pre_topc(B) & -v1_borsuk_1(B,A) & v2_tex_2(B,A) & -v3_tex_3(B,A) & v2_pre_topc(B) & -v3_struct_0(B) & v2_tex_3(B,A) & -v4_tex_3(B,A) & v1_tex_3(B,A))))) # label(rc11_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3126 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tex_3(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 -> (v1_tops_1(C,A) <-> v1_tops_1(D,B))))))))))) # label(t11_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3127 (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) -> (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]. 4.62/4.70 3128 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_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]. 4.62/4.70 3129 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) & v2_pre_topc(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (v2_tex_3(C,A) & m1_pre_topc(C,A) <-> m1_pre_topc(B,A) & v2_tex_3(B,A))))))))) # label(t22_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3130 (all A (v2_pre_topc(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_tops_1(B,A) & (all C (m1_pre_topc(C,A) & v1_pre_topc(C) & -v3_struct_0(C) & v1_tsep_1(C,A) & v1_tex_3(C,A) -> B != u1_struct_0(C))) & v3_pre_topc(B,A)))))) # label(t23_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3131 (all A (l1_pre_topc(A) & -v3_struct_0(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) -> (v1_tex_3(C,A) | v1_tex_3(B,A) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_tex_3(k1_tsep_1(A,B,C),A)))))))) # label(t25_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3132 (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 (-v3_struct_0(C) & m1_pre_topc(C,A) -> (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]. 4.62/4.70 3133 (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) -> (v2_tex_3(B,A) | v2_tex_3(C,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]. 4.62/4.70 3134 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v4_tex_3(B,A) & v3_tex_3(B,A) & -v1_tex_3(B,A) & v2_tex_2(B,A) & -v1_tsep_1(B,A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v2_tex_3(B,A) & v2_pre_topc(B))))) # label(rc12_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3135 (all A (-v3_struct_0(A) & -v3_tdlat_3(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 (v1_pre_topc(C) & v2_tex_2(C,A) & v1_tsep_1(C,A) & m1_pre_topc(C,A) & (exists D (m1_pre_topc(B,D) & r4_tsep_2(A,C,D) & v3_tex_3(D,A) & v1_borsuk_1(D,A) & v1_pre_topc(D) & m1_pre_topc(D,A) & -v3_struct_0(D))) & v1_tex_3(C,A) & -v3_struct_0(C))))))) # label(t74_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3136 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (-v3_struct_0(B) & v2_pre_topc(B) & v1_tex_3(B,A) & v2_tex_3(B,A) & m1_pre_topc(B,A) & v1_pre_topc(B))))) # label(rc2_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3137 (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_tex_2(C,k1_zfmisc_1(u1_struct_0(A))) <-> -v1_xboole_0(B))))))))) # label(t1_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3138 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) & -v3_tdlat_3(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v2_tops_1(B,A) & v4_pre_topc(B,A) & (all C (v1_borsuk_1(C,A) & v3_tex_3(C,A) & v1_pre_topc(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C)))))))) # label(t67_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3139 (all A (v2_pre_topc(A) & -v3_tdlat_3(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v4_tex_3(B,A) & -v3_struct_0(B) -> -((all C (m1_pre_topc(C,A) & v2_tex_2(C,A) & -v3_struct_0(C) & v1_pre_topc(C) & v2_tex_3(C,A) -> (all D (v1_borsuk_1(D,A) & v3_tex_3(D,A) & v1_pre_topc(D) & -v3_struct_0(D) & m1_pre_topc(D,A) -> -(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))))))) & -(v3_tex_3(B,A) & v1_borsuk_1(B,A))))))) # label(t72_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3140 (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) & v1_tsep_1(B,A) -> -v3_tex_3(B,A) & v2_pre_topc(B) & -v3_struct_0(B)))))) # label(cc11_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3141 (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) -> (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]. 4.62/4.70 3142 (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) & v1_tex_3(B,A) -> v2_tex_3(B,A) & v2_pre_topc(B) & v1_tex_3(B,A)))))) # label(cc8_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3143 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(A) -> (all B (v2_tex_2(B,A) & -v3_struct_0(B) & m1_pre_topc(B,A) -> (exists C (v1_pre_topc(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) & -v3_struct_0(C))))))) # label(t8_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3144 (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) -> (v1_tsep_1(B,A) & v1_tex_3(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_borsuk_1(B,A) & v2_pre_topc(B) & -v2_tex_2(B,A)))))) # label(cc31_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3145 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_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))) -> (D = C -> (v1_tops_3(D,B) <-> v1_tops_3(C,A))))))))))) # label(t18_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3146 (all A (-v3_struct_0(A) & -v3_tdlat_3(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (-v3_struct_0(B) & v2_pre_topc(B) & -v1_tex_3(B,A) & v2_tex_2(B,A) & -v1_tsep_1(B,A) & v1_pre_topc(B) & -v2_tex_3(B,A) & v3_tex_3(B,A) & v4_tex_3(B,A) & m1_pre_topc(B,A))))) # label(rc10_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3147 (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_3(B,A) <-> v3_tops_1(C,A))))))))) # label(t4_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3148 (all A (-v3_struct_0(A) & l1_pre_topc(A) & -v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (v1_pre_topc(C) & v3_tex_3(C,A) & m1_pre_topc(C,A) -> u1_struct_0(C) != B)) & v2_tops_1(B,A)))))) # label(t51_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3149 (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) -> (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]. 4.62/4.70 3150 (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_borsuk_1(B,A) & -v3_struct_0(B) -> -v4_tex_3(B,A) & v4_tdlat_3(B) & -v3_struct_0(B) & v2_pre_topc(B) & v5_tdlat_3(B) & -v3_tex_3(B,A) & v3_tdlat_3(B)))))) # label(cc29_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3151 (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) -> v2_pre_topc(B) & v3_tex_3(B,A) & -v2_tex_3(B,A) & v2_tex_2(B,A)))))) # label(cc15_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3152 (all A (-v3_realset2(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.70 3153 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(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))))))))) # label(d2_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3154 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -(v1_tdlat_3(A) & (exists B (v3_tex_3(B,A) & -v3_struct_0(B) & m1_pre_topc(B,A)))))) # label(t49_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3155 (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) & v1_tex_3(B,A) & v2_pre_topc(B) & -v3_struct_0(B))))) # label(rc1_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3156 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v1_tdlat_3(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & -v3_struct_0(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (v3_tex_3(B,A) & m1_pre_topc(B,A) <-> m1_pre_topc(C,A) & v3_tex_3(C,A))))))))) # label(t55_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3157 (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))) -> (C = u1_struct_0(B) -> (v3_tex_3(B,A) <-> v2_tops_1(C,A))))))))) # label(t29_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3158 (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))) & -v1_xboole_0(B) -> -(v3_tops_1(B,A) & (all C (v4_tex_3(C,A) & -v3_struct_0(C) & m1_pre_topc(C,A) & v1_pre_topc(C) -> B != u1_struct_0(C)))))))) # label(t62_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3159 (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) -> -(v3_tops_1(B,A) & (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> -(v4_tex_3(C,A) & B = u1_struct_0(C))))))))) # label(t36_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3160 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> ((exists C (m1_pre_topc(C,B) & v1_tsep_1(C,A) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tex_3(C,A))) <-> v2_tex_3(B,A)))))) # label(t24_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3161 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v3_tex_3(B,A) -> v2_pre_topc(B) & -v2_tex_3(B,A) & v2_tex_2(B,A)))))) # label(cc14_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3162 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tex_3(B,A) & -v3_struct_0(B) -> (all C (v1_tex_3(C,B) & m1_pre_topc(C,B) & -v3_struct_0(C) -> -v3_struct_0(C) & v1_tex_3(C,A) & m1_pre_topc(C,A))))))) # label(t14_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3163 (all A (-v3_realset2(A) & l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v2_tex_2(B,A) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & -v2_tex_3(B,A) & -v1_tex_3(B,A) & -v5_tex_2(B,A) & v1_tsep_1(B,A) & v2_pre_topc(B))))) # label(rc5_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3164 (all A (v2_pre_topc(A) & -v3_tdlat_3(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_2(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_pre_topc(C,A) & v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_3(C,A) & v2_tex_2(C,A) -> B != u1_struct_0(C))) & v3_pre_topc(B,A) & v1_tops_1(B,A)))))) # label(t68_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3165 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(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))))))))) # label(d1_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3166 (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) -> (v2_tops_1(C,A) <-> v1_tops_1(B,A))))))))) # label(t2_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3167 (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))) -> -(v2_tops_1(B,A) & (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> -(v3_tex_3(C,A) & u1_struct_0(C) = B)))))))) # label(t30_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3168 (all A (-v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) & v2_tex_3(B,A) -> -((all C (v1_pre_topc(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) & v1_tex_3(C,A) & -v3_struct_0(C) & v2_tex_2(C,A) -> (all D (v4_tex_3(D,A) & m1_pre_topc(D,A) & -v3_struct_0(D) & v1_pre_topc(D) -> -(r1_tsep_1(A,C,D) & k1_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))))) & -(v1_tex_3(B,A) & v1_tsep_1(B,A))))))) # label(t73_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3169 (all A (v2_pre_topc(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))) -> (r2_tsep_2(A,B,C) -> (v1_tops_1(C,A) <-> v2_tops_1(B,A))))))))) # label(t3_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3170 (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) & v4_tdlat_3(B) & -v4_tex_3(B,A) & v5_tdlat_3(B) & v3_tdlat_3(B) & v1_pre_topc(B))))) # label(rc8_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3171 (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) -> v2_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc7_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3172 (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_tex_3(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (m1_pre_topc(B,C) -> m1_pre_topc(B,C) & v1_tex_3(B,C)))))))) # label(t13_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3173 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -((exists B (-v3_struct_0(B) & v1_borsuk_1(B,A) & v3_tex_3(B,A) & m1_pre_topc(B,A))) & v3_tdlat_3(A)))) # label(t59_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3174 (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_struct_0(B) -> -v3_struct_0(B) & -v4_tex_3(B,A) & v3_tdlat_3(B) & v2_pre_topc(B) & v5_tdlat_3(B) & v4_tdlat_3(B)))))) # label(cc25_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3175 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -((exists B (v2_tex_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) & v2_tex_3(B,A))) & v3_tdlat_3(A)))) # label(t60_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3176 (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) -> (v3_tex_3(B,A) & m1_pre_topc(C,B) -> v3_tex_3(C,A)))))))) # label(t34_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3177 (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) -> v2_pre_topc(B) & v1_tex_3(B,A)))))) # label(cc4_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3178 (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]. 4.62/4.70 3179 (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(t9_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3180 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> v2_pre_topc(B) & -v3_tex_3(B,A)))))) # label(cc13_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3181 (all A (l1_pre_topc(A) & -v3_struct_0(A) & -v3_tdlat_3(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v2_tex_2(B,A) & v2_tex_3(B,A) -> (exists C (r4_tsep_2(A,B,C) & v4_tex_3(C,A) & -v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A))))))) # label(t65_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3182 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) -> v1_tdlat_3(B) & -v2_tex_2(B,A) & v1_tex_3(B,A) & v2_tex_3(B,A) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & v5_tex_2(B,A) & v3_tdlat_3(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_borsuk_1(B,A)))))) # label(cc24_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3183 (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) -> -((all C (v1_pre_topc(C) & -v3_struct_0(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> -(v3_tex_3(C,A) & B = u1_struct_0(C)))) & v2_tops_1(B,A) & v4_pre_topc(B,A)))))) # label(t41_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3184 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(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]. 4.62/4.70 3185 (all A (v3_tdlat_3(A) & -v3_realset2(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_tex_2(B,A) & -v2_tex_3(B,A) & v2_pre_topc(B))))) # label(rc9_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3186 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) & -v3_tdlat_3(A) -> (all B (v2_tex_3(B,A) & m1_pre_topc(B,A) & v2_tex_2(B,A) -> (exists C (v1_pre_topc(C) & v2_tex_2(C,A) & m1_pre_topc(C,A) & (exists D (m1_pre_topc(D,A) & m1_pre_topc(C,B) & v1_borsuk_1(D,A) & v1_pre_topc(D) & v3_tex_3(D,A) & r3_tsep_2(A,C,D))) & v1_tex_3(C,A) & v1_tsep_1(C,A))))))) # label(t75_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3187 (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) -> ((exists C (v1_pre_topc(C) & -v3_struct_0(C) & m1_pre_topc(B,C) & v3_tex_3(C,A) & m1_pre_topc(C,A) & v1_borsuk_1(C,A))) <-> v4_tex_3(B,A)))))) # label(t42_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3188 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> -(v3_tdlat_3(A) & (exists B (v1_tsep_1(B,A) & v2_tex_2(B,A) & m1_pre_topc(B,A) & v1_tex_3(B,A) & -v3_struct_0(B)))))) # label(t61_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3189 (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))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -((all C (m1_pre_topc(C,A) & v2_tex_2(C,A) & v1_tex_3(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]. 