0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.32 % Computer : n007.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1440 0.11/0.32 % WCLimit : 180 0.11/0.32 % DateTime : Mon Jul 3 09:35:13 EDT 2023 0.11/0.32 % CPUTime : 8.47/8.55 ============================== Prover9 =============================== 8.47/8.55 Prover9 (32) version 2009-11A, November 2009. 8.47/8.55 Process 24180 was started by sandbox2 on n007.cluster.edu, 8.47/8.55 Mon Jul 3 09:35:21 2023 8.47/8.55 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_24027_n007.cluster.edu". 8.47/8.55 ============================== end of head =========================== 8.47/8.55 8.47/8.55 ============================== INPUT ================================= 8.47/8.55 8.47/8.55 % Reading from file /tmp/Prover9_24027_n007.cluster.edu 8.47/8.55 8.47/8.55 set(prolog_style_variables). 8.47/8.55 set(auto2). 8.47/8.55 % set(auto2) -> set(auto). 8.47/8.55 % set(auto) -> set(auto_inference). 8.47/8.55 % set(auto) -> set(auto_setup). 8.47/8.55 % set(auto_setup) -> set(predicate_elim). 8.47/8.55 % set(auto_setup) -> assign(eq_defs, unfold). 8.47/8.55 % set(auto) -> set(auto_limits). 8.47/8.55 % set(auto_limits) -> assign(max_weight, "100.000"). 8.47/8.55 % set(auto_limits) -> assign(sos_limit, 20000). 8.47/8.55 % set(auto) -> set(auto_denials). 8.47/8.55 % set(auto) -> set(auto_process). 8.47/8.55 % set(auto2) -> assign(new_constants, 1). 8.47/8.55 % set(auto2) -> assign(fold_denial_max, 3). 8.47/8.55 % set(auto2) -> assign(max_weight, "200.000"). 8.47/8.55 % set(auto2) -> assign(max_hours, 1). 8.47/8.55 % assign(max_hours, 1) -> assign(max_seconds, 3600). 8.47/8.55 % set(auto2) -> assign(max_seconds, 0). 8.47/8.55 % set(auto2) -> assign(max_minutes, 5). 8.47/8.55 % assign(max_minutes, 5) -> assign(max_seconds, 300). 8.47/8.55 % set(auto2) -> set(sort_initial_sos). 8.47/8.55 % set(auto2) -> assign(sos_limit, -1). 8.47/8.55 % set(auto2) -> assign(lrs_ticks, 3000). 8.47/8.55 % set(auto2) -> assign(max_megs, 400). 8.47/8.55 % set(auto2) -> assign(stats, some). 8.47/8.55 % set(auto2) -> clear(echo_input). 8.47/8.55 % set(auto2) -> set(quiet). 8.47/8.55 % set(auto2) -> clear(print_initial_clauses). 8.47/8.55 % set(auto2) -> clear(print_given). 8.47/8.55 assign(lrs_ticks,-1). 8.47/8.55 assign(sos_limit,10000). 8.47/8.55 assign(order,kbo). 8.47/8.55 set(lex_order_vars). 8.47/8.55 clear(print_given). 8.47/8.55 8.47/8.55 % formulas(sos). % not echoed (4815 formulas) 8.47/8.55 8.47/8.55 ============================== end of input ========================== 8.47/8.55 8.47/8.55 % From the command line: assign(max_seconds, 1440). 8.47/8.55 8.47/8.55 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 8.47/8.55 8.47/8.55 % Formulas that are not ordinary clauses: 8.47/8.55 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 2 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> C = B)) -> (exists A all B (r2_hidden(B,A) <-> (exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 3 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 4 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 5 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 6 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 7 (all A all B ((all C ((exists D (r2_hidden(C,D) & r2_hidden(D,A))) <-> r2_hidden(C,B))) <-> k3_tarski(A) = B)) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 8 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 9 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 11 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 12 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 13 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 14 (all A all B k2_tarski(k2_tarski(A,B),k1_tarski(A)) = k4_tarski(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.55 15 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C))))) & (all D all E all F all G (r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) -> (F = D <-> G = E))) & (all D -(r2_hidden(D,A) & (all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 16 (all A all B all C ((all D (r2_hidden(D,C) <-> D = A | D = B)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 17 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 18 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 19 (all A all B (k1_tarski(A) = B <-> (all C (r2_hidden(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 20 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 21 (all A exists B (r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -((all E (r1_tarski(E,C) -> r2_hidden(E,D))) & r2_hidden(D,B))))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 23 (all A all B -(r2_hidden(A,B) & (all C -((all D -(r2_hidden(D,B) & r2_hidden(D,C))) & r2_hidden(C,B))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 24 (all A all B all C ((all D (-r2_hidden(D,A) <-> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 25 (all A all B all C -(r1_xboole_0(A,B) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & -(-r2_hidden(C,B) & r2_hidden(C,A)) & r2_hidden(C,k2_xboole_0(A,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 26 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 27 (all A all B (A = B <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 28 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) | r2_hidden(D,A))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 29 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 30 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 31 (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]. 8.47/8.56 32 (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]. 8.47/8.56 33 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 34 (all A all B k3_xboole_0(B,A) = k3_xboole_0(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 35 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 36 (all A all B k3_xboole_0(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 37 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -(-r1_xboole_0(A,B) & (all C -r2_hidden(C,k3_xboole_0(A,B)))))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 38 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 39 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 40 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 41 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (-r2_hidden(D,B) & r2_hidden(D,A) <-> r2_hidden(D,C))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 42 (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]. 8.47/8.56 43 (all A all B (B != A & r1_tarski(A,B) <-> r2_xboole_0(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 44 (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]. 8.47/8.56 45 (all A all B (-(-r1_xboole_0(A,B) & (all C -(r2_hidden(C,A) & r2_hidden(C,B)))) & -(r1_xboole_0(A,B) & (exists C (r2_hidden(C,A) & r2_hidden(C,B)))))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 46 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 47 (all A all B (k1_xboole_0 = k3_xboole_0(A,B) <-> r1_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 48 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 49 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 50 (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))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 51 (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]. 8.47/8.56 52 (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]. 8.47/8.56 53 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 54 (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]. 8.47/8.56 55 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (r2_hidden(C,B) <-> p1_s3_xboole_0(C))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 56 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 57 (all A all B all C (r2_hidden(A,k5_xboole_0(B,C)) <-> -(r2_hidden(A,C) <-> r2_hidden(A,B)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 58 (all A (A = k1_xboole_0 <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 59 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 60 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 61 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 63 (all A k4_xboole_0(k1_xboole_0,A) = k1_xboole_0) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 64 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 65 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 66 (all A k5_xboole_0(A,k1_xboole_0) = A) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 67 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 68 (all A (v1_xboole_0(A) -> k1_xboole_0 = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 69 (all A all B all C (r1_xboole_0(A,B) & r1_xboole_0(C,B) & k2_xboole_0(C,B) = k2_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 70 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 71 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 72 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 73 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 74 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 75 (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]. 8.47/8.56 76 (all A all B (k2_xboole_0(A,B) = k1_xboole_0 -> A = k1_xboole_0)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 77 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 78 (all A all B (r1_xboole_0(A,B) -> k4_xboole_0(k2_xboole_0(A,B),B) = A)) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 79 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 80 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 81 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 82 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 83 (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]. 8.47/8.56 84 (all A all B all C k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k5_xboole_0(A,C),B)) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 85 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 86 (all A all B all C (r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,k2_xboole_0(B,C)) <-> r1_tarski(A,k5_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 87 (all A all B all C all D (k2_xboole_0(C,D) = k2_xboole_0(A,B) & r1_xboole_0(D,B) & r1_xboole_0(C,A) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 88 (all A all B all C (r1_tarski(A,B) & (all D (r1_tarski(A,D) & r1_tarski(C,D) -> r1_tarski(B,D))) & r1_tarski(C,B) -> k2_xboole_0(A,C) = B)) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 89 (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]. 8.47/8.56 90 (all A all B (-(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 91 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 92 (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]. 8.47/8.56 93 (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]. 8.47/8.56 94 (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]. 8.47/8.56 95 (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]. 8.47/8.56 96 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 97 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 98 (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]. 8.47/8.56 99 (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]. 8.47/8.56 100 (all A (-(k1_xboole_0 = A & -r1_xboole_0(A,A)) & -(k1_xboole_0 != A & r1_xboole_0(A,A)))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 101 (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]. 8.47/8.56 102 (all A all B all C k3_xboole_0(k4_xboole_0(A,C),B) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 103 (all A all B all C k4_xboole_0(A,k4_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 104 (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]. 8.47/8.56 105 (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]. 8.47/8.56 106 (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]. 8.47/8.56 107 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 108 (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]. 8.47/8.56 109 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 110 (all A all B k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 111 (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]. 8.47/8.56 112 (all A all B all C k2_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k2_xboole_0(A,B),C)) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 113 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 114 (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]. 8.47/8.56 115 (all A all B k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 116 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 117 (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]. 8.47/8.56 118 (all A all B all C ((all D (r1_tarski(D,C) & r1_tarski(D,B) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> A = k3_xboole_0(B,C))) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 119 (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]. 8.47/8.56 120 (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]. 8.47/8.56 121 (all A all B all C k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 122 (all A all B all C (r1_tarski(A,C) & r1_tarski(A,B) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 123 (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]. 8.47/8.56 124 (all A all B k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 125 (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]. 8.47/8.56 126 (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]. 8.47/8.56 127 (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]. 8.47/8.56 128 (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]. 8.47/8.56 129 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(B,D) & r1_xboole_0(C,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 130 (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]. 8.47/8.56 131 (all A all B all C -(-r1_xboole_0(A,k3_xboole_0(B,C)) & r1_xboole_0(A,B))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 132 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 133 (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]. 8.47/8.56 134 (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]. 8.47/8.56 135 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 136 (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]. 8.47/8.56 137 (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]. 8.47/8.56 138 (all A (k1_xboole_0 != A -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 139 (all A all B all C k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),C)) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 140 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 141 (all A all B k4_xboole_0(A,B) = k4_xboole_0(A,k3_xboole_0(A,B))) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 142 (all A all B all C k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) = k3_xboole_0(A,k2_xboole_0(B,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 143 (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]. 8.47/8.56 144 (all A all B k5_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 145 (all A all B k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 146 (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]. 8.47/8.56 147 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 148 (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]. 8.47/8.56 149 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k4_xboole_0(B,A))) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 150 (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]. 8.47/8.56 151 (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]. 8.47/8.56 152 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 153 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 154 (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]. 8.47/8.56 155 (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]. 8.47/8.56 156 (all A all B all C (r1_tarski(A,C) & r1_xboole_0(B,C) & r1_tarski(A,B) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 157 (all A all B (r1_tarski(A,B) <-> k1_xboole_0 = k4_xboole_0(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 158 (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]. 8.47/8.56 159 (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]. 8.47/8.56 160 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 161 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 162 (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]. 8.47/8.56 163 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 164 (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]. 8.47/8.56 165 (all A all B all C (r1_tarski(A,B) -> k2_xboole_0(A,k3_xboole_0(C,B)) = k3_xboole_0(k2_xboole_0(A,C),B))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 166 (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]. 8.47/8.56 167 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 168 (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]. 8.47/8.56 169 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 170 (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]. 8.47/8.56 171 (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]. 8.47/8.56 172 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 173 (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]. 8.47/8.56 174 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 175 (all A all B all C all D (r1_tarski(C,D) & r1_xboole_0(B,D) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 176 (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]. 8.47/8.56 177 (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]. 8.47/8.56 178 (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]. 8.47/8.56 179 (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]. 8.47/8.56 180 (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]. 8.47/8.56 181 (all A all B -(k4_xboole_0(B,A) = k1_xboole_0 & r2_xboole_0(A,B))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 182 (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]. 8.47/8.56 183 (all A all B (A != B -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 184 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> B = k1_xboole_0 | A = B | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 185 (all A all B all C all D -(r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F -(r2_hidden(F,C) & D = k4_tarski(E,F) & r2_hidden(E,B))) & r2_hidden(D,A))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 186 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 187 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 188 (all A all B (A = k4_xboole_0(A,k1_tarski(B)) <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 189 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 190 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 191 (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]. 8.47/8.56 192 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 193 (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]. 8.47/8.56 194 (all A all B all C k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 195 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> k1_xboole_0 = B | B = D & C = A | k1_xboole_0 = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 196 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 197 (all A all B (-r2_hidden(A,B) -> B = k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 198 (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]. 8.47/8.56 199 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & -(C = k1_tarski(A) & k1_tarski(A) = B) & -(B = k1_tarski(A) & k1_xboole_0 = C) & -(B = k1_xboole_0 & C = k1_tarski(A)))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 200 (all A all B all C all D (r1_xboole_0(C,D) | r1_xboole_0(A,B) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 201 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 202 (all A all B -(r1_xboole_0(k1_tarski(A),k1_tarski(B)) & B = A)) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 203 (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]. 8.47/8.56 204 (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) | D = C)) -> 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]. 8.47/8.56 205 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 206 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 207 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 208 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> C = A)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 209 (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]. 8.47/8.56 210 (all A all B all C (k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 211 (all A exists B (r2_hidden(A,B) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C -(r1_tarski(C,B) & -r2_hidden(C,B) & -r2_tarski(C,B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 212 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 213 (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]. 8.47/8.56 214 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> C = A & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 215 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 216 (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]. 8.47/8.56 217 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 -> B = A)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 218 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 219 (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]. 8.47/8.56 220 (all A all B all C (k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) & k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) = k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 221 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 222 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)) & k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 223 (all A all B all C all D (r2_hidden(A,C) & B = D <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 224 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> B = A)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.56 225 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 226 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 227 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 228 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 229 (all A all B all C (r2_hidden(B,C) & r2_hidden(A,C) <-> k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0)) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 230 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 231 (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]. 8.47/8.57 232 (all A all B (B != A -> k2_tarski(A,B) = k5_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 233 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 234 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 235 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 236 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> k2_zfmisc_1(A,C) = k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 237 (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]. 8.47/8.57 238 (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]. 8.47/8.57 239 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> k1_xboole_0 = k2_zfmisc_1(A,B) | r1_tarski(A,C) & r1_tarski(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 240 (all A all B all C -(r2_hidden(A,C) & r1_xboole_0(k2_tarski(A,B),C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 241 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 242 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> D = B & A = C)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 243 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 244 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 245 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 246 (all A all B -(r2_hidden(A,B) & r1_xboole_0(k1_tarski(A),B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 247 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 248 (all A all B (B != A -> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),k1_tarski(B)))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 249 (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]. 8.47/8.57 250 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 251 (all A all B (r1_tarski(A,k1_tarski(B)) <-> A = k1_xboole_0 | k1_tarski(B) = A)) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 252 (all A all B all C -(k2_xboole_0(B,C) = k1_tarski(A) & C != B & k1_xboole_0 != B & k1_xboole_0 != C)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 253 (all A all B -(k1_tarski(B) != A & A != k1_xboole_0 & (all C -(r2_hidden(C,A) & B != C)))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 254 (all A all B all C all D (B = D & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 255 (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]. 8.47/8.57 256 (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]. 8.47/8.57 257 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 258 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 259 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 260 (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]. 8.47/8.57 261 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 262 (all A all B k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 263 (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]. 8.47/8.57 264 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 265 (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]. 8.47/8.57 266 (all A all B all C all D -(k2_tarski(C,D) = k2_tarski(A,B) & D != A & A != C)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 267 (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 -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 268 (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]. 8.47/8.57 269 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 270 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 271 (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]. 8.47/8.57 272 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 273 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k2_tarski(A,B) = k1_tarski(C))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 274 (all A all B all C (-(k1_tarski(B) != A & k2_tarski(B,C) != A & k1_tarski(C) != A & k1_xboole_0 != A) <-> r1_tarski(A,k2_tarski(B,C)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 275 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 276 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (k4_tarski(E,F) = D & r2_hidden(F,B) & r2_hidden(E,A))))) <-> C = k2_zfmisc_1(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 277 (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]. 8.47/8.57 278 (all A all B -(A != k1_xboole_0 & A != k1_tarski(B) & k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 279 (all A all B all C -((all D all E A != k4_tarski(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 280 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> A = D)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 281 (all A all B all C all D k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) = k4_zfmisc_1(A,B,C,D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 282 (all A all B ((all C (r1_tarski(C,A) <-> r2_hidden(C,B))) <-> k1_zfmisc_1(A) = B)) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 283 (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)) & k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 284 (all A all B k1_tarski(k4_tarski(A,B)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 285 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 286 (all A all B (r2_hidden(A,B) <-> r1_tarski(k1_tarski(A),B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 287 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 288 (all A all B (k1_xboole_0 = B | A = k1_xboole_0 <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 289 (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]. 8.47/8.57 290 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 291 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 292 (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]. 