4.62/4.70 3190 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -((exists B (-v3_struct_0(B) & v2_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A))) & v1_tdlat_3(A)))) # label(t50_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3191 (all A (v2_pre_topc(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) -> (r4_tsep_2(A,B,C) -> (v1_tex_3(C,A) <-> v3_tex_3(B,A))))))))) # label(t32_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3192 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v1_tdlat_3(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) -> -v3_struct_0(B) & v1_tdlat_3(B) & v5_tdlat_3(B) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & v1_tsep_1(B,A) & v1_borsuk_1(B,A) & v3_tdlat_3(B) & v4_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc22_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3193 (all A (v2_pre_topc(A) & -v3_struct_0(A) & -v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (v1_borsuk_1(B,A) & v3_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) & -v3_struct_0(C) & v1_tex_3(C,A) & v2_tex_2(C,A) & v1_pre_topc(C))))))) # label(t69_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3194 (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) -> -((v3_tex_3(B,A) | v3_tex_3(C,A)) & -r1_tsep_1(A,B,C) & -v3_tex_3(k2_tsep_1(A,B,C),A)))))))) # label(t43_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3195 (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_pre_topc(B) & -v1_tex_3(B,A) & v2_tex_2(B,A) & -v2_tex_3(B,A)))))) # label(cc17_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3196 (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) -> (v2_tex_3(B,A) & v1_tex_3(C,A) | v1_tex_3(B,A) & v2_tex_3(C,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]. 4.62/4.70 3197 (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) -> (v3_tops_1(B,A) <-> v1_tops_3(C,A))))))))) # label(t5_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3198 (all A (-v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (v2_tex_2(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) & v1_tex_3(B,A) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & v3_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C))))))) # label(t54_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3199 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) & -v3_tdlat_3(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & v2_tex_2(B,A) & m1_pre_topc(B,A) & v1_tex_3(B,A) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & r4_tsep_2(A,B,C) & v1_borsuk_1(C,A) & v3_tex_3(C,A) & m1_pre_topc(C,A))))))) # label(t70_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3200 (all A (v2_pre_topc(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 -> v2_tops_1(C,A)))) <-> v3_tex_3(B,A)))))) # label(d3_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3201 (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) & v2_tex_2(B,A) -> -v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc3_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3202 (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) -> v2_pre_topc(B) & v2_tex_3(B,A)))))) # label(cc6_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3203 (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) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v3_tops_1(C,A))))))))) # label(d4_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3204 (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) -> v1_tsep_1(B,A) & v1_borsuk_1(B,A) & -v2_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc1_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3205 (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_tex_3(B,A) -> v4_tex_3(B,A) & v2_tex_2(B,A) & -v2_tex_3(B,A) & v3_tex_3(B,A) & -v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc19_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3206 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & -v3_tdlat_3(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) & v4_tex_3(B,A) -> (exists C (v2_tex_3(C,A) & r4_tsep_2(A,B,C) & m1_pre_topc(C,A) & v2_tex_2(C,A) & v1_pre_topc(C) & -v3_struct_0(C))))))) # label(t64_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3207 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_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))) -> (r1_tarski(C,u1_struct_0(B)) -> v2_tops_1(C,A))))))))) # label(t33_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3208 (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) -> (v4_tex_3(B,A) & m1_pre_topc(C,B) -> v4_tex_3(C,A)))))))) # label(t40_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3209 (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_tdlat_3(A)))) # label(t56_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3210 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tex_3(B,A) -> v2_pre_topc(B) & -v2_tex_3(B,A)))))) # label(cc5_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3211 (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) -> -((all C (v1_tex_3(C,A) & v1_pre_topc(C) & m1_pre_topc(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C))) & v1_tops_1(B,A)))))) # label(t10_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3212 (all A (-v1_tdlat_3(A) & v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v2_tex_2(B,A) & v1_tex_3(B,A) & v2_pre_topc(B) & m1_pre_topc(B,A) & -v1_borsuk_1(B,A) & -v4_tex_3(B,A) & -v3_struct_0(B))))) # label(rc7_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3213 (all A (v2_pre_topc(A) & -v3_realset2(A) & l1_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))) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & u1_struct_0(C) = B & m1_pre_topc(C,A) & v2_tex_2(C,A))))))) # label(t7_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3214 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(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]. 4.62/4.70 3215 (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]. 4.62/4.70 3216 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(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]. 4.62/4.70 3217 (all A (v3_tdlat_3(A) & l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_3(B,A) -> v2_pre_topc(B) & v1_tsep_1(B,A) & -v2_tex_2(B,A) & v2_tex_3(B,A) & -v4_tex_3(B,A) & v1_tex_3(B,A) & -v3_tex_3(B,A) & v1_borsuk_1(B,A)))))) # label(cc27_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3218 (all A (v2_pre_topc(A) & -v3_struct_0(A) & -v1_tdlat_3(A) & l1_pre_topc(A) -> (all B (v3_tex_3(B,A) & m1_pre_topc(B,A) & -v3_struct_0(B) -> (exists C (-v3_struct_0(C) & v2_tex_2(C,A) & v1_tex_3(C,A) & r4_tsep_2(A,B,C) & v1_pre_topc(C) & m1_pre_topc(C,A))))))) # label(t53_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3219 (all A (l1_pre_topc(A) & -v3_struct_0(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))) -> (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]. 4.62/4.70 3220 (all A (l1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(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]. 4.62/4.70 3221 (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_tex_3(B,A) -> v2_pre_topc(B) & -v1_borsuk_1(B,A) & v2_tex_2(B,A)))))) # label(cc20_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3222 (all A (v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(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_tsep_1(B,A) & v2_tex_2(B,A)))))) # label(cc30_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3223 (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_tex_3(B,A) -> -v2_tex_3(B,A) & v2_tex_2(B,A) & -v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc10_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.70 3224 (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) & -v3_struct_0(B) -> ((exists C (v1_pre_topc(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) & m1_pre_topc(B,C) & v3_tex_3(C,A))) <-> v4_tex_3(B,A)))))) # label(t71_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3225 (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]. 4.62/4.71 3226 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_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) & v2_tex_3(C,A) -> B != u1_struct_0(C))) & v1_tops_3(B,A)))))) # label(t17_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3227 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_tdlat_3(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(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 -> (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]. 4.62/4.71 3228 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -((exists B (-v3_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A))) & v3_tdlat_3(A)))) # label(t58_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3229 (all A (l1_pre_topc(A) & v1_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_pre_topc(B) & v1_tsep_1(B,A) & -v3_tex_3(B,A) & -v4_tex_3(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v3_tdlat_3(B) & v5_tdlat_3(B) & v4_tdlat_3(B) & v1_tdlat_3(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A))))) # label(rc4_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3230 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(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]. 4.62/4.71 3231 (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) & v3_tex_3(B,A) -> v2_tex_2(B,A) & -v3_struct_0(B) & -v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc12_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3232 (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) -> v1_borsuk_1(B,A) & v3_tdlat_3(B) & v2_tex_2(B,A) & -v1_tex_3(B,A) & v1_tdlat_3(B) & v1_tsep_1(B,A) & -v2_tex_3(B,A) & -v5_tex_2(B,A) & v2_pre_topc(B)))))) # label(cc23_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3233 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tex_3(B,A) & v2_tex_2(B,A) -> v2_tex_2(B,A) & v2_pre_topc(B) & -v1_borsuk_1(B,A)))))) # label(cc2_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3234 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & v1_tex_3(B,A) & v2_pre_topc(B) & m1_pre_topc(B,A) & v2_tex_3(B,A) & v1_tsep_1(B,A))))) # label(rc3_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3235 (all A (v2_pre_topc(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_3(B,A) <-> v3_tops_1(C,A))))))))) # label(t35_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3236 (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) & v1_tsep_1(B,A) & v1_tex_3(B,A) & -v3_tex_3(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & -v1_borsuk_1(B,A) & v2_tex_3(B,A) & -v4_tex_3(B,A) & v2_tex_2(B,A))))) # label(rc13_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3237 (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]. 4.62/4.71 3238 (all A (l1_pre_topc(A) & -v3_struct_0(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(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]. 4.62/4.71 3239 (all A (l1_pre_topc(A) & -v3_struct_0(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) -> (v2_tex_3(C,A) & v2_tex_3(B,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]. 4.62/4.71 3240 (all A (v2_pre_topc(A) & -v3_struct_0(A) & v3_tdlat_3(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) -> -v2_tex_3(B,A) & v2_pre_topc(B) & v2_tex_2(B,A)))))) # label(cc26_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3241 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v2_pre_topc(C) & l1_pre_topc(C) & -v3_struct_0(C) -> (C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> (m1_pre_topc(C,A) & v1_tex_3(C,A) <-> m1_pre_topc(B,A) & v1_tex_3(B,A))))))))) # label(t15_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3242 (all A (-v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (v2_tex_2(B,A) & -v2_tex_3(B,A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_pre_topc(B) & -v1_tsep_1(B,A) & v3_tex_3(B,A) & v1_pre_topc(B))))) # label(rc6_tex_3) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3243 (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]. 4.62/4.71 3244 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> ((exists C (v1_funct_2(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v3_tops_2(C,k3_t_0topsp(B),k3_t_0topsp(A)) & 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)) & m2_relset_1(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v1_funct_1(C))) -> r1_t_0topsp(A,B)))))) # label(t14_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3245 (all A (-v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.71 3246 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(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]. 4.62/4.71 3247 (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) & v2_t_0topsp(B) -> (all C (v5_pre_topc(C,A,B) & 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,u1_struct_0(A)) -> k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) = k4_pre_topc(A,B,C,k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),D)))))))))) # label(t16_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3248 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (r1_t_0topsp(A,B) <-> (exists C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_tops_2(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))))))))) # label(d1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3249 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) <-> (exists C (B = k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),C) & m1_subset_1(C,u1_struct_0(A)))))))) # label(t7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3250 (all A (-v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.71 3251 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> k3_t_0topsp(A) = k16_borsuk_1(A,k2_t_0topsp(A)))) # label(d5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3252 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,u1_struct_0(A),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(k4_tarski(C,D),B) <-> (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)))))))))) <-> B = k1_t_0topsp(A)))))) # label(d3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3253 (all A (v2_pre_topc(A) & -v3_struct_0(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),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) -> r2_hidden(D,B))))))))))) # label(t10_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3254 (exists A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) & v2_t_0topsp(A))) # label(rc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3255 (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_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]. 4.62/4.71 3256 (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_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]. 4.62/4.71 3257 (all A (l1_pre_topc(A) -> (v2_t_0topsp(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))) -> -(v3_pre_topc(D,A) & (r2_hidden(B,D) & -r2_hidden(C,D) | r2_hidden(C,D) & -r2_hidden(B,D))))) & C != B)))))))) # label(d7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3258 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists C (r2_hidden(k3_tarski(C),u1_pre_topc(B)) & m1_subset_1(C,k1_zfmisc_1(k2_t_0topsp(B))) & C = A)) <-> r2_hidden(A,a_1_0_t_0topsp(B))))) # label(fraenkel_a_1_0_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3259 (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)) -> (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]. 4.62/4.71 3260 (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,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]. 4.62/4.71 3261 (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(k3_t_0topsp(A)))) -> (v3_pre_topc(B,k3_t_0topsp(A)) <-> r2_hidden(k3_tarski(B),u1_pre_topc(A))))))) # label(t6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3262 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(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]. 4.62/4.71 3263 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) & v2_t_0topsp(B) & v2_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) -> (exists D (v1_funct_2(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & k4_borsuk_1(A,k3_t_0topsp(A),B,k4_t_0topsp(A),D) = C & v1_funct_1(D) & v5_pre_topc(D,k3_t_0topsp(A),B) & m2_relset_1(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)))))))))) # label(t17_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3264 (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]. 4.62/4.71 3265 (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]. 4.62/4.71 3266 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> v1_funct_1(k4_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_2(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))))) # label(dt_k4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3267 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(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]. 4.62/4.71 3268 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (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,F) = k8_funct_2(A,B,C,E) -> 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]. 4.62/4.71 3269 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> v3_relat_2(k1_t_0topsp(A)) & v8_relat_2(k1_t_0topsp(A)) & m2_relset_1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3270 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> -v3_struct_0(k3_t_0topsp(A)) & v2_t_0topsp(k3_t_0topsp(A)) & l1_pre_topc(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(t13_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3271 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> k17_borsuk_1(A,k2_t_0topsp(A)) = k4_t_0topsp(A))) # label(d6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3272 (all A (l1_pre_topc(A) -> (all 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)) -> ((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]. 4.62/4.71 3273 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_t_0topsp(B) & v2_pre_topc(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)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (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]. 4.62/4.71 3274 (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))) -> 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]. 4.62/4.71 3275 (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))))) # label(t17_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3276 (all A all B (l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_pre_topc(k5_tex_4(A,B),A) & v1_pre_topc(k5_tex_4(A,B)))) # label(dt_k5_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3277 (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]. 4.62/4.71 3278 (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_tex_4(C,A) & D = C -> v1_tex_4(D,B)))))))))) # label(t6_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3279 (all A all B all C (l1_pre_topc(B) & -v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(C,D) & v4_pre_topc(D,B) & A = D)) <-> r2_hidden(A,a_2_4_tex_4(B,C))))) # label(fraenkel_a_2_4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3280 (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))) -> k6_pre_topc(A,B) = k6_pre_topc(A,k3_tex_4(A,B)))))) # label(t64_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3281 (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))) -> (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]. 4.62/4.71 3282 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_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) -> B = C))) & v1_tex_4(B,A)))))) # label(d7_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3283 (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]. 4.62/4.71 3284 (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]. 4.62/4.71 3285 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v1_xboole_0(B) -> -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]. 4.62/4.71 3286 (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]. 4.62/4.71 3287 (all A all B (l1_pre_topc(A) & -v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> -v1_xboole_0(k1_tex_4(A,B)))) # label(fc8_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3288 (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))) -> m1_pre_topc(k6_tex_4(A,B),k7_tex_4(A,B)))))) # label(t84_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3289 (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_subset_1(k4_tex_4(A,B),k4_tex_4(A,C)) <-> -((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)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k4_tex_4(A,C),D) & v3_pre_topc(D,A) & r1_xboole_0(D,k4_tex_4(A,B))))))))))))) # label(t55_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3290 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((exists C (r2_hidden(C,B) & m1_subset_1(C,u1_struct_0(A)) & B = k2_tex_4(A,C))) <-> v3_tex_4(B,A)))))) # label(d9_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3291 (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))) -> (v4_pre_topc(C,A) | v4_pre_topc(B,A) -> k5_subset_1(u1_struct_0(A),k3_tex_4(A,B),k3_tex_4(A,C)) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C))))))))) # label(t66_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3292 (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,B) & v1_tex_4(B,A) -> v1_tex_4(C,A)))))))) # label(t7_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3293 (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]. 4.62/4.71 3294 (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))) -> (C = u1_struct_0(B) & v2_tdlat_3(B) -> v1_tex_4(C,A)))))))) # label(t68_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3295 (all A all B all C (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists D (D = A & v3_pre_topc(D,B) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_9_tex_4(B,C))))) # label(fraenkel_a_2_9_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3296 (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,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))) | 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]. 4.62/4.71 3297 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v4_pre_topc(k1_tops_1(A,B),A) & v1_tex_2(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v1_xboole_0(k1_tops_1(A,B)) & v3_pre_topc(k1_tops_1(A,B),A) & v3_tops_1(k1_tops_1(A,B),A) & v1_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)))) # label(fc7_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3298 (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))) -> (u1_struct_0(B) = C & v1_tex_4(C,A) -> v2_tdlat_3(B))))))))) # label(t69_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3299 (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),k2_tex_4(A,B)))))) # label(t20_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3300 (all A all B (l1_pre_topc(A) & -v1_xboole_0(B) & -v1_realset1(B) & v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_realset2(A) & -v3_struct_0(A) -> -v1_realset1(k6_pre_topc(A,B)) & -v1_xboole_0(k6_pre_topc(A,B)) & v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3301 (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))) -> 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]. 4.62/4.71 3302 (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)) -> -(r1_xboole_0(k2_tex_4(A,C),B) & -r1_xboole_0(k2_tex_4(A,C),k3_tex_4(A,B))))))))) # label(t31_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3303 (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_subset_1(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(t52_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3304 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.71 3305 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> ((all C (m1_pre_topc(C,A) & v1_tsep_1(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]. 4.62/4.71 3306 (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),k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B))))))) # label(t14_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3307 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v2_tdlat_3(B) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) -> m1_pre_topc(B,C) | r1_tsep_1(A,B,C))))))) # label(t73_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3308 (all A all B (l1_pre_topc(A) & -v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_pre_topc(k5_tex_4(A,B)) & -v3_struct_0(k5_tex_4(A,B)))) # label(fc14_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3309 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v4_tex_4(B,A) -> v3_tdlat_3(B) & v2_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3310 (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) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> v2_tdlat_3(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v4_tex_4(B,A) & -v3_struct_0(B)))))) # label(cc6_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3311 (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))) -> 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]. 4.62/4.71 3312 (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))) -> (v4_pre_topc(B,A) & v1_tex_4(B,A) -> v3_tex_4(B,A)))))) # label(t19_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3313 (all A all B all C (l1_pre_topc(B) & -v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(A,a_2_5_tex_4(B,C)) <-> (exists D (D = A & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v3_pre_topc(D,B)))))) # label(fraenkel_a_2_5_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3314 (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]. 4.62/4.71 3315 (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]. 4.62/4.71 3316 (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))) -> 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)))) = g1_pre_topc(u1_struct_0(k7_tex_4(A,B)),u1_pre_topc(k7_tex_4(A,B))))))) # label(t87_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3317 (all A (-v3_struct_0(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))) -> (r2_hidden(C,D) & r2_hidden(C,B) & v4_pre_topc(D,A) -> r1_tarski(B,D))))))))))) # label(d2_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3318 $T # label(t3_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3319 (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)) -> v4_tex_4(k1_tex_2(A,B),A)))))) # label(t80_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3320 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> (r2_hidden(A,a_2_6_tex_4(B,C)) <-> (exists D (r2_hidden(D,C) & A = k2_tex_4(B,D) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_6_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3321 (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]. 4.62/4.71 3322 (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,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]. 4.62/4.71 3323 (all A all B (-v1_xboole_0(B) & -v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k7_tex_4(A,B)) & -v3_struct_0(k7_tex_4(A,B)))) # label(fc19_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 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))) -> (v3_pre_topc(B,A) & v1_tex_4(B,A) -> v3_tex_4(B,A)))))) # label(t18_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3325 (all A all B (m1_subset_1(B,u1_struct_0(A)) & v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> m1_subset_1(k4_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(k4_tex_4(A,B)))) # label(dt_k4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3326 (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,B) & v3_pre_topc(B,A) -> r1_tarski(k3_tex_4(A,C),B)))))))) # label(t40_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3327 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> -v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(k3_tex_4(A,B)))) # label(fc12_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3328 (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) & 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]. 4.62/4.71 3329 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != a_2_8_tex_4(A,B) -> 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]. 4.62/4.71 3330 (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))) -> ((exists D (v3_pre_topc(D,B) & A = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & r1_tarski(C,D))) <-> r2_hidden(A,a_2_10_tex_4(B,C))))) # label(fraenkel_a_2_10_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3331 (all A (v2_pre_topc(A) & -v3_struct_0(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]. 4.62/4.71 3332 (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_pre_topc(B,A) -> r1_tarski(k2_tex_4(A,C),B)))))))) # label(t26_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3333 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(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) -> k6_pre_topc(A,k1_struct_0(A,C)) = B)))))))) # label(t45_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3334 (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) -> (v3_tex_4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> k2_tex_4(A,C) = B)))))))) # label(d10_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3335 (all A all B all C (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists D (v4_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(C,D) & D = A)) <-> r2_hidden(A,a_2_1_tex_4(B,C))))) # label(fraenkel_a_2_1_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3336 (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]. 