8.47/8.57 293 (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]. 8.47/8.57 294 (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]. 8.47/8.57 295 (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]. 8.47/8.57 296 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 297 (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]. 8.47/8.57 298 (all A all B all C -(k1_tarski(A) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(B) & k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 299 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 300 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 301 (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]. 8.47/8.57 302 (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]. 8.47/8.57 303 (all A all B all C -(-r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(C,B) & -r2_hidden(A,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 304 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 305 (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_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 306 (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]. 8.47/8.57 307 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 308 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 309 (all A all B all C -(r2_hidden(B,C) & A != B & k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 310 (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]. 8.47/8.57 311 (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]. 8.47/8.57 312 (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]. 8.47/8.57 313 (all A all B all C (k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 314 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 315 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 316 (all A all B all C -(A != k1_xboole_0 & -r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 317 (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]. 8.47/8.57 318 (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]. 8.47/8.57 319 (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]. 8.47/8.57 320 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 321 (all A all B (r2_hidden(A,B) <-> k1_xboole_0 = k4_xboole_0(k1_tarski(A),B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 322 (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]. 8.47/8.57 323 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 324 (all A all B all C all D k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 325 (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]. 8.47/8.57 326 (all A all B (r1_xboole_0(k1_tarski(A),B) | k3_xboole_0(k1_tarski(A),B) = k1_tarski(A))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 327 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 328 (all A all B (k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 329 (all A all B all C (-(A != k1_xboole_0 & A != k1_tarski(C) & A != k2_tarski(B,C) & k1_tarski(B) != A) <-> k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0)) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 330 (all A all B all C all D -(A != D & A != C & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 331 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 332 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 333 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 334 (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,k4_subset_1(A,B,C)) = k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 335 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,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]. 8.47/8.57 336 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> B = A))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 337 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 338 (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)))) -> A = B))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 339 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 340 (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,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))) = k3_subset_1(A,k7_subset_1(A,B,C)))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 341 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 342 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 343 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 344 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 345 (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]. 8.47/8.57 346 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 347 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 348 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 349 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k3_subset_1(A,B)))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 350 (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]. 8.47/8.57 351 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k7_subset_1(A,C,B) = k7_subset_1(A,B,C))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 352 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 353 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> k3_subset_1(A,C) = B))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 354 (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]. 8.47/8.57 355 (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]. 8.47/8.57 356 (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]. 8.47/8.57 357 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 358 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 359 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 360 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 361 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 362 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (A != k1_xboole_0 -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 363 (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]. 8.47/8.57 364 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 365 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)) & (all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_subset_1) & p1_s1_subset_1(B))))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 366 (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]. 8.47/8.57 367 (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]. 8.47/8.57 368 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 369 (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)))) -> k4_subset_1(A,C,D) = B))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 370 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 371 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 372 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 373 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 374 (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]. 8.47/8.57 375 (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]. 8.47/8.57 376 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) <-> r1_tarski(B,k3_subset_1(A,C))))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 377 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 378 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 379 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 380 (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]. 8.47/8.57 381 (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]. 8.47/8.57 382 (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))))) -> k7_subset_1(A,C,D) = B))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 383 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 385 (all A all B (m1_subset_1(B,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 386 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 387 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 388 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 389 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.57 390 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 391 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 392 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 393 (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]. 8.47/8.58 394 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 395 (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]. 8.47/8.58 396 (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]. 8.47/8.58 397 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 398 (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 = k6_subset_1(A,C,D)))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 399 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 400 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 401 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 402 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 403 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k2_subset_1(A) = B <-> r1_tarski(k3_subset_1(A,B),B)))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 404 (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]. 8.47/8.58 405 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 406 (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]. 8.47/8.58 407 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 408 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 409 (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,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]. 8.47/8.58 410 (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]. 8.47/8.58 411 (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]. 8.47/8.58 412 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 413 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 414 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 415 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 416 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 417 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 418 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 419 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 420 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 421 (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,C) <-> -r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 422 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(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]. 8.47/8.58 423 (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]. 8.47/8.58 424 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 425 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 426 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 427 (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) -> (A != k1_xboole_0 -> 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]. 8.47/8.58 428 (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]. 8.47/8.58 429 (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]. 8.47/8.58 430 (all A all B ((v1_xboole_0(A) -> (v1_xboole_0(B) <-> m1_subset_1(B,A))) & (-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 431 (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]. 8.47/8.58 432 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 433 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 434 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 435 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 436 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 437 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 438 (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]. 8.47/8.58 439 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 440 (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)))) -> C = B))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 441 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 442 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k7_setfam_1(A,B) = k1_tarski(k1_xboole_0)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 443 (all A all B all C (k4_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k4_xboole_0(E,F) & r2_hidden(E,A))))))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 444 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 445 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),k7_setfam_1(A,C)) -> r1_tarski(B,C)))))) # label(t51_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 446 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B))))))) # label(t59_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 447 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 448 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 449 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 450 (all A all B (B != k1_xboole_0 -> k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) = k2_xboole_0(A,k1_setfam_1(B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 451 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 452 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 453 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(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) <-> r2_hidden(D,B)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 454 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)) = k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 455 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.47/8.58 456 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k3_xboole_0(E,F))))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 457 (all A all B (r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),A))) # label(t4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 458 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 459 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 460 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 461 (all A all B (r2_setfam_1(A,B) <-> (all C -((all D -(r1_tarski(D,C) & r2_hidden(D,A))) & r2_hidden(C,B))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 462 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 463 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 464 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 465 (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))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 466 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> B = k7_setfam_1(A,k7_setfam_1(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 467 (all A (v2_setfam_1(A) <-> (all B (-v1_xboole_0(B) -> -r2_hidden(B,A))))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 468 (all A all B all C (r1_tarski(k3_tarski(A),B) & r2_hidden(C,A) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 469 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 470 (all A all B k3_setfam_1(B,A) = k3_setfam_1(A,B)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 471 (all A (-v1_xboole_0(A) & v1_setfam_1(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 472 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(B) = k5_setfam_1(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 473 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 474 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 475 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 476 (all A (r2_hidden(k1_xboole_0,A) -> k1_xboole_0 = k1_setfam_1(A))) # label(t5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 477 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 478 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 479 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> r1_tarski(B,k1_setfam_1(A)) | A = k1_xboole_0)) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 480 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 481 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_xboole_0(B) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 482 (all A (-v2_setfam_1(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 483 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 484 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 485 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 486 (all A all B k3_xboole_0(A,B) = k1_setfam_1(k2_tarski(A,B))) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 487 (all A all B k3_tarski(k3_setfam_1(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 488 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 489 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 490 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 491 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 492 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),C) <-> r1_tarski(B,k7_setfam_1(A,C))))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 493 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 494 (all A all B (-r1_xboole_0(A,B) -> k1_setfam_1(k3_setfam_1(A,B)) = k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t34_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 495 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 496 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k6_setfam_1(A,B) = k1_setfam_1(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_xboole_0 -> k8_setfam_1(A,B) = A) & (k1_xboole_0 != B -> k6_setfam_1(A,B) = k8_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 498 (all A all B all C (r1_setfam_1(A,B) & r1_setfam_1(B,C) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 499 (all A all B all C (C = k2_setfam_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & k2_xboole_0(E,F) = D & r2_hidden(E,A))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 500 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 501 (all A all B (k1_xboole_0 != B -> k1_setfam_1(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k3_tarski(B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 502 (all A all B all C (r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) & (all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 503 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 504 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,A) & -r1_tarski(D,B))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 505 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 506 (all A all B (r1_setfam_1(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t18_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 507 (all A all B k2_setfam_1(A,B) = k2_setfam_1(B,A)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 508 (all A all B all C (r1_tarski(A,C) & r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 509 (all A all B ((A != k1_xboole_0 -> ((all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))) <-> B = k1_setfam_1(A))) & (A = k1_xboole_0 -> (B = k1_setfam_1(A) <-> k1_xboole_0 = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 510 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (C = k7_setfam_1(A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(k3_subset_1(A,D),B))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 511 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 512 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 513 (all A all B (r2_setfam_1(B,A) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 514 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 515 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 516 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 517 (all A all B (v1_setfam_1(A) & v1_setfam_1(B) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 518 (all A all B ((all C -((all D -(r2_hidden(D,B) & r1_tarski(C,D))) & r2_hidden(C,A))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 519 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 520 (all A all B all C (r2_hidden(A,B) & r1_xboole_0(A,C) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 521 (all A all B (r1_setfam_1(B,k1_tarski(A)) -> (all C (r2_hidden(C,B) -> r1_tarski(C,A))))) # label(t24_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 522 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> ((all D (r2_hidden(D,C) -> r2_hidden(B,D))) <-> r2_hidden(B,k8_setfam_1(A,C)))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 523 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 524 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 525 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 526 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B)) <-> r2_hidden(C,B)))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 527 (all A all B r1_tarski(k1_setfam_1(k4_setfam_1(A,B)),k4_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t41_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 528 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 529 (all A all B -(k1_xboole_0 != B & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & k1_xboole_0 != A)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 530 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 531 (all A all B -(k1_xboole_0 != A & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 532 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 533 (all A all B k3_xboole_0(A,k3_tarski(B)) = k3_tarski(k3_setfam_1(k1_tarski(A),B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 534 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 8.54/8.58 535 (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]. 8.54/8.59 536 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 537 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 538 (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]. 8.54/8.59 539 (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]. 8.54/8.59 540 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> A = k1_relat_1(k7_relat_1(B,A))))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 541 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 542 (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]. 8.54/8.59 543 (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]. 8.54/8.59 544 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) <-> v1_relat_1(A))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 545 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 546 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 547 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_tarski(A,B) = k3_relat_1(C)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 548 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 549 (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]. 8.54/8.59 550 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 551 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 552 (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]. 8.54/8.59 553 (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]. 8.54/8.59 554 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 555 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 556 (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]. 8.54/8.59 557 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 558 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 559 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 560 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 561 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 562 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 563 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 564 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) = k3_relat_1(k2_xboole_0(A,B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 565 (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]. 8.54/8.59 566 (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]. 8.54/8.59 567 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 568 (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]. 8.54/8.59 569 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k2_xboole_0(A,B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 570 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 571 (all A all B (v1_relat_1(B) -> k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 572 (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]. 8.54/8.59 573 (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]. 8.54/8.59 574 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 575 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k9_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 576 (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]. 8.54/8.59 577 (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]. 8.54/8.59 578 (all A (v1_relat_1(A) -> ((all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B)) <-> v3_relat_1(A)))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 579 (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]. 8.54/8.59 580 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 581 (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]. 8.54/8.59 582 (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]. 8.54/8.59 583 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 584 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 585 (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]. 8.54/8.59 586 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 587 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 588 (all A (A = k1_relat_1(k6_relat_1(A)) & k2_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 589 (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]. 8.54/8.59 590 (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]. 8.54/8.59 591 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 592 (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]. 8.54/8.59 593 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 594 (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]. 8.54/8.59 595 (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]. 8.54/8.59 596 (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]. 8.54/8.59 597 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 598 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B) <-> r2_hidden(k4_tarski(D,E),C))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 599 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 600 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 601 (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]. 8.54/8.59 602 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 603 (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]. 8.54/8.59 604 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 605 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 606 (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]. 8.54/8.59 607 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 608 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 609 (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]. 8.54/8.59 610 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 611 (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]. 8.54/8.59 612 (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]. 8.54/8.59 613 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k7_relat_1(k7_relat_1(B,A),A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 614 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(B,f1_s1_relat_1) & r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 615 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 616 (all A all B (v1_relat_1(B) -> -(k1_xboole_0 != A & k1_xboole_0 = k9_relat_1(B,A) & r1_tarski(A,k1_relat_1(B))))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 617 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 618 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 619 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 620 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 621 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> 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]. 8.54/8.59 622 (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]. 8.54/8.59 623 (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]. 8.54/8.59 624 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 625 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 626 (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]. 8.54/8.59 627 (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]. 