4.62/4.71 3337 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != a_2_7_tex_4(A,B) -> 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]. 4.62/4.71 3338 (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) & -v4_tex_4(B,A) & -v3_struct_0(B) -> -v4_tex_4(B,A) & -v3_realset2(B) & -v3_struct_0(B) & -v2_tdlat_3(B) & v2_pre_topc(B)))))) # label(cc7_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3339 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_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]. 4.62/4.71 3340 (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]. 4.62/4.71 3341 (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) & -v4_tex_4(B,A) & v2_tdlat_3(B) -> -v3_struct_0(B) & v2_pre_topc(B) & v2_tex_2(B,A) & -v1_tsep_1(B,A)))))) # label(cc5_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3342 (all A (l1_pre_topc(A) & -v3_struct_0(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)) -> (k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) <-> k2_tex_4(A,C) = k2_tex_4(A,B)))))))) # label(t51_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3343 (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 & 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(C,A) -> v3_tex_4(D,B)))))))))) # label(t16_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3344 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & -v3_struct_0(A) & l1_pre_topc(A) -> -v1_xboole_0(k3_tex_4(A,B)))) # label(fc10_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3345 (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) & -v3_struct_0(B) & v2_tdlat_3(B) -> v4_tex_4(B,A) & v3_tdlat_3(B) & v2_tdlat_3(B) & -v3_struct_0(B) & v2_pre_topc(B)))))) # label(cc3_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3346 (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)) -> (v1_tex_4(B,A) & r2_hidden(C,B) -> r1_tarski(B,k2_tex_4(A,C))))))))) # label(t21_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3347 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_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))) -> 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]. 4.62/4.71 3348 (all A (v2_pre_topc(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_tarski(k4_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(t54_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3349 (all A (l1_pre_topc(A) & v2_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)) -> v3_tex_4(k1_struct_0(A,B),A)))))) # label(t47_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3350 (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))) -> k1_tops_1(A,B) = k3_tarski(a_2_2_tex_4(A,B)))))) # label(t4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3351 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(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) & -v1_xboole_0(k1_tops_1(A,B)))) # label(fc5_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3352 (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]. 4.62/4.71 3353 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v3_tdlat_3(B) & v2_pre_topc(B) & v1_pre_topc(B) & v4_tex_4(B,A) & v2_tdlat_3(B) & m1_pre_topc(B,A))))) # label(rc1_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3354 (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) & -r1_tarski(B,C) & -r1_xboole_0(B,C)))) <-> v1_tex_4(B,A)))))) # label(d4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3355 (all A all B all C (l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) & v2_pre_topc(B) -> ((exists D (D = A & r1_tarski(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v3_pre_topc(D,B))) <-> r2_hidden(A,a_2_2_tex_4(B,C))))) # label(fraenkel_a_2_2_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3356 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_realset2(A) & -v1_xboole_0(B) & -v1_realset1(B) & l1_pre_topc(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]. 4.62/4.71 3357 (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 (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (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]. 4.62/4.71 3358 (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))) -> (k3_tex_4(A,C) = k3_tex_4(A,B) -> k6_pre_topc(A,C) = k6_pre_topc(A,B)))))))) # label(t65_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3359 (all A all B (l1_pre_topc(A) & -v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v3_struct_0(k6_tex_4(A,B)) & v1_pre_topc(k6_tex_4(A,B)))) # label(fc16_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.71 3360 (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) -> (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]. 4.62/4.71 3361 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & D = A & v1_tex_4(D,B) & r2_hidden(C,D))) <-> r2_hidden(A,a_2_3_tex_4(B,C))))) # label(fraenkel_a_2_3_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3362 (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) -> (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(t90_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3363 (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) -> r1_tarski(B,k6_pre_topc(A,k1_struct_0(A,C))))))))))) # label(d12_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3364 (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)) -> r1_subset_1(k2_tex_4(A,B),k2_tex_4(A,C)) | k2_tex_4(A,B) = k2_tex_4(A,C))))))) # label(t24_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3365 (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))) -> 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]. 4.62/4.72 3366 (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))) -> k3_tex_4(A,k1_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t59_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3367 (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 (v4_pre_topc(D,B) & r1_tarski(C,D) & D = A & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_8_tex_4(B,C))))) # label(fraenkel_a_2_8_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3368 (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,k3_tex_4(A,B)) = k3_tex_4(A,B))))) # label(t35_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3369 (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]. 4.62/4.72 3370 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) -> k4_tex_4(A,B) = k2_tex_4(A,B))) # label(redefinition_k4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3371 (all A all B (l1_pre_topc(A) & -v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_pre_topc(k7_tex_4(A,B),A) & v1_pre_topc(k7_tex_4(A,B)))) # label(dt_k7_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3372 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(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]. 4.62/4.72 3373 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) & -v3_realset2(A) & l1_pre_topc(A) & -v1_realset1(B) & -v1_xboole_0(B) -> -v3_realset2(k7_tex_4(A,B)) & v1_pre_topc(k7_tex_4(A,B)) & -v3_struct_0(k7_tex_4(A,B)))) # label(fc20_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3374 (all A all B (-v1_xboole_0(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))) -> -v3_struct_0(k7_tex_4(A,B)) & -v2_tex_2(k7_tex_4(A,B),A) & v1_pre_topc(k7_tex_4(A,B)))) # label(fc21_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3375 (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]. 4.62/4.72 3376 (all A (l1_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v2_tex_2(B,A) & v1_pre_topc(B))))) # label(rc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3377 (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,C) -> r1_tarski(k3_tex_4(A,B),k3_tex_4(A,C))))))))) # label(t33_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3378 (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]. 4.62/4.72 3379 (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),k1_setfam_1(a_2_1_tex_4(A,B))))))) # label(t49_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3380 (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)) -> (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))) <-> m1_subset_1(C,u1_struct_0(k5_tex_4(A,B)))))))))) # label(t76_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3381 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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]. 4.62/4.72 3382 (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) -> 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]. 4.62/4.72 3383 (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]. 4.62/4.72 3384 (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]. 4.62/4.72 3385 (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]. 4.62/4.72 3386 (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,B) & v4_pre_topc(B,A) -> r1_tarski(k3_tex_4(A,C),B)))))))) # label(t42_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3387 (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]. 4.62/4.72 3388 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.72 3389 (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 (v1_pre_topc(C) & m1_pre_topc(C,A) -> (u1_struct_0(C) = k3_tex_4(A,B) <-> C = k7_tex_4(A,B)))))))) # label(d19_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3390 (all A all B (-v3_struct_0(A) & v2_pre_topc(A) & l1_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))) -> -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]. 4.62/4.72 3391 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_realset1(B) & l1_pre_topc(A) & -v3_realset2(A) -> v1_pre_topc(k6_tex_4(A,B)) & -v3_struct_0(k6_tex_4(A,B)) & -v3_realset2(k6_tex_4(A,B)))) # label(fc17_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3392 (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))) -> -(v3_pre_topc(C,A) & -r1_tarski(B,C) & -r1_xboole_0(B,C))))))))) # label(d3_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3393 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) & l1_pre_topc(B) -> (r2_hidden(A,a_2_7_tex_4(B,C)) <-> (exists D (r1_tarski(C,D) & A = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v3_pre_topc(D,B)))))) # label(fraenkel_a_2_7_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3394 (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))) -> (k3_tex_4(A,C) = k3_tex_4(A,B) <-> r1_tarski(C,k3_tex_4(A,B)) & r1_tarski(B,k3_tex_4(A,C))))))))) # label(t37_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3395 (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)) -> (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]. 4.62/4.72 3396 (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) -> 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]. 4.62/4.72 3397 (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]. 4.62/4.72 3398 (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) -> B = k3_tex_4(A,B)))))) # label(t62_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3399 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & -v3_struct_0(A) -> v1_tex_2(k3_tex_4(A,B),k1_zfmisc_1(u1_struct_0(A))) & v5_membered(k3_tex_4(A,B)) & v4_membered(k3_tex_4(A,B)) & v1_membered(k3_tex_4(A,B)) & v2_membered(k3_tex_4(A,B)) & v3_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]. 4.62/4.72 3400 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) & -v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_pre_topc(A) -> -v2_tex_2(k6_tex_4(A,B),A) & v1_pre_topc(k6_tex_4(A,B)) & -v3_struct_0(k6_tex_4(A,B)))) # label(fc18_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3401 $T # label(t5_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3402 (all 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) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v1_tex_4(C,A))))))))) # label(d5_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3403 (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_pre_topc(B) & v2_tex_2(B,A) & -v1_borsuk_1(B,A) & -v3_struct_0(B)))))) # label(cc8_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3404 (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]. 4.62/4.72 3405 (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(k1_setfam_1(a_2_9_tex_4(A,C)),k1_setfam_1(a_2_9_tex_4(A,B)))))))))) # label(t53_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3406 (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) -> (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]. 4.62/4.72 3407 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.72 3408 (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]. 4.62/4.72 3409 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> -v3_struct_0(k5_tex_4(A,B)) & v2_tdlat_3(k5_tex_4(A,B)) & v4_tex_4(k5_tex_4(A,B),A) & v1_pre_topc(k5_tex_4(A,B)) & v3_tdlat_3(k5_tex_4(A,B)) & v2_pre_topc(k5_tex_4(A,B)))) # label(fc15_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3410 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (k2_tex_4(A,B) = u1_struct_0(C) <-> k5_tex_4(A,B) = C))))))) # label(d17_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3411 (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,C)) = k6_pre_topc(A,k1_struct_0(A,D)))))))))))) # label(d14_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3412 (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) & v2_pre_topc(A) -> v3_pre_topc(k6_pre_topc(A,B),A) & v4_pre_topc(k6_pre_topc(A,B),A) & v5_membered(k6_pre_topc(A,B)) & v2_membered(k6_pre_topc(A,B)) & v1_membered(k6_pre_topc(A,B)) & v2_tops_1(k6_pre_topc(A,B),A) & v1_xboole_0(k6_pre_topc(A,B)) & v3_tops_1(k6_pre_topc(A,B),A) & v1_tex_2(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) & v3_membered(k6_pre_topc(A,B)) & v4_membered(k6_pre_topc(A,B)))) # label(fc2_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3413 (all A (l1_pre_topc(A) & -v3_struct_0(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]. 4.62/4.72 3414 (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 (m1_pre_topc(C,A) & v1_tsep_1(C,A) -> r1_tsep_1(A,B,C) | m1_pre_topc(B,C))))))) # label(t72_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3415 (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]. 4.62/4.72 3416 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_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) & -v4_tex_4(B,A) & -v3_struct_0(B) & v2_pre_topc(B) & -v2_tdlat_3(B)))))) # label(cc4_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3417 (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)) -> (-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]. 4.62/4.72 3418 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(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(C) = u1_struct_0(B)))) <-> v4_tex_4(B,A)))))) # label(d16_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3419 (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) & 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]. 