8.54/8.59 628 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 629 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 630 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 631 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 632 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 633 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 634 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 635 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 636 (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]. 8.54/8.59 637 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 638 (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]. 8.54/8.59 639 (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]. 8.54/8.59 640 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 641 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 642 (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]. 8.54/8.59 643 (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]. 8.54/8.59 644 (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]. 8.54/8.59 645 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,k5_relat_1(B,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 646 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B) & r2_hidden(D,k2_relat_1(C)))) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 647 (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]. 8.54/8.59 648 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 649 (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]. 8.54/8.59 650 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 651 (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]. 8.54/8.59 652 (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]. 8.54/8.59 653 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 654 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 655 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 656 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 657 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 658 (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]. 8.54/8.59 659 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> 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]. 8.54/8.59 660 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k9_relat_1(C,B)) <-> (exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C)))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 661 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 662 (all A (v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 663 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_tarski(A,C) = k1_relat_1(E) & k2_relat_1(E) = k2_tarski(B,D)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 664 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_relat_1(C) = k1_tarski(B) & k1_relat_1(C) = k1_tarski(A)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 665 (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]. 8.54/8.59 666 (all A (v1_relat_1(A) -> k1_xboole_0 = k8_relat_1(k1_xboole_0,A))) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 667 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k2_xboole_0(A,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 668 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 669 (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]. 8.54/8.59 670 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 671 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 672 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 673 (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]. 8.54/8.59 674 (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))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 675 (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]. 8.54/8.59 676 (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]. 8.54/8.59 677 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 678 (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]. 8.54/8.59 679 (all A (v1_relat_1(A) -> k1_xboole_0 = k7_relat_1(A,k1_xboole_0))) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 680 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 681 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> (exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))))) <-> C = k5_relat_1(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 682 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & k7_relat_1(B,C) = k7_relat_1(A,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]. 8.54/8.59 683 (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]. 8.54/8.59 684 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 685 (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]. 8.54/8.59 686 (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]. 8.54/8.59 687 (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]. 8.54/8.59 688 (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]. 8.54/8.59 689 (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]. 8.54/8.59 690 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 691 (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]. 8.54/8.59 692 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 693 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 694 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 695 (all A (v1_relat_1(A) -> k1_relat_1(k4_relat_1(A)) = k2_relat_1(A) & k2_relat_1(k4_relat_1(A)) = k1_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 696 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 697 (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]. 8.54/8.59 698 (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(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 699 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k10_relat_1(B,A) = k1_xboole_0))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 700 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k2_xboole_0(B,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 701 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 702 (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]. 8.54/8.59 703 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 704 (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]. 8.54/8.59 705 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 706 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.59 707 (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]. 8.54/8.59 708 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 709 (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]. 8.54/8.60 710 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0 & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 711 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 712 (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]. 8.54/8.60 713 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 714 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 715 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_relat_1(A) = k1_xboole_0 -> k1_xboole_0 = A))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 716 (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]. 8.54/8.60 717 (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]. 8.54/8.60 718 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 719 (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]. 8.54/8.60 720 (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]. 8.54/8.60 721 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 722 (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]. 8.54/8.60 723 (all A k6_relat_1(A) = k4_relat_1(k6_relat_1(A))) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 724 (all A (v1_relat_1(A) -> k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) = k3_relat_1(A))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 725 (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]. 8.54/8.60 726 (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]. 8.54/8.60 727 (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]. 8.54/8.60 728 (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]. 8.54/8.60 729 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 730 (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]. 8.54/8.60 731 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 732 (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]. 8.54/8.60 733 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 734 (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]. 8.54/8.60 735 (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]. 8.54/8.60 736 (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]. 8.54/8.60 737 (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]. 8.54/8.60 738 (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]. 8.54/8.60 739 (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]. 8.54/8.60 740 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 741 (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]. 8.54/8.60 742 (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]. 8.54/8.60 743 (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]. 8.54/8.60 744 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(A,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D))))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 745 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 746 (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]. 8.54/8.60 747 (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]. 8.54/8.60 748 (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]. 8.54/8.60 749 (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]. 8.54/8.60 750 (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]. 8.54/8.60 751 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k6_relat_1(A),B) = B))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 752 (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]. 8.54/8.60 753 (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]. 8.54/8.60 754 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(k5_relat_1(A,B),C))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 755 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 756 (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]. 8.54/8.60 757 (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)) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 758 (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]. 8.54/8.60 759 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 760 (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]. 8.54/8.60 761 (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]. 8.54/8.60 762 (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]. 8.54/8.60 763 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 764 (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]. 8.54/8.60 765 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k5_relat_1(B,D) = k6_relat_1(A) & k6_relat_1(k1_relat_1(D)) = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(B) -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 766 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 767 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 768 (all A k6_relat_1(A) = k2_funct_1(k6_relat_1(A))) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 769 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 8.54/8.60 770 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 771 (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,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]. 8.54/8.60 772 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 773 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 774 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 775 (all A all B (v1_relat_1(B) -> (k10_relat_1(B,k1_tarski(A)) != k1_xboole_0 <-> r2_hidden(A,k2_relat_1(B))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 776 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 777 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 778 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 779 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B -((all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)) & r2_hidden(B,k2_relat_1(A))))))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 780 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 781 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 8.54/8.60 782 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_funct_1(A) = k4_relat_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 783 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 784 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 785 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 786 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 787 (all A all B -((all C (v1_relat_1(C) & v1_funct_1(C) -> -(B = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A)))) & -(k1_xboole_0 = A & B != k1_xboole_0))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 788 (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]. 8.54/8.60 789 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 790 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 791 (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]. 8.54/8.60 792 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 793 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 794 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 795 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 796 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 797 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 798 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 799 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 800 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k5_relat_1(A,B) = A & k2_relat_1(A) = k1_relat_1(B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 801 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 802 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 803 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 804 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 805 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 806 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_tarski(A) = k2_relat_1(B) & k1_tarski(A) = k2_relat_1(C) & k1_relat_1(C) = k1_relat_1(B) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 807 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 8.54/8.60 808 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 809 (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]. 8.54/8.60 810 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 811 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_funct_1(k2_funct_1(A)) = A))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 812 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 813 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 814 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k4_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 815 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 816 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 817 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 818 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 819 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 820 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 821 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_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]. 8.54/8.60 822 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 823 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 8.54/8.60 824 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 825 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A)))) <-> v2_relat_1(A)))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 826 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 827 (all A all B (r2_hidden(B,A) -> B = k1_funct_1(k6_relat_1(A),B))) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 828 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 829 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 830 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 831 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 832 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 833 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 834 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 835 (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]. 8.54/8.60 836 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 837 (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]. 8.54/8.60 838 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 839 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 840 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 841 (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,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]. 8.54/8.60 842 (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(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 843 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 844 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(C) = k1_relat_1(B) & k5_relat_1(B,A) = k5_relat_1(C,A) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> B = C))))) <-> v2_funct_1(A)))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 845 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)))))) <-> k2_relat_1(A) = B)))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 846 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 847 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 848 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 849 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 850 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 851 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 852 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 853 (all A all B k6_relat_1(k3_xboole_0(A,B)) = k5_relat_1(k6_relat_1(B),k6_relat_1(A))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 854 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 855 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_funct_1(B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 856 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A & k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 857 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 8.54/8.60 858 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 859 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.60 860 (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]. 8.54/8.61 861 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(A,k2_funct_1(A))) = k1_relat_1(A) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 862 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 863 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 864 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & k2_relat_1(B) = k1_relat_1(A) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 865 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 866 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k2_relat_1(B) = k1_relat_1(A) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 867 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 868 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 869 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B) & k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 870 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 871 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & (all C all D ((k1_funct_1(B,C) = D & r2_hidden(C,k2_relat_1(A)) -> C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A))) & (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> D = k1_funct_1(B,C) & r2_hidden(C,k2_relat_1(A))))) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 872 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B))))))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 873 (all A (v1_relat_1(A) & v1_funct_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]. 8.54/8.61 874 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 875 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 876 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> B = C)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_funct_1(B,C) & r2_hidden(B,f1_s1_funct_1))))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 877 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k2_funct_1(A)) = k1_relat_1(A) & k1_relat_1(k2_funct_1(A)) = k2_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 878 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) & r2_hidden(B,k1_relat_1(C)) -> 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]. 8.54/8.61 879 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 880 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 881 (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 = k2_relat_1(B) & k1_relat_1(D) = A & k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(C) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 882 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 883 (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]. 8.54/8.61 884 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 885 (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]. 8.54/8.61 886 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(k1_funct_1(B,D) = C & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 887 (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]. 8.54/8.61 888 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 889 (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)) -> k9_relat_1(C,k2_tarski(A,B)) = k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 890 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 891 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(A) = k1_relat_1(B) & (all C all D (r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(B)) -> (C = k1_funct_1(B,D) <-> D = k1_funct_1(A,C)))) & k2_relat_1(B) = k1_relat_1(A) -> B = k2_funct_1(A)))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 892 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 893 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 894 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 895 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k8_relat_1(A,C)))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 896 (exists A (v1_relat_1(A) & v1_funct_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 897 (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]. 8.54/8.61 898 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C))) & k1_relat_1(B) = A))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 899 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 900 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 901 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 902 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 903 (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_relat_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 904 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) & (all B -((all C all D B != k4_tarski(C,D)) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 905 (all A all B (v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & k1_xboole_0 = k10_relat_1(B,k1_tarski(C)))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 906 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k2_relat_1(A) = k1_relat_1(B) & v2_funct_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 907 (exists A (v1_relat_1(A) & v1_funct_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 908 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 909 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 910 (all A (k1_xboole_0 != A -> (all B exists C (v1_funct_1(C) & A = k1_relat_1(C) & k1_tarski(B) = k2_relat_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 911 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 912 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 913 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 914 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 915 (all 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) = A & A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 916 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C)) & k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 917 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A & k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 918 (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(k5_relat_1(k6_relat_1(A),C),B) = k1_funct_1(C,B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 919 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 920 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,k1_relat_1(A)) & D = k1_funct_1(A,E) & r2_hidden(E,B))) <-> r2_hidden(D,C))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 921 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 922 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 923 (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]. 8.54/8.61 924 (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,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 925 (all A (v1_funct_1(A) & v1_relat_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]. 8.54/8.61 926 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 927 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 928 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (A = k1_relat_1(D) & k5_relat_1(B,D) = k5_relat_1(B,C) & A = k1_relat_1(C) -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 929 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 930 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 8.54/8.61 931 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 932 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 933 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 934 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 935 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 936 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 937 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 938 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 939 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 940 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 941 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> A = k1_xboole_0)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 942 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 943 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> C = k1_xboole_0)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 944 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 945 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k6_relat_1(k2_relat_1(A)) = k5_relat_1(k2_funct_1(A),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]. 8.54/8.61 946 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 947 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 948 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 949 (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]. 8.54/8.61 950 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 951 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 952 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 953 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((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(B,k1_funct_1(A,D)) = k1_funct_1(C,D))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 954 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 955 (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]. 8.54/8.61 956 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 957 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k4_xboole_0(A,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(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]. 8.54/8.61 959 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k8_relat_1(A,C) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C)) <-> r2_hidden(D,k1_relat_1(B))))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 960 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 961 (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]. 