4.62/4.72 3420 (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]. 4.62/4.72 3421 (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)) -> (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]. 4.62/4.72 3422 (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]. 4.62/4.72 3423 (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))) -> (r1_tarski(k6_pre_topc(A,k1_struct_0(A,B)),C) & v1_tex_4(C,A) -> C = k6_pre_topc(A,k1_struct_0(A,B))))))))) # label(t44_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3424 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.72 3425 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_xboole_0 != a_2_4_tex_4(A,B) -> 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]. 4.62/4.72 3426 (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_tarski(a_2_6_tex_4(A,B)))))) # label(d11_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3427 (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) -> v3_pre_topc(B,A) | v2_tops_1(B,A)))))) # label(t46_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3428 (all A (v2_pre_topc(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)) -> (-((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_xboole_0(D,k4_tex_4(A,B)) & r1_tarski(k4_tex_4(A,C),D) & v4_pre_topc(D,A)))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r1_xboole_0(D,k4_tex_4(A,C)) & r1_tarski(k4_tex_4(A,B),D))))) <-> r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C))))))))) # label(t56_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3429 (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_struct_0(B) -> (r2_hidden(A,a_2_0_tex_4(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v4_pre_topc(D,B) & r1_tarski(C,D)))))) # label(fraenkel_a_2_0_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3430 (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(k5_setfam_1(u1_struct_0(A),B),A) | k1_xboole_0 = k6_setfam_1(u1_struct_0(A),B)))))) # label(t10_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3431 (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) -> (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(t91_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3432 (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,B) = k2_tex_4(A,C) <-> r2_hidden(C,k2_tex_4(A,B))))))))) # label(t23_tex_4) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3433 (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]. 4.62/4.72 3434 (all A (-v2_t_0topsp(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 (m2_tsp_1(C,A) & -v2_t_0topsp(C) & v1_pre_topc(C) -> B != u1_struct_0(C)))))))) # label(t21_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3435 (all A (l1_pre_topc(A) -> (v2_t_0topsp(A) & v2_pre_topc(A) & -v3_struct_0(A) & v3_tdlat_3(A) -> -v3_struct_0(A) & v4_tdlat_3(A) & v1_tdlat_3(A) & v2_pre_topc(A) & v5_tdlat_3(A) & v2_t_0topsp(A) & v3_tdlat_3(A)))) # label(cc8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3436 (all A (l1_pre_topc(A) & v2_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)) -> -(k6_pre_topc(A,k1_struct_0(A,B)) = k6_pre_topc(A,k1_struct_0(A,C)) & B != C)))))))) # label(d5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3437 (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_tsp_1(B,A))))) # label(t13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3438 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v2_t_0topsp(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]. 4.62/4.72 3439 (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) -> -(-v1_realset1(B) & v1_tex_4(B,A) & v1_tsp_1(B,A)))))) # label(t12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3440 (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(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tsp_1(C,A) & D = C -> v1_tsp_1(D,B)))))))))) # label(t5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3441 (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,B) & v1_tsp_1(B,A) -> v1_tsp_1(C,A)))))))) # label(t7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3442 (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) & r2_hidden(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(d11_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3443 (all A (l1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (-v3_struct_0(B) & v1_pre_topc(B) & m1_pre_topc(B,A) & v2_t_0topsp(B) & v2_tex_2(B,A))))) # label(rc6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3444 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v1_pre_topc(A) & v2_t_0topsp(A) & v2_pre_topc(A))) # label(rc1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3445 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & -v3_struct_0(B) -> (all C (m2_tsp_1(C,A) & v2_t_0topsp(C) & -v3_struct_0(C) -> (m2_tsp_1(B,C) -> v2_t_0topsp(B)))))))) # label(t16_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3446 (all A (l1_pre_topc(A) -> (-v1_tdlat_3(A) & v3_tdlat_3(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -v2_t_0topsp(A) & -v3_realset2(A) & -v3_struct_0(A) & v2_pre_topc(A) & -v1_tdlat_3(A)))) # label(cc9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3447 $T # label(t1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3448 (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)) -> -((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)))) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B)) & (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)))) & C != D))))) | v3_struct_0(B) <-> v2_t_0topsp(B)))))) # label(d13_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3449 (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]. 4.62/4.72 3450 (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]. 4.62/4.72 3451 (all A (l1_pre_topc(A) -> (exists B m2_tsp_1(B,A)))) # label(existence_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3452 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & -v3_struct_0(B) & v2_t_0topsp(B) & m1_pre_topc(B,A))))) # label(rc5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3453 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & v1_pre_topc(A) & -v3_realset2(A) & -v2_tdlat_3(A) & v2_t_0topsp(A))) # label(rc3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 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_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]. 4.62/4.72 3455 (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]. 4.62/4.72 3456 (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,C)),k6_pre_topc(A,k1_struct_0(A,B))) & B != C & r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C)))))))) <-> v2_t_0topsp(A)))) # label(d7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3457 (all A all B (l1_pre_topc(A) & m1_pre_topc(B,A) -> (v2_t_0topsp(B) <-> v3_tsp_1(B,A)))) # label(redefinition_v3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3458 (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(D,u1_struct_0(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(D,E) & -r2_hidden(C,E)))) & m1_subset_1(C,u1_struct_0(B)) & C != D))))) <-> v2_t_0topsp(B)))))) # label(d14_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3459 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (m1_tsp_1(B,A) <-> r1_tarski(u1_struct_0(B),u1_struct_0(A)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (v3_pre_topc(D,A) & C = k3_xboole_0(D,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v3_pre_topc(C,B))))))))) # label(d1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3460 (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]. 4.62/4.72 3461 (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_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(C != D & k6_pre_topc(A,k1_struct_0(A,D)) = k6_pre_topc(A,k1_struct_0(A,C)) & r2_hidden(C,B) & r2_hidden(D,B))))))))))) # label(d10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3462 (all A (-v2_t_0topsp(A) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & m1_pre_topc(B,A) & -v2_t_0topsp(B))))) # label(rc7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3463 (all A (l1_pre_topc(A) -> (-v2_t_0topsp(A) & -v3_struct_0(A) & v2_pre_topc(A) -> -v1_tdlat_3(A) & v2_pre_topc(A) & -v3_realset2(A) & -v3_struct_0(A)))) # label(cc4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3464 (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]. 4.62/4.72 3465 (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))) -> -(v1_tsp_1(B,A) & (all C (m2_tsp_1(C,A) & v1_pre_topc(C) & v2_t_0topsp(C) & -v3_struct_0(C) -> B != u1_struct_0(C)))))))) # label(t20_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3466 (exists A (-v3_struct_0(A) & -v3_realset2(A) & v2_pre_topc(A) & v1_pre_topc(A) & l1_pre_topc(A) & -v2_t_0topsp(A))) # label(rc2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3467 (all A (-v3_struct_0(A) & l1_pre_topc(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]. 4.62/4.72 3468 (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(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]. 4.62/4.72 3469 (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))) -> -(v4_pre_topc(D,A) & r2_hidden(B,D) & -r2_hidden(C,D)))) & C != B & (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))))))))) | v3_struct_0(A) <-> v2_t_0topsp(A)))) # label(d4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3470 (all A (v2_pre_topc(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(D,B) & C != D & 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))) & r2_hidden(C,B)))))) <-> v1_tsp_1(B,A)))))) # label(d12_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3471 (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))) -> ((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)) <-> v4_pre_topc(C,B)))) <-> m2_tsp_1(B,A)))))) # label(d2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3472 (all A (l1_pre_topc(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)) -> -((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)))) & B != C & (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))))))))) | v3_struct_0(A)))) # label(d3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3473 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) & -v3_struct_0(A) & v1_tdlat_3(A) -> v2_t_0topsp(A) & v2_pre_topc(A) & -v3_struct_0(A)))) # label(cc3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3474 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v2_t_0topsp(B) <-> v1_tsp_1(C,A))))))))) # label(t15_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3475 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_t_0topsp(B) & -v3_struct_0(B) & m2_tsp_1(B,A) -> (all C (v2_t_0topsp(C) & -v3_struct_0(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]. 4.62/4.72 3476 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_tdlat_3(A) & v2_t_0topsp(A) & v2_pre_topc(A) -> -v3_struct_0(A) & v3_realset2(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v3_tdlat_3(A) & v5_tdlat_3(A) & v4_tdlat_3(A) & v2_tdlat_3(A) & v2_t_0topsp(A)))) # label(cc6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3477 (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)) -> -((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(D,B) & r2_hidden(C,B) & C != D & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(C,E) & v3_pre_topc(E,A) & r2_hidden(D,E)))))))))))))) # label(d8_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3478 (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))) -> -(k3_xboole_0(C,u1_struct_0(B)) = D & v3_pre_topc(D,B)))) & v3_pre_topc(C,A)))))))) # label(t2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3479 (all A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(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]. 4.62/4.72 3480 (exists A (-v3_struct_0(A) & -v1_tdlat_3(A) & -v2_t_0topsp(A) & v1_pre_topc(A) & -v3_realset2(A) & v2_pre_topc(A) & l1_pre_topc(A))) # label(rc4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3481 (all A (l1_pre_topc(A) -> (exists B m1_tsp_1(B,A)))) # label(existence_m1_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3482 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_t_0topsp(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]. 4.62/4.72 3483 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_t_0topsp(A) & -v1_tdlat_3(A) & v2_pre_topc(A) -> -v3_struct_0(A) & v2_pre_topc(A) & -v1_tdlat_3(A) & -v2_tdlat_3(A) & -v3_tdlat_3(A) & -v3_realset2(A)))) # label(cc10_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3484 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) <-> m2_tsp_1(B,A))))) # label(redefinition_m2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3485 $T # label(t3_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3486 (all A (l1_pre_topc(A) & v2_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)) -> -(r2_hidden(B,k6_pre_topc(A,k1_struct_0(A,C))) & C != B & r2_hidden(C,k6_pre_topc(A,k1_struct_0(A,B))))))))))) # label(d6_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3487 (all A (l1_pre_topc(A) -> (v2_tdlat_3(A) & -v3_realset2(A) & -v3_struct_0(A) & v2_pre_topc(A) -> -v2_t_0topsp(A) & -v3_struct_0(A) & -v3_realset2(A) & v2_pre_topc(A)))) # label(cc5_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.72 3488 (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(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]. 4.62/4.72 3489 (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]. 4.62/4.72 3490 (all A (-v3_struct_0(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)) -> -((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)))) & r2_hidden(C,B) & r2_hidden(D,B) & D != C & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(-r2_hidden(C,E) & v4_pre_topc(E,A) & r2_hidden(D,E)))))))))))))) # label(d9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3491 (all A (v2_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_t_0topsp(B) & m2_tsp_1(B,A) -> (all C (v2_t_0topsp(C) & -v3_struct_0(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]. 4.62/4.73 3492 (all A all B (l1_pre_topc(A) & m1_pre_topc(B,A) -> (v2_tsp_1(B,A) <-> v2_t_0topsp(B)))) # label(redefinition_v2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3493 (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))) -> -(v4_pre_topc(D,B) & D = k3_xboole_0(C,u1_struct_0(B)))))))))))) # label(t4_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3494 (all A (l1_pre_topc(A) -> (-v2_t_0topsp(A) & -v3_struct_0(A) -> -v3_struct_0(A) & -v3_realset2(A)))) # label(cc2_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3495 (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(C,A) & v1_tsp_1(B,A) -> -v3_pre_topc(B,A) & -v3_pre_topc(C,A) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t9_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3496 (all A (l1_pre_topc(A) -> (-v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & -v3_realset2(A) -> v2_pre_topc(A) & -v3_struct_0(A) & -v2_tdlat_3(A) & -v3_realset2(A)))) # label(cc7_tsp_1) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3497 (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_tsp_2(B,A) -> v2_pre_topc(B) & -v2_tex_2(B,A)))))) # label(cc8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3498 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -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)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (D = u1_struct_0(B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))) -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))))))))))) # label(t18_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3499 (all A all B (-v3_struct_0(A) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) & l1_pre_topc(A) & 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]. 4.62/4.73 3500 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(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,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (D = E -> k3_tex_4(A,D) = k5_pre_topc(A,B,C,E))))))))))))) # label(l37_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3501 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) -> m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))))))) # label(l19_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3502 (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) & u1_struct_0(A) = k3_tex_4(A,B) <-> v1_tsp_2(B,A)))))) # label(d5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3503 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v1_tsp_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t10_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3504 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> (exists C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_borsuk_1(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C))))))) # label(t22_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3505 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -v3_struct_0(B) -> r1_borsuk_1(A,B))))) # label(t23_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3506 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_t_0topsp(B) -> (exists C (v2_tsp_2(C,A) & m2_tsp_1(B,C) & m2_tsp_1(C,A) & v1_pre_topc(C))))))) # label(t13_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3507 (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) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & (v3_pre_topc(B,A) | v4_pre_topc(B,A))))))) # label(t3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3508 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -v3_struct_0(B) -> (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(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> k4_tex_4(A,D) = k5_pre_topc(A,B,C,k1_struct_0(B,E)))))))))))))) # label(l36_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3509 (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,k1_tops_1(A,C))) = k1_tops_1(A,C)))))))) # label(t8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3510 (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)) & m2_relset_1(k2_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k2_tsp_2(A,B),A,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]. 4.62/4.73 3511 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) & -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) -> (v3_borsuk_1(C,A,B) <-> C = k1_tsp_2(A,B)))))))) # label(d9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3512 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tsp_2(B,A) -> v1_tex_3(B,A) & v2_pre_topc(B)))))) # label(cc3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3513 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) <-> (exists D (D = k3_xboole_0(C,u1_struct_0(B)) & v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) & k3_tex_4(A,C) = C))))))) # label(t15_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3514 (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_tsp_2(B,A) -> v2_pre_topc(B) & -v2_tex_2(B,A)))))) # label(cc5_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3515 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (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) -> (v3_borsuk_1(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = D -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)))))))))))))) # label(l34_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3516 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (all C (m2_relset_1(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_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (D = u1_struct_0(B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k5_subset_1(u1_struct_0(A),D,k4_tex_4(A,E)))) -> v3_borsuk_1(C,A,B)))))))))) # label(t20_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3517 (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)) -> (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)))))))))) # label(d1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3518 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & -v2_t_0topsp(B) -> -v2_tsp_2(B,A) & -v3_struct_0(B)))))) # label(cc2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3519 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tsp_2(B,A) & v2_tex_2(B,A) -> v2_pre_topc(B) & -v1_borsuk_1(B,A)))))) # label(cc10_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3520 (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))) -> (v1_tsp_2(C,A) & D = C & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> v1_tsp_2(D,B)))))))))) # label(t1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3521 (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))) -> -((all C (m2_tsp_1(C,A) & v1_pre_topc(C) & -v3_struct_0(C) -> -(u1_struct_0(C) = B & v2_tsp_2(C,A)))) & v1_tsp_2(B,A)))))) # label(t12_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3522 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_tsp_2(C,A) <-> v2_tsp_2(B,A))))))))) # label(t11_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3523 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) & l1_pre_topc(A) & v2_pre_topc(A) -> k2_tsp_2(A,B) = k1_tsp_2(A,B))) # label(redefinition_k2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3524 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(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 -> (v3_pre_topc(k3_tex_4(A,C),A) & k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)) = D <-> v3_pre_topc(D,B))))))))))) # label(t14_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3525 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (v4_pre_topc(D,B) & k3_xboole_0(C,u1_struct_0(B)) = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) & C = k3_tex_4(A,C) <-> v4_pre_topc(C,A)))))))) # label(t17_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3526 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (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,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> k6_pre_topc(A,k1_struct_0(A,D)) = k5_pre_topc(A,B,C,k6_pre_topc(B,k1_struct_0(B,E))))))))))))))) # label(l33_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3527 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) & v1_tsep_1(B,A) -> -v2_tsp_2(B,A) & v2_pre_topc(B)))))) # label(cc6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3528 (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) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,C) = k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))))))))) # label(t7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3529 (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))) -> (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]. 4.62/4.73 3530 (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,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_struct_0(A,C) = k5_subset_1(u1_struct_0(A),B,D) & v3_tex_4(D,A))))))) <-> v1_tsp_1(B,A)))))) # label(d3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3531 (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) -> k3_tex_4(A,k5_subset_1(u1_struct_0(A),B,C)) = C)))))))) # label(t6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3532 (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,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tsp_1(C,A) & r1_tarski(B,C) -> C = B))) <-> v1_tsp_2(B,A)))))) # label(d4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3533 (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,u1_struct_0(A)) -> (r2_hidden(C,B) -> k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)) = k1_struct_0(A,C)))) <-> v1_tsp_1(B,A)))))) # label(d2_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3534 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_tsp_2(B,A) & m2_tsp_1(B,A) -> (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)) -> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)))) -> m2_relset_1(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_funct_1(C)))))))) # label(t19_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3535 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(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 -> (v4_pre_topc(D,B) <-> v4_pre_topc(k3_tex_4(A,C),A) & D = k3_xboole_0(k3_tex_4(A,C),u1_struct_0(B)))))))))))) # label(t16_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3536 (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) & v1_tsp_2(C,A)))) & v1_tsp_1(B,A)))))) # label(t9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3537 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(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) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k4_tex_4(A,D)))) -> v3_borsuk_1(C,A,B)))))))) # label(t21_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3538 (all A all B (v2_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_funct_1(k3_tsp_2(A,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_2(k3_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3539 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_pre_topc(B) & v1_tex_3(B,A) & v2_t_0topsp(B) & v2_tsp_2(B,A) & v2_pre_topc(B))))) # label(rc1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3540 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & v2_pre_topc(A) -> v1_funct_2(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k4_tsp_2(A,B),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k4_tsp_2(A,B),A,B) & v1_funct_1(k4_tsp_2(A,B)))) # label(dt_k4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3541 (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))) -> -v1_tsp_2(B,A))))) # label(t4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3542 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) -> (v2_tsp_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v1_tsp_2(C,A))))))))) # label(d7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3543 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m2_tsp_1(B,A) & -v3_struct_0(B) -> (v2_tsp_2(B,A) <-> (all C (m2_tsp_1(C,A) & v2_t_0topsp(C) & -v3_struct_0(C) -> (m2_tsp_1(B,C) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))) & v2_t_0topsp(B)))))) # label(d8_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3544 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (-v3_struct_0(B) & v2_tsp_2(B,A) -> v2_t_0topsp(B) & -v3_struct_0(B)))))) # label(cc1_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3545 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) -> (-v1_tex_3(B,A) -> -v2_tsp_2(B,A) & v2_pre_topc(B)))))) # label(cc4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3546 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & v2_pre_topc(A) -> k1_tsp_2(A,B) = k3_tsp_2(A,B))) # label(redefinition_k3_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3547 (all A all B (v2_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_tsp_2(B,A) & l1_pre_topc(A) & -v3_struct_0(A) -> k4_tsp_2(A,B) = k1_tsp_2(A,B))) # label(redefinition_k4_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3548 (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_tsp_2(B,A) & v2_pre_topc(B)))))) # label(cc9_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3549 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_tsp_2(B,A) & m2_tsp_1(B,A) & -v3_struct_0(B) -> (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(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> r1_tarski(k4_tex_4(A,D),k5_pre_topc(A,B,C,k1_struct_0(B,E))))))))))))))) # label(l35_tsp_2) # label(axiom) # label(non_clause). [assumption]. 4.62/4.73 3550 (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,u1_struct_0(A)) -> (exists D (k5_subset_1(u1_struct_0(A),B,k4_tex_4(A,C)) = k1_struct_0(A,D) & r2_hidden(D,B) & m1_subset_1(D,u1_struct_0(A))))))))))) # label(d6_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.13/5.22 3551 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v2_tex_2(B,A) & v2_tsp_2(B,A) -> -v1_tsep_1(B,A) & v2_pre_topc(B)))))) # label(cc7_tsp_2) # label(axiom) # label(non_clause). [assumption]. 5.13/5.22 3552 (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]. 5.13/5.22 3553 -(all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m2_tsp_1(B,A) & v2_tsp_2(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)) -> (C = D -> k6_pre_topc(A,k1_struct_0(A,C)) = k5_pre_topc(A,B,k1_tsp_2(A,B),k6_pre_topc(B,k1_struct_0(B,D)))))))))))) # label(t24_tsp_2) # label(negated_conjecture) # label(non_clause). [assumption]. 5.13/5.22 5.13/5.22 ============================== end of process non-clausal formulas === 5.13/5.22 5.13/5.22 ============================== PROCESS INITIAL CLAUSES =============== 5.13/5.22 5.13/5.22 ============================== PREDICATE ELIMINATION ================= 5.13/5.22 3554 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | -r2_hidden(k4_tarski(f15(A,B,D),E),D) | -r2_hidden(E,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 3555 -r2_tarski(A,B) | r2_hidden(f8(A,B,C),A) | -r2_hidden(C,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 3556 -r2_tarski(A,B) | r2_hidden(k4_tarski(f8(A,B,C),C),f7(A,B)) | -r2_hidden(C,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 3557 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f7(A,B)) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | D != F | C = E # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 3558 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f7(A,B)) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | D = F | C != E # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 3559 -r2_tarski(A,B) | r2_hidden(k4_tarski(C,f9(A,B,C)),f7(A,B)) | -r2_hidden(C,A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 3560 -r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | -r2_hidden(C,A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f8(B,C,F),B) | -r2_hidden(F,C). [resolve(3554,a,3555,a)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f8(B,C,F),F),f7(B,C)) | -r2_hidden(F,C). [resolve(3554,a,3556,a)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 != V8 | F = V7. [resolve(3554,a,3557,a)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 = V8 | F != V7. [resolve(3554,a,3558,a)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(F,f9(B,C,F)),f7(B,C)) | -r2_hidden(F,B). [resolve(3554,a,3559,a)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f9(B,C,F),C) | -r2_hidden(F,B). [resolve(3554,a,3560,a)]. 