8.54/8.61 962 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 963 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 964 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,B) | r2_hidden(B,A))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 965 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 966 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_ordinal1(A,B) <-> r1_tarski(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 967 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 968 (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]. 8.54/8.61 969 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A) & v3_ordinal1(B))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 970 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 971 (all A -((all B (v3_ordinal1(B) -> -r1_tarski(A,B))) & (all B (r2_hidden(B,A) -> v3_ordinal1(B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.61 972 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 973 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_xboole_0(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 974 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 975 (all A all B all C all D -(r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 976 (all A ((all B (r2_hidden(B,A) -> v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v1_relat_1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 977 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 978 (all A (v3_ordinal1(A) -> -v1_xboole_0(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 979 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 980 (all A ((all B all C -(r2_hidden(B,A) & r2_hidden(C,A) & -r2_hidden(B,C) & -r2_hidden(C,B) & B != C)) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 981 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 982 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 983 (all A (v1_ordinal1(A) & v2_ordinal1(A) <-> v3_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 984 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 985 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 986 (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]. 8.54/8.62 987 (all A all B (v3_ordinal1(B) -> -(k1_xboole_0 != A & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & r1_tarski(A,B)))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 988 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 989 (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) -> (all B ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_relat_1(C) = A & f3_s5_ordinal1(C) = B & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> f2_s5_ordinal1(A) = B)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A))))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 990 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 991 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 992 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 993 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 994 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 995 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(B,A) | r1_ordinal1(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 996 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(B,A) & A != B & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 997 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 998 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r2_hidden(A,k1_ordinal1(B))))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 999 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1000 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1001 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1002 (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]. 8.54/8.62 1003 (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]. 8.54/8.62 1004 (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]. 8.54/8.62 1005 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1006 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1007 (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]. 8.54/8.62 1008 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1009 (all A (v3_ordinal1(A) -> -(v4_ordinal1(A) & (exists B (A = k1_ordinal1(B) & v3_ordinal1(B)))) & -((all B (v3_ordinal1(B) -> A != k1_ordinal1(B))) & -v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1010 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1011 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1012 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) -> k2_ordinal1(A,B) = k7_relat_1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1013 (all A all B (v5_ordinal1(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1014 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A)))) <-> v4_ordinal1(A)))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1015 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1016 (all A all B all C all D all E -(r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,A) & r2_hidden(A,B))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1017 (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]. 8.54/8.62 1018 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1019 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1020 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1021 (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]. 8.54/8.62 1022 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> A = B | r2_hidden(A,B))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1023 (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]. 8.54/8.62 1024 (exists A (v1_relat_1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k2_ordinal1(A,B) = C & r2_hidden(B,f1_s4_ordinal1) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v5_ordinal1(A) & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1025 (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]. 8.54/8.62 1026 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1027 (all A (k3_tarski(A) = A <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1028 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1029 (all A all B all C all D all E all F -(r2_hidden(B,C) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(D,E) & r2_hidden(C,D) & r2_hidden(A,B))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1030 (all A all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1031 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1032 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1033 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1034 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1035 (exists A (p1_s1_ordinal1(A) & v3_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]. 8.54/8.62 1036 (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]. 8.54/8.62 1037 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1038 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1039 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1040 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1041 (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]. 8.54/8.62 1042 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(A,B) & r2_hidden(C,A) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1043 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1044 f1_s3_ordinal1 = k1_relat_1(f4_s3_ordinal1) & (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k2_ordinal1(f4_s3_ordinal1,A) = B & r2_hidden(A,f1_s3_ordinal1) -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) & (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (B = k2_ordinal1(f3_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & f1_s3_ordinal1 = k1_relat_1(f3_s3_ordinal1) -> f3_s3_ordinal1 = f4_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1045 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1046 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1047 (all A all B all C (m2_relset_1(C,A,B) -> k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1048 (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]. 8.54/8.62 1049 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> D = k9_relset_1(A,B,C,D)))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1050 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> 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]. 8.54/8.62 1051 (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]. 8.54/8.62 1052 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,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]. 8.54/8.62 1053 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k11_relset_1(A,B,C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1054 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,D) = k3_xboole_0(C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1055 (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]. 8.54/8.62 1056 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1057 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1058 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C)))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1059 (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]. 8.54/8.62 1060 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1061 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(A,B) & r1_tarski(C,D) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1062 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(D,E),C)))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1063 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> B = k5_relset_1(A,B,C) & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1064 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1065 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,D,C) = k1_relset_1(A,B,C,D))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1066 (all A all B all C (m1_relset_1(C,A,B) <-> m2_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1067 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(k4_tarski(E,F) = C & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1068 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,D,C) = k2_relset_1(A,B,C,D))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1069 (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]. 8.54/8.62 1070 (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]. 8.54/8.62 1071 (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]. 8.54/8.62 1072 (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]. 8.54/8.62 1073 (all A all B all C (m2_relset_1(C,A,B) -> (k5_relset_1(A,B,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C))))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1074 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1075 (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]. 8.54/8.62 1076 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> k1_xboole_0 = C))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1077 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1078 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C) & k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1079 (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]. 8.54/8.62 1080 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1081 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1082 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k5_relset_1(A,B,D)) & r1_tarski(C,k4_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1083 (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]. 8.54/8.62 1084 (all A all B all C (m1_relset_1(C,A,B) -> k4_relat_1(C) = k6_relset_1(A,B,C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1085 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1086 (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]. 8.54/8.62 1087 (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]. 8.54/8.62 1088 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1089 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1090 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1091 (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]. 8.54/8.62 1092 (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]. 8.54/8.62 1093 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relset_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1094 (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]. 8.54/8.62 1095 (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]. 8.54/8.62 1096 (all A all B all C (m1_relset_1(C,A,B) <-> r1_tarski(C,k2_zfmisc_1(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1097 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1098 (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]. 8.54/8.62 1099 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1100 (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]. 8.54/8.62 1101 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> k1_xboole_0 = C))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1102 (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]. 8.54/8.62 1103 (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]. 8.54/8.62 1104 (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]. 8.54/8.62 1105 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1106 (all A all B all C (m1_relset_1(C,A,B) -> k2_relat_1(C) = k5_relset_1(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1107 (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]. 8.54/8.62 1108 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1109 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> C = k1_relset_1(A,B,C,C))) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1110 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1111 (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]. 8.54/8.62 1112 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1113 (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]. 8.54/8.62 1114 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1115 (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]. 8.54/8.62 1116 (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]. 8.54/8.62 1117 (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]. 8.54/8.62 1118 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1119 (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]. 8.54/8.62 1120 (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(F,B) & r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1121 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1122 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & B = k5_relat_1(B,k6_relat_1(A)))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1123 (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]. 8.54/8.62 1124 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1125 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1126 (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,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1127 (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]. 8.54/8.62 1128 (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]. 8.54/8.62 1129 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1130 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1131 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k4_relset_1(A,B,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C))))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1132 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1133 (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]. 8.54/8.62 1134 (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]. 8.54/8.62 1135 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1136 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1137 (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]. 8.54/8.62 1138 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1139 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.62 1140 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1141 (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]. 8.54/8.63 1142 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1143 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1144 (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]. 8.54/8.63 1145 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1146 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1147 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)) & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1148 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1149 (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]. 8.54/8.63 1150 (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]. 8.54/8.63 1151 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1152 (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]. 8.54/8.63 1153 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1154 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1155 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1156 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k1_tarski(C) = k5_partfun1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1157 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1158 (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) & r2_hidden(A,k1_relat_1(D)) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1159 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1160 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1161 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1162 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1163 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1164 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1165 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 8.54/8.63 1166 (all A exists B (m1_relset_1(B,A,A) & v1_relat_1(B) & v1_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1167 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1168 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1169 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1170 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 8.54/8.63 1171 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1172 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k2_relat_1(C) = k9_relat_1(C,A))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1173 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),C,B))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1174 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1175 (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 -> k1_xboole_0 = A)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1176 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k2_relat_1(B) = k1_xboole_0 & k4_relset_1(A,k1_xboole_0,B) = k1_xboole_0)) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1177 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1178 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1179 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1180 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1181 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1182 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(k1_xboole_0,A,B))) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1183 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,E) = k1_funct_1(C,D) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1184 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1185 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1186 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1187 (exists A (v1_funct_1(A) & f1_s1_partfun1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> k1_funct_1(A,B) = f3_s1_partfun1(B)) & (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1188 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1189 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1190 (all A all B all C all D (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) -> C = D)) & (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))) -> (exists A (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(B,f1_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1))) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1191 (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]. 8.54/8.63 1192 (all A (v1_relat_1(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1193 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1194 (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]. 8.54/8.63 1195 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1196 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1197 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1198 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1199 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1200 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1201 (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]. 8.54/8.63 1202 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> D = C)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1203 (all A all B exists C (v1_funct_1(C) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1204 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1205 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D)) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1206 (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]. 8.54/8.63 1207 (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 (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1208 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1209 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1210 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1211 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1212 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1213 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1214 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & B = k1_xboole_0 -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1215 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1216 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1217 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)) & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1218 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1219 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1220 (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]. 8.54/8.63 1221 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k10_relat_1(C,B))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1222 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1223 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1224 (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) -> (r1_partfun1(D,E) & v1_partfun1(E,A,B) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1225 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1226 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1227 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1228 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1229 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1230 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1231 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1232 (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) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & r1_partfun1(C,D)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1233 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (v1_relat_1(C) & r1_tarski(A,C) & r1_tarski(B,C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1234 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1235 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> 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]. 8.54/8.63 1236 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 8.54/8.63 1237 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1238 (all A all B (v1_funct_1(k1_xboole_0) & m2_relset_1(k1_xboole_0,A,B))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1239 (all A all B all C all D (v1_relat_1(D) & v1_funct_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) -> 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(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1240 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1241 (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]. 8.54/8.63 1242 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (k5_partfun1(A,B,C) = D <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & E = F & r1_partfun1(C,F) & v1_partfun1(F,A,B))) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1243 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1244 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1245 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1246 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> k1_funct_1(D,C) = B))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1247 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1248 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1249 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1250 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1251 (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_1(D) & m2_relset_1(D,A,B))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.63 1252 (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]. 8.54/8.64 1253 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1254 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1255 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1256 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1257 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_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]. 8.54/8.64 1258 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1259 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1260 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1261 (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) -> (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]. 8.54/8.64 1262 (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]. 8.54/8.64 1263 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1264 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1265 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1266 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) & v1_funct_1(F) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1267 (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]. 8.54/8.64 1268 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1269 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1270 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1271 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1272 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1273 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1274 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1275 (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]. 8.54/8.64 1276 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1277 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1278 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> k1_xboole_0 = A)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1279 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (C = k2_xboole_0(A,B) & v1_funct_1(C) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1280 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1281 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k1_tarski(A) & r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1282 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k9_relset_1(B,C,A,k3_partfun1(D,B,C)) = k3_partfun1(D,B,k3_xboole_0(A,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1283 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (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]. 8.54/8.64 1284 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1285 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1286 (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]. 8.54/8.64 1287 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(A,C) & r1_tarski(B,D) -> v1_funct_1(E) & m2_relset_1(E,C,D)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1288 (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,E) = k4_relset_1(k2_zfmisc_1(A,B),C,D) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1289 (all A all B all C (m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1290 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) & (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]. 8.54/8.64 1291 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1292 (all A all B all C ((all D ((exists E (r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k4_partfun1(A,B))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1293 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1294 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1295 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1296 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1297 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1298 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1299 (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]. 8.54/8.64 1300 (all A (v1_relat_1(A) & v1_funct_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]. 8.54/8.64 1301 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1302 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1303 (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]. 8.54/8.64 1304 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(k6_relat_1(A),C) = C)) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1305 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1306 (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]. 8.54/8.64 1307 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists 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)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))) & (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))) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1308 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_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(A,C) = k1_funct_1(B,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1309 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1310 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1311 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1312 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1313 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1314 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1315 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1316 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1317 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1318 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1319 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1320 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1321 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1322 (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) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1323 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1324 (all A (v1_relat_1(A) & v8_relat_2(A) & v3_relat_2(A) -> v1_relat_1(A) & v1_relat_2(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1325 (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]. 8.54/8.64 1326 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1327 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_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]. 8.54/8.64 1328 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1329 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1330 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1331 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> B = k1_xboole_0)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1332 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) & p1_s2_partfun1(A,C) -> B = C)) & (all A all B (p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> r2_hidden(B,f2_s2_partfun1))) -> (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 ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1333 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1334 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1335 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1336 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1337 (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]. 8.54/8.64 1338 (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]. 8.54/8.64 1339 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1340 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1341 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1342 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1343 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k1_xboole_0,B) & v1_funct_1(D) -> C = D)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1344 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1345 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1346 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1347 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1348 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1349 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1350 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1351 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1352 (all A all B (m1_relset_1(B,A,A) -> (v1_partfun1(B,A,A) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_funct_1(B) -> v1_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v2_funct_1(B)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1353 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1354 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (v1_relat_1(E) & D = E & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1355 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D)) & r2_hidden(D,B)))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1356 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> 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) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1357 (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) -> k1_tarski(C) = k5_partfun1(A,B,k3_partfun1(C,A,B))))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1358 (all A all B all C (m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1359 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1360 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1361 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1362 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1363 (all A all B all C (v1_funct_1(B) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,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) & m2_relset_1(k5_funct_2(A,B,C),A,A))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1364 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1365 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1366 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1367 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1368 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1369 (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),B) | B = k1_xboole_0))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1370 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1371 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1372 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1373 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1374 (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(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1375 (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 & -v2_funct_1(C) & (exists D (v1_funct_2(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & m2_relset_1(D,B,A) & v1_funct_1(D)))))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1376 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1377 (all A all B all C all D (v1_funct_2(D,k1_tarski(A),B) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> (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]. 8.54/8.64 1378 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1379 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1380 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (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]. 8.54/8.64 1381 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1382 (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_2(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1383 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1384 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1385 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1386 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1387 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1388 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1389 (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]. 8.54/8.64 1390 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1391 (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]. 8.54/8.64 1392 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1393 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> v2_funct_1(C) & k2_relat_1(D) = A | k1_xboole_0 = B))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.64 1394 (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)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1395 (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 -> ((all D (k1_xboole_0 != D -> (all E (v1_funct_2(E,B,D) & m2_relset_1(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) -> E = F))))))) <-> B = k2_relat_1(C))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1396 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1397 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1398 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1399 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1400 (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 ((all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1401 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,k10_relat_1(D,C)) <-> r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C)))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1402 (all A all B all C all D (m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1403 (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) -> -((B = k1_xboole_0 -> 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]. 8.54/8.65 1404 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1405 (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,C) = k5_partfun1(A,B,D) & (all E B != k1_tarski(E)) -> D = C))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1406 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (-(B = k1_xboole_0 & A != k1_xboole_0 & C != k1_xboole_0) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1407 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1408 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & 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) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(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]. 8.54/8.65 1409 (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) -> B = k1_xboole_0 & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1410 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1411 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (k2_relat_1(C) = B & v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> k1_xboole_0 = B | k2_funct_1(C) = D | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1412 (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]. 8.54/8.65 1413 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k2_relat_1(B) = k2_funct_2(A,A,B,A))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1414 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1415 (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) -> v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1416 (all A all B k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B)) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1417 (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_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1418 (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_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]. 8.54/8.65 1419 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1420 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1421 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & B = k2_relat_1(C) -> k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k5_relat_1(k2_funct_1(C),C) = k6_partfun1(B) | B = k1_xboole_0))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1422 f3_s11_funct_2 != f4_s11_funct_2 -> (exists A (v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(f7_s11_funct_2(B) != k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) & B != f4_s11_funct_2 & B != f3_s11_funct_2))) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_1(A))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1423 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1424 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1425 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1426 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1427 (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) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1428 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1429 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1430 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(C),B) & k1_relat_1(C) = A))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1431 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1432 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_xboole_0 -> v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1433 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1434 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1435 (all A all B all C all D all E (v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) & -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]. 8.54/8.65 1436 (all A all B all C (v1_funct_1(B) & v1_funct_1(C) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & m1_relset_1(B,A,A) & 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]. 8.54/8.65 1437 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & B = k3_funct_2(A,A,C,k2_funct_2(A,A,C,B))))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1438 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (k1_xboole_0 != B -> (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]. 8.54/8.65 1439 (all A all B -(r2_hidden(A,f1_s5_funct_2) & (all C -(r2_hidden(C,f3_s5_funct_2) & p1_s5_funct_2(A,B,C))) & r2_hidden(B,f2_s5_funct_2))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & (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))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1440 (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) -> k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0)) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1441 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1442 (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) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1443 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1444 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (r2_hidden(C,A) & r2_hidden(D,A) & k1_funct_1(B,C) = k1_funct_1(B,D) -> D = C))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1445 (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) -> k1_xboole_0 = B & A != k1_xboole_0 | v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & m2_relset_1(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1446 (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,B) & B = k2_relat_1(D) & (all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C))))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.54/8.65 1447 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | k1_xboole_0 = B))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1448 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1449 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1450 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1451 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1452 (all A all B all C (m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1453 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1454 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1455 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1456 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k4_funct_2(A,C,B) = B & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1457 (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) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1458 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1459 (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]. 8.60/8.65 1460 (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]. 8.60/8.65 1461 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_funct_1(D,C) = B))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1462 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_1(A) & 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))))))) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1463 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D -((all E -(D = k1_funct_1(C,E) & r2_hidden(E,A))) & r2_hidden(D,B))) -> k1_xboole_0 = B | k2_relat_1(C) = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1464 (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]. 8.60/8.65 1465 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1466 (all A all B (-v1_xboole_0(A) & -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_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1467 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (B = k2_relat_1(D) & k2_relat_1(E) = C -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | k1_xboole_0 = B))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1468 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C & C = k7_relset_1(A,A,A,B,k6_partfun1(A),C))) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1469 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1470 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> v1_partfun1(C,A,B) | A != k1_xboole_0 & k1_xboole_0 = B))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1471 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k4_relset_1(A,A,B) = A & r1_tarski(k2_relat_1(B),A))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1472 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1473 (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(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1474 (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]. 8.60/8.65 1475 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1476 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & 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) -> k1_xboole_0 = B & k1_xboole_0 != A | C = D))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1477 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1478 (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) <-> k2_relat_1(C) = B))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1479 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1480 (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 -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1481 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1482 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1483 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1484 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,k2_funct_2(A,B,C,A)) = A))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1485 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A ((all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1486 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1487 (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(C,D) = k1_funct_1(B,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1488 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1489 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1490 (exists A ((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)))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1491 (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)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1492 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1493 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) & v2_funct_1(D) -> 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]. 8.60/8.65 1494 (all 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,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (A = k2_relat_1(B) & k2_relat_1(C) = A -> k2_relat_1(k4_funct_2(A,B,C)) = A))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1495 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_1(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) -> (C = k5_funct_2(A,B,C) -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1496 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1497 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1498 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1499 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1500 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1501 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1502 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1503 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1504 (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(B,C) -> k1_xboole_0 != A & k1_xboole_0 = B | v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1505 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1506 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1507 (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 -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1508 (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) -> -(-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))) & (B = k1_xboole_0 -> k1_xboole_0 = A) & (k1_xboole_0 = C -> k1_xboole_0 = B)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1509 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> -(A != k1_xboole_0 & k1_xboole_0 != B & -(v2_funct_1(C) <-> (all D all E (v1_funct_2(E,D,A) & m2_relset_1(E,D,A) & v1_funct_1(E) -> (all F (m2_relset_1(F,D,A) & v1_funct_2(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,E,C) = k1_partfun1(D,A,A,B,F,C) -> E = F))))))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1510 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1511 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> k1_xboole_0 != A & k1_xboole_0 = B | r1_partfun1(C,D)))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1512 (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) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> f4_s9_funct_2(B) = k1_funct_1(A,B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1513 (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 (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 -> k1_xboole_0 = C | B = k2_relat_1(D)))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1514 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F -(r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1515 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1516 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> B = k1_xboole_0 & k1_xboole_0 != A | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1517 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.65 1518 (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]. 8.60/8.65 1519 (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) -> (v2_funct_1(C) <-> (all D all E (r2_hidden(D,A) & k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,A) -> E = D)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1520 (exists A (k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2 & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> f5_s10_funct_2(B) = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1521 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1522 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k2_relat_1(C) = k2_funct_2(A,B,C,A)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1523 (all A exists B (m1_relset_1(B,A,A) & v1_relat_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A) & v2_funct_1(B) & v1_funct_1(B))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1524 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1525 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1526 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1527 (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 -> A = k1_xboole_0) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1528 (all A all B all C all D all E (-v1_xboole_0(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_2(D,A,B) & v1_funct_1(D) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1529 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> B = k1_xboole_0 & A != k1_xboole_0 | v2_funct_1(D) | B != k1_xboole_0 & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1530 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1531 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1532 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1533 (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 (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)) & B = k2_relat_1(D) -> k1_xboole_0 = C & k1_xboole_0 != B | v2_funct_1(D) & v2_funct_1(E)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1534 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (v2_funct_1(B) & A = k2_relat_1(B) -> v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1535 (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 (v1_funct_1(A) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1536 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A)))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1537 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_xboole_0 = B | k1_funct_1(E,C) = k1_funct_1(k9_relset_1(A,B,D,E),C)))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1538 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((B = k1_xboole_0 -> k1_xboole_0 = A) & (all D (m2_relset_1(D,A,B) & v1_funct_2(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)))))))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1539 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> (k4_relset_1(A,B,C) = A <-> v1_funct_2(C,A,B))) & (k1_xboole_0 = B -> (C = k1_xboole_0 <-> v1_funct_2(C,A,B)) | k1_xboole_0 = A))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1540 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1541 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_1(C) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1542 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1543 (all A all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> k1_xboole_0 = C | r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C)))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1544 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B & B = k7_relset_1(A,A,A,A,k6_partfun1(A),B))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1545 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1546 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1547 (exists A (v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_1(A))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1548 (all A (A != k1_xboole_0 -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1549 (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_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1550 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1551 (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]. 8.60/8.66 1552 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & 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]. 