5.13/5.22 3561 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | r2_hidden(f15(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.22 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f8(B,C,E),B) | -r2_hidden(E,C). [resolve(3561,a,3555,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(f8(B,C,E),E),f7(B,C)) | -r2_hidden(E,C). [resolve(3561,a,3556,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F != V7 | E = V6. [resolve(3561,a,3557,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F = V7 | E != V6. [resolve(3561,a,3558,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(E,f9(B,C,E)),f7(B,C)) | -r2_hidden(E,B). [resolve(3561,a,3559,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f9(B,C,E),C) | -r2_hidden(E,B). [resolve(3561,a,3560,a)]. 5.13/5.25 3562 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | r2_hidden(k4_tarski(f11(A,B,D),f12(A,B,D)),D) | -r2_hidden(k4_tarski(f15(A,B,D),E),D) | -r2_hidden(E,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f8(B,C,F),B) | -r2_hidden(F,C). [resolve(3562,a,3555,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f8(B,C,F),F),f7(B,C)) | -r2_hidden(F,C). [resolve(3562,a,3556,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 != V8 | F = V7. [resolve(3562,a,3557,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 = V8 | F != V7. [resolve(3562,a,3558,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(F,f9(B,C,F)),f7(B,C)) | -r2_hidden(F,B). [resolve(3562,a,3559,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f9(B,C,F),C) | -r2_hidden(F,B). [resolve(3562,a,3560,a)]. 5.13/5.25 3563 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | r2_hidden(k4_tarski(f11(A,B,D),f12(A,B,D)),D) | r2_hidden(f15(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f8(B,C,E),B) | -r2_hidden(E,C). [resolve(3563,a,3555,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(f8(B,C,E),E),f7(B,C)) | -r2_hidden(E,C). [resolve(3563,a,3556,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F != V7 | E = V6. [resolve(3563,a,3557,a)]. 5.13/5.25 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F = V7 | E != V6. [resolve(3563,a,3558,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(E,f9(B,C,E)),f7(B,C)) | -r2_hidden(E,B). [resolve(3563,a,3559,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | r2_hidden(k4_tarski(f11(B,C,D),f12(B,C,D)),D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f9(B,C,E),C) | -r2_hidden(E,B). [resolve(3563,a,3560,a)]. 5.22/5.28 3564 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | f14(A,B,D) = f12(A,B,D) | f13(A,B,D) = f11(A,B,D) | -r2_hidden(k4_tarski(f15(A,B,D),E),D) | -r2_hidden(E,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f8(B,C,F),B) | -r2_hidden(F,C). [resolve(3564,a,3555,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f8(B,C,F),F),f7(B,C)) | -r2_hidden(F,C). [resolve(3564,a,3556,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 != V8 | F = V7. [resolve(3564,a,3557,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 = V8 | F != V7. [resolve(3564,a,3558,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(F,f9(B,C,F)),f7(B,C)) | -r2_hidden(F,B). [resolve(3564,a,3559,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f9(B,C,F),C) | -r2_hidden(F,B). [resolve(3564,a,3560,a)]. 5.22/5.28 3565 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | f14(A,B,D) = f12(A,B,D) | f13(A,B,D) = f11(A,B,D) | r2_hidden(f15(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f8(B,C,E),B) | -r2_hidden(E,C). [resolve(3565,a,3555,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(f8(B,C,E),E),f7(B,C)) | -r2_hidden(E,C). [resolve(3565,a,3556,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F != V7 | E = V6. [resolve(3565,a,3557,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F = V7 | E != V6. [resolve(3565,a,3558,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(E,f9(B,C,E)),f7(B,C)) | -r2_hidden(E,B). [resolve(3565,a,3559,a)]. 5.22/5.28 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) = f12(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f9(B,C,E),C) | -r2_hidden(E,B). [resolve(3565,a,3560,a)]. 5.25/5.30 3566 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | f14(A,B,D) != f12(A,B,D) | f13(A,B,D) != f11(A,B,D) | -r2_hidden(k4_tarski(f15(A,B,D),E),D) | -r2_hidden(E,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f8(B,C,F),B) | -r2_hidden(F,C). [resolve(3566,a,3555,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f8(B,C,F),F),f7(B,C)) | -r2_hidden(F,C). [resolve(3566,a,3556,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 != V8 | F = V7. [resolve(3566,a,3557,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(F,V6),f7(B,C)) | -r2_hidden(k4_tarski(V7,V8),f7(B,C)) | V6 = V8 | F != V7. [resolve(3566,a,3558,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(k4_tarski(F,f9(B,C,F)),f7(B,C)) | -r2_hidden(F,B). [resolve(3566,a,3559,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(k4_tarski(f15(B,C,D),E),D) | -r2_hidden(E,C) | r2_hidden(f9(B,C,F),C) | -r2_hidden(F,B). [resolve(3566,a,3560,a)]. 5.25/5.30 3567 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f10(A,B,D)),D) | f14(A,B,D) != f12(A,B,D) | f13(A,B,D) != f11(A,B,D) | r2_hidden(f15(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f8(B,C,E),B) | -r2_hidden(E,C). [resolve(3567,a,3555,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(f8(B,C,E),E),f7(B,C)) | -r2_hidden(E,C). [resolve(3567,a,3556,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F != V7 | E = V6. [resolve(3567,a,3557,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f15(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f7(B,C)) | -r2_hidden(k4_tarski(V6,V7),f7(B,C)) | F = V7 | E != V6. [resolve(3567,a,3558,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(k4_tarski(E,f9(B,C,E)),f7(B,C)) | -r2_hidden(E,B). [resolve(3567,a,3559,a)]. 5.25/5.30 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f10(B,C,D)),D) | f14(B,C,D) != f12(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f15(B,C,D),B) | r2_hidden(f9(B,C,E),C) | -r2_hidden(E,B). [resolve(3567,a,3560,a)]. 5.25/5.30 3568 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.25/5.30 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f8(A,B,E),A) | -r2_hidden(E,B). [resolve(3568,a,3555,a)]. 5.25/5.30 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f8(A,B,E),E),f7(A,B)) | -r2_hidden(E,B). [resolve(3568,a,3556,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F != V7 | E = V6. [resolve(3568,a,3557,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F = V7 | E != V6. [resolve(3568,a,3558,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(E,f9(A,B,E)),f7(A,B)) | -r2_hidden(E,A). [resolve(3568,a,3559,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f9(A,B,E),B) | -r2_hidden(E,A). [resolve(3568,a,3560,a)]. 5.28/5.33 3569 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f8(A,B,D),A) | -r2_hidden(D,B). [resolve(3569,a,3555,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(f8(A,B,D),D),f7(A,B)) | -r2_hidden(D,B). [resolve(3569,a,3556,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E != V6 | D = F. [resolve(3569,a,3557,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E = V6 | D != F. [resolve(3569,a,3558,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(D,f9(A,B,D)),f7(A,B)) | -r2_hidden(D,A). [resolve(3569,a,3559,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f9(A,B,D),B) | -r2_hidden(D,A). [resolve(3569,a,3560,a)]. 5.28/5.33 3570 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f8(A,B,E),A) | -r2_hidden(E,B). [resolve(3570,a,3555,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f8(A,B,E),E),f7(A,B)) | -r2_hidden(E,B). [resolve(3570,a,3556,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F != V7 | E = V6. [resolve(3570,a,3557,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F = V7 | E != V6. [resolve(3570,a,3558,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(E,f9(A,B,E)),f7(A,B)) | -r2_hidden(E,A). [resolve(3570,a,3559,a)]. 5.28/5.33 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f9(A,B,E),B) | -r2_hidden(E,A). [resolve(3570,a,3560,a)]. 5.28/5.33 3571 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f8(A,B,D),A) | -r2_hidden(D,B). [resolve(3571,a,3555,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(f8(A,B,D),D),f7(A,B)) | -r2_hidden(D,B). [resolve(3571,a,3556,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E != V6 | D = F. [resolve(3571,a,3557,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E = V6 | D != F. [resolve(3571,a,3558,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(D,f9(A,B,D)),f7(A,B)) | -r2_hidden(D,A). [resolve(3571,a,3559,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | r2_hidden(k4_tarski(f11(A,B,C),f12(A,B,C)),C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f9(A,B,D),B) | -r2_hidden(D,A). [resolve(3571,a,3560,a)]. 5.28/5.36 3572 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f8(A,B,E),A) | -r2_hidden(E,B). [resolve(3572,a,3555,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f8(A,B,E),E),f7(A,B)) | -r2_hidden(E,B). [resolve(3572,a,3556,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F != V7 | E = V6. [resolve(3572,a,3557,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F = V7 | E != V6. [resolve(3572,a,3558,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(E,f9(A,B,E)),f7(A,B)) | -r2_hidden(E,A). [resolve(3572,a,3559,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f9(A,B,E),B) | -r2_hidden(E,A). [resolve(3572,a,3560,a)]. 5.28/5.36 3573 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f8(A,B,D),A) | -r2_hidden(D,B). [resolve(3573,a,3555,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(f8(A,B,D),D),f7(A,B)) | -r2_hidden(D,B). [resolve(3573,a,3556,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E != V6 | D = F. [resolve(3573,a,3557,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E = V6 | D != F. [resolve(3573,a,3558,a)]. 5.28/5.36 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(D,f9(A,B,D)),f7(A,B)) | -r2_hidden(D,A). [resolve(3573,a,3559,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) = f12(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f9(A,B,D),B) | -r2_hidden(D,A). [resolve(3573,a,3560,a)]. 5.28/5.40 3574 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f8(A,B,E),A) | -r2_hidden(E,B). [resolve(3574,a,3555,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f8(A,B,E),E),f7(A,B)) | -r2_hidden(E,B). [resolve(3574,a,3556,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F != V7 | E = V6. [resolve(3574,a,3557,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(E,F),f7(A,B)) | -r2_hidden(k4_tarski(V6,V7),f7(A,B)) | F = V7 | E != V6. [resolve(3574,a,3558,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(k4_tarski(E,f9(A,B,E)),f7(A,B)) | -r2_hidden(E,A). [resolve(3574,a,3559,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(k4_tarski(f15(A,B,C),D),C) | -r2_hidden(D,B) | r2_hidden(f9(A,B,E),B) | -r2_hidden(E,A). [resolve(3574,a,3560,a)]. 5.28/5.40 3575 r2_tarski(A,B) | r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(17)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f8(A,B,D),A) | -r2_hidden(D,B). [resolve(3575,a,3555,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(f8(A,B,D),D),f7(A,B)) | -r2_hidden(D,B). [resolve(3575,a,3556,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E != V6 | D = F. [resolve(3575,a,3557,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f7(A,B)) | -r2_hidden(k4_tarski(F,V6),f7(A,B)) | E = V6 | D != F. [resolve(3575,a,3558,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(k4_tarski(D,f9(A,B,D)),f7(A,B)) | -r2_hidden(D,A). [resolve(3575,a,3559,a)]. 5.28/5.40 Derived: r2_hidden(f10(A,B,C),B) | f14(A,B,C) != f12(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f15(A,B,C),A) | r2_hidden(f9(A,B,D),B) | -r2_hidden(D,A). [resolve(3575,a,3560,a)]. 5.28/5.40 3576 -r1_tarski(A,f19(B)) | r2_tarski(A,f19(B)) | r2_hidden(A,f19(B)) # label(t9_tarski) # label(axiom). [clausify(23)]. 5.28/5.40 Derived: -r1_tarski(A,f19(B)) | r2_hidden(A,f19(B)) | r2_hidden(f8(A,f19(B),C),A) | -r2_hidden(C,f19(B)). [resolve(3576,b,3555,a)]. 5.28/5.40 Derived: -r1_tarski(A,f19(B)) | r2_hidden(A,f19(B)) | r2_hidden(k4_tarski(f8(A,f19(B),C),C),f7(A,f19(B))) | -r2_hidden(C,f19(B)). [resolve(3576,b,3556,a)]. 5.28/5.40 Derived: -r1_tarski(A,f19(B)) | r2_hidden(A,f19(B)) | -r2_hidden(k4_tarski(C,D),f7(A,f19(B))) | -r2_hidden(k4_tarski(E,F),f7(A,f19(B))) | D != F | C = E. [resolve(3576,b,3557,a)]. 5.28/5.40 Derived: -r1_tarski(A,f19(B)) | r2_hidden(A,f19(B)) | -r2_hidden(k4_tarski(C,D),f7(A,f19(B))) | -r2_hidden(k4_tarski(E,F),f7(A,f19(B))) | D = F | C != E. [resolve(3576,b,3558,a)]. 57.12/57.22 Derived: -r1_tarski(A,f19(B)) | r2_hidden(A,f19(B)) | r2_hidden(k4_tarski(C,f9(A,f19(B),C)),f7(A,f19(B))) | -r2_hidden(C,A). [resolve(3576,b,3559,a)]. 57.12/57.22 Derived: -r1_tarski(A,f19(B)) | r2_hidden(A,f19(B)) | r2_hidden(f9(A,f19(B),C),f19(B)) | -r2_hidden(C,A). [resolve(3576,b,3560,a)]. 57.12/57.22 3577 r2_tarski(A,f34(B)) | -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) # label(t136_zfmisc_1) # label(axiom). [clausify(223)]. 57.12/57.22 Derived: -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) | r2_hidden(f8(A,f34(B),C),A) | -r2_hidden(C,f34(B)). [resolve(3577,a,3555,a)]. 57.12/57.22 Derived: -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) | r2_hidden(k4_tarski(f8(A,f34(B),C),C),f7(A,f34(B))) | -r2_hidden(C,f34(B)). [resolve(3577,a,3556,a)]. 57.12/57.22 Derived: -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) | -r2_hidden(k4_tarski(C,D),f7(A,f34(B))) | -r2_hidden(k4_tarski(E,F),f7(A,f34(B))) | D != F | C = E. [resolve(3577,a,3557,a)]. 57.12/57.22 Derived: -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) | -r2_hidden(k4_tarski(C,D),f7(A,f34(B))) | -r2_hidden(k4_tarski(E,F),f7(A,f34(B))) | D = F | C != E. [resolve(3577,a,3558,a)]. 57.12/57.22 Derived: -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) | r2_hidden(k4_tarski(C,f9(A,f34(B),C)),f7(A,f34(B))) | -r2_hidden(C,A). [resolve(3577,a,3559,a)]. 57.12/57.22 Derived: -r1_tarski(A,f34(B)) | r2_hidden(A,f34(B)) | r2_hidden(f9(A,f34(B),C),f34(B)) | -r2_hidden(C,A). [resolve(3577,a,3560,a)]. 57.12/57.22 3578 r2_hidden(A,c6) | -r2_hidden(A,f1_s1_xboole_0) | -p1_s1_xboole_0(A) # label(s1_xboole_0) # label(axiom). [clausify(37)]. 