8.60/8.66 1553 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & v2_funct_1(C) & (all E all F ((k1_funct_1(C,F) = E & r2_hidden(F,A) -> k1_funct_1(D,E) = F & r2_hidden(E,B)) & (r2_hidden(E,B) & F = k1_funct_1(D,E) -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) -> A = k1_xboole_0 | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1554 (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(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1555 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & 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) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1556 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1557 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1558 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A ((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)))) & 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))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1559 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1560 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1561 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1562 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1563 (all A (v1_funct_1(A) & v1_relat_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]. 8.60/8.66 1564 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1565 (all A all B (A != k1_xboole_0 -> k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1566 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1567 (all A all B all C (v1_relat_1(A) & v1_relat_1(C) & v1_funct_1(C) & 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]. 8.60/8.66 1568 (all A all B all C all D all E (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1569 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> 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]. 8.60/8.66 1570 (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]. 8.60/8.66 1571 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1572 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 8.60/8.66 1573 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_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]. 8.60/8.66 1574 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1575 (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) -> v1_funct_1(k5_funcop_1(C,E,D)) & m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1576 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & 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(B) -> k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)) = D)) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1577 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1578 (all A (k1_xboole_0 = k1_relat_1(k2_funcop_1(k1_xboole_0,A)) & k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1579 (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_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,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]. 8.60/8.66 1580 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1581 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_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]. 8.60/8.66 1582 (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) -> (k1_relat_1(A) = k1_relat_1(B) -> k1_relat_1(k5_relat_1(C,B)) = k1_relat_1(k5_relat_1(C,A))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1583 (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]. 8.60/8.66 1584 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1585 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1586 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1587 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B k1_funcop_1(k7_relat_1(A,B)) = k7_relat_1(k1_funcop_1(A),B)))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1588 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1589 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1590 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0 & k1_xboole_0 != B)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1591 (all A (v1_relat_1(A) & v1_funct_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]. 8.60/8.66 1592 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_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,D,k7_funct_2(A,B,B,D,E)) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1593 (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) -> 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]. 8.60/8.66 1594 (all A (v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1595 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1596 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1597 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (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]. 8.60/8.66 1598 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k3_funcop_1(k5_relat_1(D,A),B,C) = k5_relat_1(k3_funcop_1(D,B,C),A))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1599 (all A all B k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1600 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k1_relat_1(A) -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1601 (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,k2_zfmisc_1(B,C)) & m2_relset_1(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]. 8.60/8.66 1602 (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]. 8.60/8.66 1603 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1604 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (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]. 8.60/8.66 1605 (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]. 8.60/8.66 1606 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(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]. 8.60/8.66 1607 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1608 (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]. 8.60/8.66 1609 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1610 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1611 (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) -> k5_relat_1(k13_funct_3(B,C),A) = k3_funcop_1(A,B,C))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1612 (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 (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1613 (all A all B all C k2_funcop_1(k3_xboole_0(A,C),B) = k7_relat_1(k2_funcop_1(A,B),C)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.66 1614 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1615 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1616 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1617 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1618 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1619 (all A all B (A = k1_relat_1(k2_funcop_1(A,B)) & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1620 (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_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1621 (all A all B all C all D all E (-v1_xboole_0(A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) -> k4_funcop_1(C,D,E) = k7_funcop_1(A,B,C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1622 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (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]. 8.60/8.67 1623 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1624 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1625 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1626 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.60/8.67 1627 (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,A,B) & v1_funct_2(E,A,B) -> v1_funct_1(k3_funcop_1(C,D,E)) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & m2_relset_1(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1628 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1629 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1630 (all A all B all C all D (-v1_xboole_0(C) & 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(B) & -v1_xboole_0(A) -> k10_funcop_1(A,B,C,D) = k1_funcop_1(D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1631 (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),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1632 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1633 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B) & v1_funct_1(k4_funcop_1(C,D,E)))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 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_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1635 (all A all B all C all D (-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) & -v1_xboole_0(A) -> 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)) & v1_funct_1(k10_funcop_1(A,B,C,D)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1636 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k8_funcop_1(B,A,C,E,D) = k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1637 (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_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1638 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1639 (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]. 8.62/8.67 1640 (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 (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1641 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1642 (all A all B all C (r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = A)) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1643 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_2(C,k2_zfmisc_1(A,A),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]. 8.62/8.67 1644 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1645 (all A all B (v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1646 (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(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1647 (all A all B all C (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1648 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 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 (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))) = k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1650 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1651 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1652 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k1_funct_1(A,C) = k4_tarski(D,E) -> k4_tarski(E,D) = k1_funct_1(B,C))) & -((all D all E k1_funct_1(A,C) != k4_tarski(D,E)) & k1_funct_1(A,C) != k1_funct_1(B,C)))) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1653 (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]. 8.62/8.67 1654 (all A k13_funct_3(k6_partfun1(A),k6_partfun1(A)) = k12_funct_3(A)) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1655 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1656 (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 k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1657 (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) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1658 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> v1_funct_1(k8_funcop_1(A,B,C,D,E)) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1659 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_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]. 8.62/8.67 1660 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1661 (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 (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1662 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (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_2(F,A,B) & v1_funct_1(F) -> ((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))) -> F = k6_funcop_1(B,A,C,D,E)))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1663 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(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]. 8.62/8.67 1664 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1665 (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,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1666 (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]. 8.62/8.67 1667 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1668 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & 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(B) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1669 (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]. 8.62/8.67 1670 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1671 (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]. 8.62/8.67 1672 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1673 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1674 (all A all B k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B))) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1675 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1676 (all A (v1_relat_1(A) -> (all B all C (A = k2_zfmisc_1(B,C) -> k1_xboole_0 = C | C = k2_relat_1(A) & k1_relat_1(A) = B | B = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1677 (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,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1678 (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]. 8.62/8.67 1679 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1680 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1681 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(B,D),k1_relat_1(F)) & r2_hidden(k4_tarski(A,C),k1_relat_1(E)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1682 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = k2_funct_4(k2_funct_4(C))))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1683 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1684 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1685 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1686 (all A all B all C all D k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D))) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1687 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1688 (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(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1689 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_funcop_1(A,C),k2_funcop_1(B,C)))) # label(t5_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1690 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))) = k5_relat_1(B,A))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1691 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1692 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(B,C) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1693 (all A all B all C all D all E all F (k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) -> D = F & C = E | A = B)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1694 (all A all B all C all D all E all F all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1695 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> r1_tarski(A,k1_funct_4(A,B))))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1696 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(A,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1697 (all 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 (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1698 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1699 (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) -> (k1_relat_1(B) = k1_relat_1(C) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1700 (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)) -> k1_funct_4(B,A) = k1_funct_4(A,B)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1701 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.67 1702 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_funct_4(A,B)) & v1_funct_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1703 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> v1_funct_1(k5_funct_4(A,B,C,D,E)) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1704 (all A all B all C (-v1_xboole_0(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) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1705 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),E) & v1_funct_2(G,k2_zfmisc_1(A,B),E) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) -> v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1706 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1707 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(k1_relat_1(B),C) -> A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1708 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1709 (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) -> m2_relset_1(k1_funct_4(C,D),A,B) & v1_funct_1(k1_funct_4(C,D)))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1710 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(B),D) -> k7_relat_1(k1_funct_4(A,B),C) = A & k7_relat_1(k1_funct_4(A,B),D) = B)))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1711 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_funct_1(E,A) = C & D = k1_funct_1(E,B) & k1_relat_1(E) = k2_tarski(A,B) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1712 (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 (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(A,D)) & (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))) & k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) <-> C = k1_funct_4(A,B)))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1713 (all A all B all C all D (B != A -> k1_funct_1(k4_funct_4(A,B,C,D),B) = D & C = k1_funct_1(k4_funct_4(A,B,C,D),A))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1714 (all A -((all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1715 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1716 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1717 (all A all B (r1_tarski(k6_partfun1(A),k6_partfun1(B)) <-> r1_tarski(A,B))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1718 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1719 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(k2_funct_4(C),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(B,A))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1720 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_4(A)) & v1_funct_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1721 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(A,B) & B = k1_funct_4(B,A)))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1722 (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_funct_4(A,B) = C <-> (all D ((exists E exists F exists G exists H (k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)))) <-> r2_hidden(D,k1_relat_1(C)))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),k1_relat_1(B)) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) -> k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))) = k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G)))))))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1723 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funct_4(A,k1_xboole_0))) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1724 (all A all B all C (-v1_xboole_0(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) -> v1_funct_1(k2_funct_4(D)) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1725 (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)) -> k2_xboole_0(A,B) = k1_funct_4(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1726 (all A (v1_funct_1(A) & v1_relat_1(A) -> (exists B exists C r1_tarski(k1_relat_1(k2_funct_4(A)),k2_zfmisc_1(B,C))))) # label(t45_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1727 (all A all B all C all D (v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1728 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_funct_4(A,k1_funct_4(B,C)) = k1_funct_4(k1_funct_4(A,B),C))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1729 (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,k1_relat_1(B)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1730 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)) = B)))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1731 (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,k1_relat_1(k1_funct_4(B,C))) <-> r2_hidden(A,k1_relat_1(C)) | r2_hidden(A,k1_relat_1(B))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1732 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1733 (all A all B all C all D (r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) & k2_tarski(A,B) = k1_relat_1(k4_funct_4(A,B,C,D)))) # label(t65_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1734 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1735 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1736 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> B = D | A = k1_xboole_0)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1737 (all A all B all C all D (A != C -> k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = k4_funct_4(A,C,B,D))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1738 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k2_funct_4(C)),k2_zfmisc_1(B,A))))) # label(t46_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1739 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k2_funct_4(C)) = k2_zfmisc_1(B,A)))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1740 (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_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1741 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1742 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> k1_funct_4(A,A) = A)) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1743 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = k7_relat_1(A,k2_xboole_0(B,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1744 (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(B)) <-> (exists D exists E (C = k4_tarski(E,D) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)))))) & (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(B,k4_tarski(D,C)) = k1_funct_1(A,k4_tarski(C,D)))) <-> k2_funct_4(A) = B))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1745 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1746 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F))) -> k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1747 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (k1_xboole_0 != C -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1748 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1749 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1750 (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(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1751 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) = k7_relat_1(k1_funct_4(A,B),C)))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1752 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_1(k2_funct_4(D)) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1753 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(k1_xboole_0,A) = A)) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1754 (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) -> (r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_partfun1(A,B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1755 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (k1_xboole_0 != C -> D = k2_funct_4(k2_funct_4(D))))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1756 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> r1_tarski(A,C))) # label(t6_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1757 (all A all B all C all D (B != A -> k2_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(C,D))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1758 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1759 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1760 (all A all B k6_partfun1(k2_xboole_0(A,B)) = k1_funct_4(k6_partfun1(A),k6_partfun1(B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1761 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_xboole_0(A,B) = k1_funct_4(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1762 (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_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1763 (all A all B all C k4_funct_4(A,B,C,C) = k2_funcop_1(k2_tarski(A,B),C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1764 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1765 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1766 (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)) -> A = k7_relat_1(k1_funct_4(A,B),k1_relat_1(A))))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1767 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.62/8.68 1768 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_4(A,B)) & v1_relat_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1769 (all A all B all C all D all E all F all G (v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) -> -(F != k1_xboole_0 & -(v1_funct_1(k3_funct_4(G,H)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F))) & k1_xboole_0 != C))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1770 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (k2_zfmisc_1(C,D) = k1_relat_1(F) & k2_zfmisc_1(A,B) = k1_relat_1(E) -> k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k1_relat_1(k3_funct_4(E,F))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1771 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1772 (all A all B k1_tarski(k4_tarski(A,B)) = k2_funcop_1(k1_tarski(A),B)) # label(t70_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1773 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1774 (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,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1775 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1776 (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]. 8.83/8.91 1777 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1778 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> k1_xboole_0 = A | (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k15_ordinal2(A,B) = k3_tarski(k8_ordinal2(C)))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1779 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D))))) & f4_s12_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = f2_s12_ordinal2(A)))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> k1_xboole_0 = A | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> f4_s12_ordinal2 = k1_funct_1(f1_s12_ordinal2,k1_xboole_0)) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1780 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1781 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k16_ordinal2(B,D) = k1_funct_1(C,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1782 (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]. 8.83/8.91 1783 (all A all B (v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v1_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1784 (all A (v3_ordinal1(A) -> A = k3_tarski(k1_ordinal1(A)))) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1785 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k4_ordinal2 & (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))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> E = k1_xboole_0 | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal1(B) = k1_relat_1(D) & k1_ordinal2(D) = C & v5_ordinal1(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1786 (all A all B (v3_ordinal1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1787 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & k1_ordinal1(A) = k1_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)))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1788 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1789 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1790 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1791 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1792 (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]. 8.83/8.91 1793 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s5_ordinal2 & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> f2_s5_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> B = k1_xboole_0 | f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1794 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1795 (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]. 8.83/8.91 1796 (all A (v3_ordinal1(A) -> A = k15_ordinal2(k4_ordinal2,A) & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.91 1797 (all A all B (B = k2_ordinal2(A) <-> (all C (v3_ordinal1(C) & r2_hidden(C,A) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1798 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & f1_s9_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & (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))))) & v5_ordinal1(C))) <-> B = f4_s9_ordinal2(A))))) -> (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]. 8.83/8.94 1799 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | A = k1_xboole_0))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1800 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1801 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1802 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1803 (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]. 8.83/8.94 1804 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | 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(f6_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A))))) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1805 (all A (v3_ordinal1(A) -> A = k2_ordinal2(A))) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1806 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1807 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1808 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1809 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1810 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.94 1811 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = A -> (r1_ordinal2(A,B) <-> (exists C (v3_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) & r1_ordinal1(C,D) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)))))) & (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(C,k1_funct_1(B,F)) & r2_hidden(k1_funct_1(B,F),D)))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1812 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(A,k1_xboole_0))) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1813 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1814 (all A (v3_ordinal1(A) -> (all B ((exists C (k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | 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_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = f1_s8_ordinal2(A))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1815 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (B = k10_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & B = k9_ordinal2(C) & v1_ordinal2(C) & v5_ordinal1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1816 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k1_ordinal2(A) = k1_funct_1(A,k3_tarski(k1_relat_1(A))))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1817 (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]. 8.83/8.95 1818 (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]. 8.83/8.95 1819 (all A (v4_ordinal2(A) <-> r2_hidden(A,k5_ordinal2))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1820 (exists A (v1_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1821 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_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]. 8.83/8.95 1822 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)))) & f2_s10_ordinal2 = k1_relat_1(f1_s10_ordinal2) & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B (f3_s10_ordinal2(A) = B <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (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))))) & k1_relat_1(C) = k1_ordinal1(A))))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1823 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1824 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_ordinal2(A) <-> (exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1825 (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]. 8.83/8.95 1826 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1827 (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]. 8.83/8.95 1828 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1829 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k14_ordinal2(A,B) = C <-> (exists D (v5_ordinal1(D) & (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)) -> E = k1_xboole_0 | k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E))))) & A = k1_funct_1(D,k1_xboole_0) & k1_ordinal1(B) = k1_relat_1(D) & k1_ordinal2(D) = C & v1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1830 (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]. 8.83/8.95 1831 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = 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_funct_1(C,k1_xboole_0) = f2_s14_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1832 (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]. 8.83/8.95 1833 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1834 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (v2_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)))))))))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1835 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1836 (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]. 8.83/8.95 1837 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1838 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (B = k12_ordinal2(A) <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1839 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1840 (all A (v3_ordinal1(A) -> (exists B (v4_ordinal1(B) & r2_hidden(A,B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1841 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.83/8.95 1842 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1843 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1844 (exists A (v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v5_ordinal1(A) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1845 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1846 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(k4_ordinal2,A) & A = k16_ordinal2(A,k4_ordinal2))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1847 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> k1_xboole_0 = k2_ordinal2(B) | r1_ordinal1(A,k6_ordinal2(B)))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1848 (all A (v3_ordinal1(A) -> (all B all C (r1_tarski(B,C) & r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1849 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v1_funct_1(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | C = k1_xboole_0))) & A = k1_ordinal2(B) & v1_ordinal2(B) & v5_ordinal1(B))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1850 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_xboole_0 = D | f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v1_ordinal2(C))) & B != A & (exists C (v1_relat_1(C) & v5_ordinal1(C) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (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))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> D = k1_xboole_0 | f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & A = k1_ordinal2(C) & v1_ordinal2(C) & v1_funct_1(C)))))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1851 (exists A (v1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1852 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1853 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k7_ordinal2(B)) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & r1_ordinal1(A,C)))))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1854 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1855 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/8.99 1856 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & A = k1_ordinal2(B) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s7_ordinal2(C,k1_funct_1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | C = k1_xboole_0))) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(B))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1857 (all A all B -((exists C (v1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = 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))))) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_ordinal2(C) = A & v5_ordinal1(C) & v1_funct_1(C))) & A != B & (exists C (k1_ordinal2(C) = B & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & (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) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1858 (all A (v3_ordinal1(A) -> k15_ordinal2(k1_xboole_0,A) = k1_xboole_0)) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1859 (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)))) -> k1_xboole_0 = A | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1860 (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]. 8.95/9.01 1861 (all A all B (v3_ordinal1(B) -> (r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) <-> B = k7_ordinal2(A)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1862 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1863 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1864 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1865 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1866 (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]. 8.95/9.01 1867 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1868 (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]. 8.95/9.01 1869 (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]. 8.95/9.01 1870 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(A,k16_ordinal2(A,B)) = k16_ordinal2(A,k1_ordinal1(B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 8.95/9.01 1871 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (B = k11_ordinal2(A) <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(A) = k1_relat_1(C) & (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)))) & B = k8_ordinal2(C) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1872 (all A all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1873 (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]. 9.00/9.11 1874 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1875 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1876 (all A (A = k5_ordinal2 <-> v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v4_ordinal1(A) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1877 (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]. 9.00/9.11 1878 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1879 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1880 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1881 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f3_s16_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s16_ordinal2(D,k2_ordinal1(C,D)) | D = 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))))) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & v1_ordinal2(C)))))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & v4_ordinal1(f2_s16_ordinal2) & k1_xboole_0 != f2_s16_ordinal2 -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1882 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1883 (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) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_funct_1(C,k1_xboole_0) = f4_s6_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & (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))))) & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> f2_s6_ordinal2(A) = k1_funct_1(f1_s6_ordinal2,A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1884 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1885 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & (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))))) & (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))) & k1_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_relat_1(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]. 9.00/9.11 1886 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s11_ordinal2 & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> B = k1_xboole_0 | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & v5_ordinal1(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1887 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1888 (all A all B ((all C (r2_hidden(C,A) & (exists D (v3_ordinal1(D) & v4_ordinal1(D) & D = C)) <-> r2_hidden(C,B))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.00/9.11 1889 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)) & k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1890 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1891 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1892 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A)) | k1_xboole_0 = A))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1893 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1894 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & A = k14_ordinal2(B,C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1895 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1896 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1897 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1898 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1899 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1900 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1901 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1902 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_finset_1(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1903 (all A all B all C all D all E all F v1_finset_1(k4_enumset1(A,B,C,D,E,F))) # label(fc6_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1904 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1905 (all A all B all C all D all E all F all G v1_finset_1(k5_enumset1(A,B,C,D,E,F,G))) # label(fc7_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1906 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & (all C -((all D (r2_hidden(D,B) & r1_tarski(C,D) -> C = D)) & r2_hidden(C,B)))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1907 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1908 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1909 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1910 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1911 (all A exists B (v1_xboole_0(B) & v1_relat_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1912 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1913 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(t16_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1914 (all A -((all B -((all C (r2_hidden(C,A) -> r1_tarski(B,C))) & r2_hidden(B,A))) & v6_ordinal1(A) & A != k1_xboole_0 & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1915 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1916 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1917 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1918 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1919 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(D) & v1_finset_1(C) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1920 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1921 (all A all B (v1_finset_1(B) & r1_tarski(A,B) -> v1_finset_1(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1922 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1923 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1924 (all A all B (v1_finset_1(B) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1925 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> A = k1_xboole_0 | v1_finset_1(B))) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1926 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1927 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) & v1_finset_1(k10_relat_1(B,A)) -> v1_finset_1(A)))) # label(t27_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1928 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1929 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1930 v1_finset_1(f1_s2_finset_1) & (all A all B (r2_hidden(A,f1_s2_finset_1) & r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & p1_s2_finset_1(k1_xboole_0) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1931 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1932 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(C,B))))) & v6_ordinal1(A) & k1_xboole_0 != A & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1933 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1934 (all A (v1_finset_1(A) & (all B (r2_hidden(B,A) -> v1_finset_1(B))) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1935 (exists A (v1_relat_1(A) & f1_s1_finset_1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (-p1_s1_finset_1(B) -> f3_s1_finset_1(B) = k1_funct_1(A,B)) & (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B))))) & v1_funct_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1936 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1937 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1938 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1939 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1940 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1941 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1942 (all A all B all C all D all E all F all G all H v1_finset_1(k6_enumset1(A,B,C,D,E,F,G,H))) # label(fc8_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1943 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1944 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1945 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(A) <-> v1_finset_1(k1_relat_1(A))))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1946 (all A (v1_finset_1(A) <-> (exists B (r2_hidden(k1_relat_1(B),k5_ordinal2) & k2_relat_1(B) = A & v1_funct_1(B) & v1_relat_1(B))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1947 (all A all B all C all D v1_finset_1(k2_enumset1(A,B,C,D))) # label(fc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1948 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> v1_finset_1(B) | k1_xboole_0 = A)) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1949 (all A all B all C all D all E v1_finset_1(k3_enumset1(A,B,C,D,E))) # label(fc5_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1950 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(t15_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1951 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1952 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1953 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1954 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1955 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1956 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p2_s4_fraenkel(A,B) <-> p1_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1957 (all A (r2_hidden(A,a_0_36_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s20_fraenkel) & f4_s20_fraenkel = C & p1_s20_fraenkel(B,C) & A = f3_s20_fraenkel(B,C) & m1_subset_1(C,f2_s20_fraenkel))))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1958 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s19_fraenkel) & m1_subset_1(C,f2_s19_fraenkel) & p2_s19_fraenkel(B,C) & A = f3_s19_fraenkel(B,C))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1959 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & f2_s6_fraenkel(B) = A & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_10_fraenkel))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1960 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1961 (all A ((exists B (m1_subset_1(B,f1_s5_fraenkel) & p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1962 (all A (m1_subset_1(A,f1_s12_fraenkel) -> (all B (m1_subset_1(B,f2_s12_fraenkel) -> (p1_s12_fraenkel(A,B) -> p2_s12_fraenkel(f3_s12_fraenkel(A,B))))))) -> (all A (r2_hidden(A,a_0_20_fraenkel) -> p2_s12_fraenkel(A))) # label(s12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1963 (all A ((exists B (A = f3_s6_fraenkel(B) & p1_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1964 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p2_s9_fraenkel(A) <-> p1_s9_fraenkel(A))))) & k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1965 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s12_fraenkel) & p1_s12_fraenkel(B,C) & f3_s12_fraenkel(B,C) = A & m1_subset_1(B,f1_s12_fraenkel))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1966 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> k1_funct_2(C,D) = k1_xboole_0 | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1967 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1968 (all A all B all C (m1_fraenkel(C,A,B) -> v1_fraenkel(C) & -v1_xboole_0(C))) # label(dt_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1969 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (m1_subset_1(C,f2_s24_fraenkel) & B = f4_s24_fraenkel(C) & p1_s24_fraenkel(B,C) & r2_hidden(C,f3_s24_fraenkel))) <-> r2_hidden(B,A)))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1970 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1971 (all A (r2_hidden(A,a_0_37_fraenkel) <-> (exists B (f3_s20_fraenkel(B,f4_s20_fraenkel) = A & p1_s20_fraenkel(B,f4_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1972 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.11 1973 (all A ((exists B (r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel) & A = f5_s25_fraenkel(B) & m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1974 (all A (r2_hidden(A,a_0_38_fraenkel) <-> (exists B (r2_hidden(B,f2_s21_fraenkel) & A = f3_s21_fraenkel(B) & m1_subset_1(B,f1_s21_fraenkel))))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1975 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1976 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1977 (exists A (-v1_xboole_0(A) & v1_fraenkel(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1978 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> k1_xboole_0 = k1_funct_2(C,D) | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & E = k7_relat_1(F,C))))))))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1979 (all A all B (-v1_xboole_0(B) -> k1_fraenkel(A,B) = k1_funct_2(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1980 (all A (m1_subset_1(A,f1_s1_fraenkel) -> (p1_s1_fraenkel(A) -> p2_s1_fraenkel(A)))) -> r1_tarski(a_0_0_fraenkel,a_0_1_fraenkel) # label(s1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1981 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -((all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B))) & r2_hidden(A,f3_s26_fraenkel)))) -> (exists A ((all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1982 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1983 (all A (r2_hidden(A,a_0_32_fraenkel) <-> (exists B (m1_subset_1(B,f1_s17_fraenkel) & f3_s17_fraenkel(B) = A & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel) & p1_s17_fraenkel(B))))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1984 (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(A,B) & p1_s23_fraenkel(B,C) -> p1_s23_fraenkel(A,C)))))))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -((all B (m1_subset_1(B,f1_s23_fraenkel) -> -(p1_s23_fraenkel(B,A) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (r2_hidden(C,f2_s23_fraenkel) & p1_s23_fraenkel(C,B) -> p1_s23_fraenkel(B,C)))) & r2_hidden(B,f2_s23_fraenkel)))) & r2_hidden(A,f2_s23_fraenkel)))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1985 (all A ((exists B (m1_subset_1(B,f3_s13_fraenkel) & r2_hidden(B,a_0_22_fraenkel) & p2_s13_fraenkel(B) & A = B)) <-> r2_hidden(A,a_0_21_fraenkel))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1986 (all A (r2_hidden(A,a_0_19_fraenkel) -> p2_s11_fraenkel(A))) -> (all A (m1_subset_1(A,f1_s11_fraenkel) -> (all B (m1_subset_1(B,f2_s11_fraenkel) -> (p1_s11_fraenkel(A,B) -> p2_s11_fraenkel(f3_s11_fraenkel(A,B))))))) # label(s11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1987 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (m1_subset_1(B,f1_s1_fraenkel) & A = f2_s1_fraenkel(B) & p1_s1_fraenkel(B))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1988 (all A (r2_hidden(A,a_0_33_fraenkel) <-> (exists B (m1_subset_1(B,f1_s18_fraenkel) & A = f3_s18_fraenkel(B) & p1_s18_fraenkel(B) & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel))))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1989 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & A = f5_s22_fraenkel(B,C) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1990 (all A (r2_hidden(A,a_0_23_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(C,f2_s13_fraenkel))))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1991 (all A ((exists B (m1_subset_1(B,f1_s14_fraenkel) & p2_s14_fraenkel(B) & p1_s14_fraenkel(B) & f2_s14_fraenkel(B) = A)) <-> r2_hidden(A,a_0_26_fraenkel))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1992 (all A ((exists B exists C (m1_subset_1(B,f1_s11_fraenkel) & m1_subset_1(C,f2_s11_fraenkel) & p1_s11_fraenkel(B,C) & A = f3_s11_fraenkel(B,C))) <-> r2_hidden(A,a_0_19_fraenkel))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1993 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f3_s7_fraenkel(A,B) = f4_s7_fraenkel(A,B))))) -> a_0_12_fraenkel = a_0_13_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1994 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> p1_s19_fraenkel(A,B) & B = f4_s19_fraenkel))))) -> a_0_34_fraenkel = a_0_35_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1995 (all A (r2_hidden(A,a_0_6_fraenkel) <-> (exists B exists C (f3_s4_fraenkel(B,C) = A & p1_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel) & m1_subset_1(B,f1_s4_fraenkel))))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1996 (all A ((exists B exists C (m1_subset_1(C,f2_s16_fraenkel) & A = f3_s16_fraenkel(B,C) & p1_s16_fraenkel(B,C) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_30_fraenkel))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1997 v1_finset_1(f4_s22_fraenkel) & v1_finset_1(f3_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1998 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 1999 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2000 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f2_s6_fraenkel(A) = f3_s6_fraenkel(A)))) -> a_0_11_fraenkel = a_0_10_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2001 (all A (r2_hidden(A,a_0_22_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C))))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2002 (all A ((exists B exists C (f3_s16_fraenkel(B,C) = A & p2_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2003 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -((all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B))) & r2_hidden(A,f3_s27_fraenkel)))) -> (exists A (m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)) & (all B (m1_subset_1(B,f1_s27_fraenkel) -> (r2_hidden(B,f3_s27_fraenkel) -> p1_s27_fraenkel(B,k8_funct_2(f1_s27_fraenkel,f2_s27_fraenkel,A,B))))))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2004 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2005 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & A = f2_s14_fraenkel(B) & p1_s14_fraenkel(B) & r2_hidden(B,a_0_25_fraenkel))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2006 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,D,F) = k8_funct_2(A,B,C,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2007 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2008 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2009 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,C) = k7_relat_1(D,k3_xboole_0(B,C)))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2010 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & f3_s2_fraenkel(B,C) = A & p2_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2011 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2012 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p1_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2013 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (A = f3_s5_fraenkel(B) & p1_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2014 