57.12/57.22 3579 -r2_hidden(A,c6) | p1_s1_xboole_0(A) # label(s1_xboole_0) # label(axiom). [clausify(37)]. 57.12/57.22 3580 -m1_subset_1(A,f1_s3_subset_1) | r2_hidden(A,c10) | -p1_s3_subset_1(A) # label(s3_subset_1) # label(axiom). [clausify(353)]. 57.12/57.22 3581 -m1_subset_1(A,f1_s3_subset_1) | -r2_hidden(A,c10) | p1_s3_subset_1(A) # label(s3_subset_1) # label(axiom). [clausify(353)]. 57.12/57.22 3582 p1_s1_subset_1(A) | -r2_hidden(A,c13) # label(s1_subset_1) # label(axiom). [clausify(416)]. 57.12/57.22 3583 -p1_s1_subset_1(A) | -r2_hidden(A,f1_s1_subset_1) | r2_hidden(A,c13) # label(s1_subset_1) # label(axiom). [clausify(416)]. 57.12/57.22 3584 -v1_relat_1(A) | v2_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)) # label(d9_relat_1) # label(axiom). [clausify(488)]. 57.12/57.22 3585 -v1_relat_1(A) | -v2_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)) # label(d9_relat_1) # label(axiom). [clausify(488)]. 57.12/57.22 3586 -v2_relat_1(A) | -v1_relat_1(A) | -v1_funct_1(A) | v1_setfam_1(k2_relat_1(A)) # label(fc6_funct_1) # label(axiom). [clausify(678)]. 57.12/57.22 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_setfam_1(k2_relat_1(A)) | -v1_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3586,a,3584,b)]. 57.12/57.22 3587 -v1_funct_1(A) | -v1_relat_1(A) | r2_hidden(f137(A),k1_relat_1(A)) | v2_relat_1(A) # label(d15_funct_1) # label(axiom). [clausify(737)]. 57.12/57.22 Derived: -v1_funct_1(A) | -v1_relat_1(A) | r2_hidden(f137(A),k1_relat_1(A)) | -v1_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3587,d,3585,b)]. 57.12/57.22 Derived: -v1_funct_1(A) | -v1_relat_1(A) | r2_hidden(f137(A),k1_relat_1(A)) | -v1_relat_1(A) | -v1_funct_1(A) | v1_setfam_1(k2_relat_1(A)). [resolve(3587,d,3586,a)]. 57.12/57.22 3588 -v1_funct_1(A) | -v1_relat_1(A) | v1_xboole_0(k1_funct_1(A,f137(A))) | v2_relat_1(A) # label(d15_funct_1) # label(axiom). [clausify(737)]. 57.12/57.22 Derived: -v1_funct_1(A) | -v1_relat_1(A) | v1_xboole_0(k1_funct_1(A,f137(A))) | -v1_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3588,d,3585,b)]. 57.12/57.22 Derived: -v1_funct_1(A) | -v1_relat_1(A) | v1_xboole_0(k1_funct_1(A,f137(A))) | -v1_relat_1(A) | -v1_funct_1(A) | v1_setfam_1(k2_relat_1(A)). [resolve(3588,d,3586,a)]. 57.12/57.22 3589 -v1_funct_1(A) | -v1_relat_1(A) | -r2_hidden(B,k1_relat_1(A)) | -v1_xboole_0(k1_funct_1(A,B)) | -v2_relat_1(A) # label(d15_funct_1) # label(axiom). [clausify(737)]. 57.12/57.22 Derived: -v1_funct_1(A) | -v1_relat_1(A) | -r2_hidden(B,k1_relat_1(A)) | -v1_xboole_0(k1_funct_1(A,B)) | -v1_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3589,e,3584,b)]. 57.12/57.22 Derived: -v1_funct_1(A) | -v1_relat_1(A) | -r2_hidden(B,k1_relat_1(A)) | -v1_xboole_0(k1_funct_1(A,B)) | -v1_funct_1(A) | -v1_relat_1(A) | r2_hidden(f137(A),k1_relat_1(A)). [resolve(3589,e,3587,d)]. 99.92/100.01 Derived: -v1_funct_1(A) | -v1_relat_1(A) | -r2_hidden(B,k1_relat_1(A)) | -v1_xboole_0(k1_funct_1(A,B)) | -v1_funct_1(A) | -v1_relat_1(A) | v1_xboole_0(k1_funct_1(A,f137(A))). [resolve(3589,e,3588,d)]. 99.92/100.01 3590 v2_relat_1(c29) # label(rc5_funct_1) # label(axiom). [clausify(803)]. 99.92/100.01 Derived: -v1_relat_1(c29) | -r2_hidden(k1_xboole_0,k2_relat_1(c29)). [resolve(3590,a,3585,b)]. 99.92/100.01 Derived: -v1_relat_1(c29) | -v1_funct_1(c29) | v1_setfam_1(k2_relat_1(c29)). [resolve(3590,a,3586,a)]. 99.92/100.01 Derived: -v1_funct_1(c29) | -v1_relat_1(c29) | -r2_hidden(A,k1_relat_1(c29)) | -v1_xboole_0(k1_funct_1(c29,A)). [resolve(3590,a,3589,e)]. 99.92/100.01 3591 v1_xboole_0(A) | v2_relat_1(k2_funcop_1(B,A)) # label(fc9_funcop_1) # label(axiom). [clausify(1591)]. 99.92/100.01 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(3591,b,3585,b)]. 99.92/100.01 Derived: v1_xboole_0(A) | -v1_relat_1(k2_funcop_1(B,A)) | -v1_funct_1(k2_funcop_1(B,A)) | v1_setfam_1(k2_relat_1(k2_funcop_1(B,A))). [resolve(3591,b,3586,a)]. 99.92/100.01 Derived: v1_xboole_0(A) | -v1_funct_1(k2_funcop_1(B,A)) | -v1_relat_1(k2_funcop_1(B,A)) | -r2_hidden(C,k1_relat_1(k2_funcop_1(B,A))) | -v1_xboole_0(k1_funct_1(k2_funcop_1(B,A),C)). [resolve(3591,b,3589,e)]. 99.92/100.01 3592 r2_hidden(k4_tarski(A,B),c17) | -r2_hidden(A,f1_s1_relat_1) | -p1_s1_relat_1(A,B) | -r2_hidden(B,f2_s1_relat_1) # label(s1_relat_1) # label(axiom). [clausify(600)]. 99.92/100.01 3593 -r2_hidden(k4_tarski(A,B),c17) | p1_s1_relat_1(A,B) # label(s1_relat_1) # label(axiom). [clausify(600)]. 99.92/100.01 3594 -v1_relat_1(A) | r7_relat_2(A,k3_relat_1(A)) | -v7_relat_2(A) # label(d15_relat_2) # label(axiom). [clausify(881)]. 99.92/100.01 3595 -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | v7_relat_2(A) # label(d15_relat_2) # label(axiom). [clausify(881)]. 99.92/100.01 3596 -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | v7_relat_2(A) # label(t47_relat_2) # label(axiom). [clausify(894)]. 99.92/100.01 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(3596,c,3594,c)]. 99.92/100.01 3597 -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) = k2_xboole_0(A,k4_relat_1(A)) | -v7_relat_2(A) # label(t47_relat_2) # label(axiom). [clausify(894)]. 99.92/100.01 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(3597,c,3595,c)]. 99.92/100.01 3598 -v1_relat_1(A) | -v7_relat_2(A) | v1_relat_2(A) # label(t46_relat_2) # label(axiom). [clausify(902)]. 99.92/100.01 Derived: -v1_relat_1(A) | v1_relat_2(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)). [resolve(3598,b,3595,c)]. 99.92/100.01 Derived: -v1_relat_1(A) | v1_relat_2(A) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)). [resolve(3598,b,3596,c)]. 99.92/100.01 3599 -v1_relat_1(A) | -v7_relat_2(A) | v6_relat_2(A) # label(t46_relat_2) # label(axiom). [clausify(902)]. 99.92/100.01 Derived: -v1_relat_1(A) | v6_relat_2(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)). [resolve(3599,b,3595,c)]. 99.92/100.01 Derived: -v1_relat_1(A) | v6_relat_2(A) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)). [resolve(3599,b,3596,c)]. 99.92/100.01 3600 -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(889)]. 99.92/100.01 3601 -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(889)]. 99.92/100.01 3602 -v1_relat_1(A) | -r6_relat_2(A,k3_relat_1(A)) | v6_relat_2(A) # label(d14_relat_2) # label(axiom). [clausify(895)]. 99.92/100.01 Derived: -v1_relat_1(A) | -r6_relat_2(A,k3_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(3602,c,3601,b)]. 99.92/100.01 3603 -v1_relat_1(A) | r6_relat_2(A,k3_relat_1(A)) | -v6_relat_2(A) # label(d14_relat_2) # label(axiom). [clausify(895)]. 116.19/116.29 Derived: -v1_relat_1(A) | r6_relat_2(A,k3_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(3603,c,3600,b)]. 116.19/116.29 3604 -v1_relat_1(A) | v6_relat_2(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)). [resolve(3599,b,3595,c)]. 116.19/116.29 Derived: -v1_relat_1(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_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(3604,b,3601,b)]. 116.19/116.29 Derived: -v1_relat_1(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | r6_relat_2(A,k3_relat_1(A)). [resolve(3604,b,3603,c)]. 116.19/116.29 3605 -v1_relat_1(A) | v6_relat_2(A) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)). [resolve(3599,b,3596,c)]. 116.19/116.29 Derived: -v1_relat_1(A) | -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) | 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(3605,b,3601,b)]. 116.19/116.29 Derived: -v1_relat_1(A) | -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) | r6_relat_2(A,k3_relat_1(A)). [resolve(3605,b,3603,c)]. 116.19/116.29 3606 -v1_ordinal1(A) | -v2_ordinal1(A) | v3_ordinal1(A) # label(cc2_ordinal1) # label(axiom). [clausify(956)]. 116.19/116.29 3607 v1_ordinal1(k1_xboole_0) # label(fc2_ordinal1_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 116.19/116.29 3608 v1_ordinal1(c39) # label(rc1_ordinal1) # label(axiom). [clausify(945)]. 116.19/116.29 3609 v1_ordinal1(c41) # label(rc3_ordinal1) # label(axiom). [clausify(953)]. 116.19/116.29 Derived: -v2_ordinal1(c39) | v3_ordinal1(c39). [resolve(3606,a,3608,a)]. 116.19/116.29 Derived: -v2_ordinal1(c41) | v3_ordinal1(c41). [resolve(3606,a,3609,a)]. 116.19/116.29 3610 v1_ordinal1(c47) # label(rc2_ordinal1) # label(axiom). [clausify(962)]. 116.19/116.29 3611 -v3_ordinal1(A) | v1_ordinal1(k1_ordinal1(A)) # label(fc3_ordinal1) # label(axiom). [clausify(963)]. 116.19/116.29 3612 -v3_ordinal1(A) | v1_ordinal1(A) # label(cc1_ordinal1) # label(axiom). [clausify(965)]. 116.19/116.29 3613 -v3_ordinal1(A) | v1_ordinal1(k3_tarski(A)) # label(fc4_ordinal1) # label(axiom). [clausify(968)]. 116.19/116.29 3614 -v1_ordinal1(A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B) # label(t21_ordinal1) # label(axiom). [clausify(970)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(k1_xboole_0,A) | r2_hidden(k1_xboole_0,A). [resolve(3614,a,3607,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(c39,A) | r2_hidden(c39,A). [resolve(3614,a,3608,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(c41,A) | r2_hidden(c41,A). [resolve(3614,a,3609,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(c47,A) | r2_hidden(c47,A). [resolve(3614,a,3610,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(k1_ordinal1(B),A) | r2_hidden(k1_ordinal1(B),A) | -v3_ordinal1(B). [resolve(3614,a,3611,b)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(B,A) | r2_hidden(B,A) | -v3_ordinal1(B). [resolve(3614,a,3612,b)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -r2_xboole_0(k3_tarski(B),A) | r2_hidden(k3_tarski(B),A) | -v3_ordinal1(B). [resolve(3614,a,3613,b)]. 116.19/116.29 3615 -v1_xboole_0(A) | v1_ordinal1(A) # label(cc3_ordinal1) # label(axiom). [clausify(984)]. 116.19/116.29 Derived: -v1_xboole_0(A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B). [resolve(3615,b,3614,a)]. 116.19/116.29 3616 -v1_ordinal1(A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r2_hidden(B,C) | -r1_tarski(A,B) | r2_hidden(A,C) # label(t22_ordinal1) # label(axiom). [clausify(989)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(k1_xboole_0,A) | r2_hidden(k1_xboole_0,B). [resolve(3616,a,3607,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(c39,A) | r2_hidden(c39,B). [resolve(3616,a,3608,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(c41,A) | r2_hidden(c41,B). [resolve(3616,a,3609,a)]. 116.19/116.29 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(c47,A) | r2_hidden(c47,B). [resolve(3616,a,3610,a)]. 116.19/116.36 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(k1_ordinal1(C),A) | r2_hidden(k1_ordinal1(C),B) | -v3_ordinal1(C). [resolve(3616,a,3611,b)]. 116.19/116.36 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(C,A) | r2_hidden(C,B) | -v3_ordinal1(C). [resolve(3616,a,3612,b)]. 116.19/116.36 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(k3_tarski(C),A) | r2_hidden(k3_tarski(C),B) | -v3_ordinal1(C). [resolve(3616,a,3613,b)]. 116.19/116.36 Derived: -v3_ordinal1(A) | -v3_ordinal1(B) | -r2_hidden(A,B) | -r1_tarski(C,A) | r2_hidden(C,B) | -v1_xboole_0(C). [resolve(3616,a,3615,b)]. 116.19/116.36 3617 -v2_ordinal1(A) | -v1_ordinal1(A) | v3_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(1004)]. 116.19/116.36 Derived: -v2_ordinal1(k1_xboole_0) | v3_ordinal1(k1_xboole_0). [resolve(3617,b,3607,a)]. 116.19/116.36 Derived: -v2_ordinal1(c47) | v3_ordinal1(c47). [resolve(3617,b,3610,a)]. 116.19/116.36 Derived: -v2_ordinal1(k1_ordinal1(A)) | v3_ordinal1(k1_ordinal1(A)) | -v3_ordinal1(A). [resolve(3617,b,3611,b)]. 116.19/116.36 Derived: -v2_ordinal1(k3_tarski(A)) | v3_ordinal1(k3_tarski(A)) | -v3_ordinal1(A). [resolve(3617,b,3613,b)]. 116.19/116.36 Derived: -v2_ordinal1(A) | v3_ordinal1(A) | -v1_xboole_0(A). [resolve(3617,b,3615,b)]. 116.19/116.36 3618 v1_ordinal1(A) | -v3_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(1004)]. 116.19/116.36 3619 -v5_ordinal1(A) | -v1_relat_1(A) | -v1_funct_1(A) | v1_ordinal1(k1_relat_1(A)) # label(fc5_ordinal1) # label(axiom). [clausify(1005)]. 116.19/116.36 Derived: -v5_ordinal1(A) | -v1_relat_1(A) | -v1_funct_1(A) | -v3_ordinal1(B) | -r2_xboole_0(k1_relat_1(A),B) | r2_hidden(k1_relat_1(A),B). [resolve(3619,d,3614,a)]. 116.19/116.36 Derived: -v5_ordinal1(A) | -v1_relat_1(A) | -v1_funct_1(A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r2_hidden(B,C) | -r1_tarski(k1_relat_1(A),B) | r2_hidden(k1_relat_1(A),C). [resolve(3619,d,3616,a)]. 116.19/116.36 3620 r2_hidden(f196(A),A) | v1_ordinal1(A) # label(d2_ordinal1) # label(axiom). [clausify(1008)]. 116.19/116.36 Derived: r2_hidden(f196(A),A) | -v2_ordinal1(A) | v3_ordinal1(A). [resolve(3620,b,3606,a)]. 116.19/116.36 Derived: r2_hidden(f196(A),A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B). [resolve(3620,b,3614,a)]. 116.19/116.36 Derived: r2_hidden(f196(A),A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r2_hidden(B,C) | -r1_tarski(A,B) | r2_hidden(A,C). [resolve(3620,b,3616,a)]. 116.19/116.36 3621 -r1_tarski(f196(A),A) | v1_ordinal1(A) # label(d2_ordinal1) # label(axiom). [clausify(1008)]. 116.19/116.36 Derived: -r1_tarski(f196(A),A) | -v2_ordinal1(A) | v3_ordinal1(A). [resolve(3621,b,3606,a)]. 116.19/116.36 Derived: -r1_tarski(f196(A),A) | -v3_ordinal1(B) | -r2_xboole_0(A,B) | r2_hidden(A,B). [resolve(3621,b,3614,a)]. 116.19/116.36 Derived: -r1_tarski(f196(A),A) | -v3_ordinal1(B) | -v3_ordinal1(C) | -r2_hidden(B,C) | -r1_tarski(A,B) | r2_hidden(A,C). [resolve(3621,b,3616,a)]. 116.19/116.36 3622 -r2_hidden(A,B) | r1_tarski(A,B) | -v1_ordinal1(B) # label(d2_ordinal1) # label(axiom). [clausify(1008)]. 116.19/116.36 Derived: -r2_hidden(A,k1_xboole_0) | r1_tarski(A,k1_xboole_0). [resolve(3622,c,3607,a)]. 116.19/116.36 Derived: -r2_hidden(A,c39) | r1_tarski(A,c39). [resolve(3622,c,3608,a)]. 116.19/116.36 Derived: -r2_hidden(A,c41) | r1_tarski(A,c41). [resolve(3622,c,3609,a)]. 116.19/116.36 Derived: -r2_hidden(A,c47) | r1_tarski(A,c47). [resolve(3622,c,3610,a)]. 116.19/116.36 Derived: -r2_hidden(A,k1_ordinal1(B)) | r1_tarski(A,k1_ordinal1(B)) | -v3_ordinal1(B). [resolve(3622,c,3611,b)]. 116.19/116.36 Derived: -r2_hidden(A,B) | r1_tarski(A,B) | -v3_ordinal1(B). [resolve(3622,c,3612,b)]. 116.19/116.36 Derived: -r2_hidden(A,k3_tarski(B)) | r1_tarski(A,k3_tarski(B)) | -v3_ordinal1(B). [resolve(3622,c,3613,b)]. 116.19/116.36 Derived: -r2_hidden(A,B) | r1_tarski(A,B) | -v1_xboole_0(B). [resolve(3622,c,3615,b)]. 116.19/116.36 Derived: -r2_hidden(A,k1_relat_1(B)) | r1_tarski(A,k1_relat_1(B)) | -v5_ordinal1(B) | -v1_relat_1(B) | -v1_funct_1(B). [resolve(3622,c,3619,d)]. 116.19/116.36 Derived: -r2_hidden(A,B) | r1_tarski(A,B) | r2_hidden(f196(B),B). [resolve(3622,c,3620,b)]. 116.19/116.36 Derived: -r2_hidden(A,B) | r1_tarski(A,B) | -r1_tarski(f196(B),B). [resolve(3622,c,3621,b)]. 116.19/116.36 3623 -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(1010)]. 116.19/116.36 Derived: -v3_ordinal1(AAlarm clock 119.98/120.05 Prover9 interrupted 119.98/120.05 EOF