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(f3_s16_fraenkel(A,B) = f3_s16_fraenkel(C,B) & p2_s16_fraenkel(C,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2015 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2016 (all A ((exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & p1_s8_fraenkel(B,C) & f3_s8_fraenkel(B,C) = A & m1_subset_1(C,f2_s8_fraenkel))) <-> r2_hidden(A,a_0_14_fraenkel))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2017 (all A (r2_hidden(A,a_0_1_fraenkel) <-> (exists B (m1_subset_1(B,f1_s1_fraenkel) & f2_s1_fraenkel(B) = A & p2_s1_fraenkel(B))))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2018 (all A (m1_subset_1(A,f1_s2_fraenkel) -> (all B (m1_subset_1(B,f2_s2_fraenkel) -> (p1_s2_fraenkel(A,B) -> p2_s2_fraenkel(A,B)))))) -> r1_tarski(a_0_2_fraenkel,a_0_3_fraenkel) # label(s2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2019 (all A (r2_hidden(A,a_0_27_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & A = f3_s15_fraenkel(B,C) & p1_s15_fraenkel(B,C) & r2_hidden(B,a_0_28_fraenkel) & m1_subset_1(B,f1_s15_fraenkel))))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2020 (all A (r2_hidden(A,a_0_16_fraenkel) <-> (exists B (m1_subset_1(B,f1_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & p1_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel))))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2021 (all A (r2_hidden(A,a_0_15_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C))))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2022 (all A all B r1_tarski(k1_funct_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B)))) # label(t5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2023 (all A ((exists B (m1_subset_1(B,f1_s10_fraenkel) & p1_s10_fraenkel(B) & A = B)) <-> r2_hidden(A,a_0_18_fraenkel))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2024 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (f2_s3_fraenkel(B) = A & p2_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2025 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & p1_s7_fraenkel(B,C) & A = f4_s7_fraenkel(B,C) & m1_subset_1(C,f2_s7_fraenkel))))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2026 (all A ((exists B (r2_hidden(B,f3_s9_fraenkel) & p2_s9_fraenkel(B) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) = A & m1_subset_1(B,f1_s9_fraenkel))) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2027 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2028 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(B,A) = f3_s8_fraenkel(A,B))))) -> a_0_14_fraenkel = a_0_15_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2029 (all A (r2_hidden(A,a_0_25_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & p2_s14_fraenkel(B) & B = A)))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2030 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f2_s5_fraenkel(A) = f3_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2031 (all A ((exists B (m1_subset_1(B,f1_s19_fraenkel) & f3_s19_fraenkel(B,f4_s19_fraenkel) = A & p1_s19_fraenkel(B,f4_s19_fraenkel))) <-> r2_hidden(A,a_0_35_fraenkel))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2032 (all A (r2_hidden(A,a_0_7_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & m1_subset_1(C,f2_s4_fraenkel) & p2_s4_fraenkel(B,C) & f3_s4_fraenkel(B,C) = A)))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2033 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p1_s3_fraenkel(A) <-> p2_s3_fraenkel(A)))) -> a_0_5_fraenkel = a_0_4_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2034 (all A ((exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & p1_s15_fraenkel(B,C) & A = f3_s15_fraenkel(B,C) & m1_subset_1(C,f2_s15_fraenkel))) <-> r2_hidden(A,a_0_29_fraenkel))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2035 (all A ((exists B (A = B & p2_s15_fraenkel(B) & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_28_fraenkel))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2036 (all A all B all C (v1_fraenkel(C) & -v1_xboole_0(C) -> ((all D (m1_subset_1(D,C) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2037 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2038 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2039 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2040 (all A (v1_fraenkel(A) <-> (all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2041 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & f3_s7_fraenkel(B,C) = A & m1_subset_1(B,f1_s7_fraenkel))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2042 (all A all B (-v1_xboole_0(B) -> m1_fraenkel(k1_fraenkel(A,B),A,B))) # label(dt_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2043 (all A ((exists B exists C (m1_subset_1(B,f1_s2_fraenkel) & m1_subset_1(C,f2_s2_fraenkel) & f3_s2_fraenkel(B,C) = A & p1_s2_fraenkel(B,C))) <-> r2_hidden(A,a_0_2_fraenkel))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2044 v1_finset_1(f3_s25_fraenkel) & v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(A,f3_s25_fraenkel) = k7_relat_1(B,f3_s25_fraenkel) -> f5_s25_fraenkel(B) = f5_s25_fraenkel(A)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2045 (all A (-v1_xboole_0(A) -> (all B m1_fraenkel(k1_funct_2(B,A),B,A)))) # label(t11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2046 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2047 (all A ((exists B (np__0 = k1_funct_1(B,k13_arytm_3) & A = B & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))) <-> r2_hidden(A,a_0_0_numbers))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2048 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2049 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2050 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2051 (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]. 9.07/9.12 2052 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2053 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v3_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]. 9.07/9.12 2054 (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]. 9.07/9.12 2055 (all A (v1_xreal_0(A) & v3_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]. 9.07/9.12 2056 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2057 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2058 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & -v3_xreal_0(B) & v1_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]. 9.07/9.12 2059 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2060 (exists A (-v1_xboole_0(A) & v1_xcmplx_0(A) & -v2_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2061 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2062 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2063 (all A (v1_xreal_0(A) -> (-r1_xreal_0(np__0,A) <-> v3_xreal_0(A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2064 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2065 (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]. 9.07/9.12 2066 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2067 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2068 (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]. 9.07/9.12 2069 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2070 (all A (-v1_xboole_0(A) & -v3_xreal_0(A) & v1_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]. 9.07/9.12 2071 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2072 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2073 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> ((exists C ((exists D (r1_arytm_2(C,D) & D = B & C = A & m1_subset_1(D,k2_arytm_2))) & m1_subset_1(C,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_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) & k4_tarski(np__0,D) = B & m1_subset_1(D,k2_arytm_2))))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2) <-> r1_xreal_0(A,B)) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2074 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,B) | r1_xreal_0(B,A))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2075 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2076 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2077 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(A) & v1_xboole_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2078 (all A all B (-v2_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> 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]. 9.07/9.12 2079 (all A all B (v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2080 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & 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)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2081 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_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]. 9.07/9.12 2082 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2083 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2084 (all A (v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) -> v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2085 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2086 (all A (v1_xreal_0(A) & v1_xboole_0(A) -> -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2087 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2088 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2089 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2090 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v2_xreal_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2091 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2092 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2093 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2094 (all A all B (v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.12 2095 (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]. 9.07/9.12 2096 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2097 (all A (-v1_xboole_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2098 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2099 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2100 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2101 (exists A (v1_xreal_0(A) & v1_int_1(A) & v1_xcmplx_0(A) & m1_subset_1(A,k1_numbers))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2102 (all A (v1_xreal_0(A) -> k1_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2103 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k2_int_1(A) = A))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2104 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),k1_int_1(A))) & -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),k1_int_1(A))))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2105 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> np__0 = k4_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2106 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2107 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2108 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(C = k6_xcmplx_0(B,A) & r1_xreal_0(np__1,C)))) & -r1_xreal_0(B,A)))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2109 (all A (v1_int_1(A) -> (r1_xreal_0(np__0,A) -> r2_hidden(A,k5_numbers)))) # label(t16_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2110 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2111 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,B,C) & r1_int_1(B,D,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2112 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k4_int_1(A)) & -r1_xreal_0(np__1,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2113 (all A (v1_int_1(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2114 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)) & -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2115 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_int_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2116 (exists A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) & (all B (v1_int_1(B) -> (p1_s1_int_1(B) <-> r2_hidden(B,A)))))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2117 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (k6_xcmplx_0(A,B) = k3_xcmplx_0(C,D) & v1_int_1(D))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2118 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2119 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2120 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k5_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2121 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2122 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B != np__0 -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)) & (B = np__0 -> np__0 = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2123 (all A (v1_xreal_0(A) -> k3_int_1(A) = k4_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2124 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2125 (all A (v1_xreal_0(A) -> k2_int_1(A) = k2_int_1(k2_int_1(A)))) # label(t64_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2126 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (C = k3_xcmplx_0(A,B) & r1_int_1(D,E,C) -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2127 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2128 (all A (v1_xreal_0(A) -> k2_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2129 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2130 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2131 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(A,k1_int_1(A))) & -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2132 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2133 (all A (v1_int_1(A) -> (A != np__0 -> np__1 = k5_int_1(A,A)))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2134 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))) # label(t20_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2135 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k1_int_1(A) = k2_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2136 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,B) & r1_xreal_0(A,C) -> r1_xreal_0(k2_xcmplx_0(A,np__1),C) | C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2137 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(B,A) & r1_xreal_0(C,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | B = C | r1_xreal_0(C,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2138 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k2_xcmplx_0(A,np__1)) & v1_int_1(k6_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2139 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2140 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2141 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2142 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> ((exists C (v1_int_1(C) & B = k3_xcmplx_0(A,C))) <-> r2_int_1(A,B)))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2143 (all A (v1_int_1(A) -> k6_int_1(A,A) = np__0)) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2144 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (C = k2_xcmplx_0(B,A) -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2145 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2146 (all A ((all B (r2_hidden(B,A) <-> -(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != k1_real_1(C) & C != B)))) <-> k4_numbers = A)) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2147 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2148 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(np__0,k5_int_1(A,B)))))) # label(t82_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2149 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) & -r1_xreal_0(k2_xcmplx_0(A,np__1),B) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2150 p1_s4_int_1(f1_s4_int_1) & (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k2_xcmplx_0(A,np__1)) & p1_s4_int_1(k6_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2151 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2152 (all A (v1_xreal_0(A) -> (k1_int_1(A) = A <-> v1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2153 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2154 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = B & k1_real_1(np__1) = A | np__1 = B & A = np__1 <-> np__1 = k3_xcmplx_0(A,B)))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2155 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k2_xcmplx_0(A,C),B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2156 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2157 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2158 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2159 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2160 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) -> r2_hidden(k6_xcmplx_0(B,A),k5_numbers)))))) # label(t18_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2161 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,A,B))))) # label(t32_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2162 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xreal_0(A) & v1_int_1(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2163 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2164 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2165 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2166 (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) & (exists A (v1_int_1(A) & p1_s5_int_1(A))) -> (exists A (v1_int_1(A) & p1_s5_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2167 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_int_1(A),np__0) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(k4_int_1(A),np__0)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2168 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (B = A | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2169 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),C)))))))))))) # label(t38_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2170 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2171 p1_s2_int_1(f1_s2_int_1) & (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) & p1_s2_int_1(A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2172 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)) & -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2173 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2174 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2175 (all A all B (v1_int_1(B) & v1_int_1(A) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2176 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2177 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2178 (all A (v1_int_1(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k1_int_1(B))))))) # label(t81_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2179 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2180 (all A (v1_xreal_0(A) -> -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)) & -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2181 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2182 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),A))) # label(t52_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2183 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2184 (all A (v1_xreal_0(A) -> np__0 = k1_int_1(k4_int_1(A)))) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2185 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) -> r1_int_1(B,A,C)))))))) # label(t35_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2186 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2187 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2188 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (k1_int_1(A) = B <-> -r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2189 (all A (v1_int_1(A) -> r1_int_1(A,np__0,A) & r1_int_1(np__0,A,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2190 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = B & A = np__1 | A = k1_real_1(np__1) & B = np__1 <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2191 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2192 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2193 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_int_1(A),k2_int_1(A)))) # label(t61_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2194 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k3_int_1(A)) & v1_xreal_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2195 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2196 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2197 (all A (v1_int_1(A) -> (-r1_xreal_0(np__0,A) -> r1_xreal_0(A,k1_real_1(np__1))))) # label(t21_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2198 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k1_int_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k1_int_1(A),B))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2199 (exists A (v1_int_1(A) & p1_s6_int_1(A))) & (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) -> (exists A (v1_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))) & p1_s6_int_1(A))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2200 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(A,k6_xcmplx_0(B,np__1))))))) # label(t79_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2201 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,B,np__1))))) # label(t34_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2202 (all A (v1_xreal_0(A) -> (k1_int_1(A) = k2_int_1(A) <-> k2_xcmplx_0(k1_int_1(A),np__1) != k2_int_1(A)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2203 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,k6_xcmplx_0(C,B),D) <-> r1_int_1(k2_xcmplx_0(A,B),C,D)))))))))) # label(t40_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2204 (all A (v1_int_1(A) -> (p1_s3_int_1(A) & r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(k6_xcmplx_0(A,np__1))))) & p1_s3_int_1(f1_s3_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(A)))) # label(s3_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2205 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_int_1(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2206 (all A (m1_subset_1(A,k5_numbers) -> -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2207 (all A (v1_xreal_0(A) -> k2_int_1(A) = k1_int_1(k2_int_1(A)))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2208 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & r1_xreal_0(np__0,k1_int_1(A)) & r1_xreal_0(np__0,k2_int_1(A))))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2209 (all A (v1_xreal_0(A) -> k6_xcmplx_0(A,k1_int_1(A)) = k3_int_1(A))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2210 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != B & A != k1_real_1(B))) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2211 (all A (v1_int_1(A) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2212 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2213 (all A (v1_xreal_0(A) -> m1_subset_1(k4_int_1(A),k1_numbers))) # label(dt_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2214 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2215 (all A (v1_xreal_0(A) -> (np__0 != A -> k1_int_1(k7_xcmplx_0(A,A)) = np__1))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2216 (all A (v1_xreal_0(A) -> k2_xcmplx_0(k1_int_1(A),k4_int_1(A)) = A)) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2217 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2218 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k6_xcmplx_0(A,C),B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2219 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2220 (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]. 9.07/9.13 2221 (all A all B (v2_membered(B) & r2_hidden(B,A) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2222 (all A (-v1_xboole_0(A) & v4_membered(A) -> (exists B (v1_int_1(B) & r2_hidden(B,A))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2223 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2224 (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]. 9.07/9.13 2225 (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]. 9.07/9.13 2226 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2227 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2228 (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]. 9.07/9.13 2229 (all A ((all B (r2_hidden(B,A) -> v1_rat_1(B))) <-> v3_membered(A))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2230 (exists A ((all B (v1_int_1(B) -> (p1_s4_membered(B) <-> r2_hidden(B,A)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2231 (all A all B all C (v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2232 (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]. 9.07/9.13 2233 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2234 (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]. 9.07/9.13 2235 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2236 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (A = B <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2237 (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]. 9.07/9.13 2238 (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]. 9.07/9.13 2239 (all A (v4_membered(A) <-> (all B (r2_hidden(B,A) -> v1_int_1(B))))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2240 (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]. 9.07/9.13 2241 (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]. 9.07/9.13 2242 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2243 (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]. 9.07/9.13 2244 (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]. 9.07/9.13 2245 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2246 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2247 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v1_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2248 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2249 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2250 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_rat_1(B) & v1_int_1(B) & v4_ordinal2(B) & v1_xcmplx_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2251 (all A all B all C (v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2252 (all A all B (r2_hidden(B,A) & v4_membered(B) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2253 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2254 (all A (v1_xboole_0(A) -> v1_membered(A) & v2_membered(A) & v5_membered(A) & v4_membered(A) & v3_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2255 (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]. 9.07/9.13 2256 (exists A (v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v1_membered(A) & -v1_xboole_0(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2257 (all A all B (v1_int_1(A) & v1_int_1(B) -> v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2258 (all A all B (v4_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2259 (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]. 9.07/9.13 2260 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2261 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2262 (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]. 9.07/9.13 2263 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2264 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.13 2265 (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]. 9.07/9.13 2266 (all A all B (v5_membered(B) & v5_membered(A) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2267 (all A all B (v3_membered(B) & v3_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2268 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> k2_numbers = A))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2269 (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]. 9.07/9.14 2270 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2271 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2272 (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]. 9.07/9.14 2273 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2274 (exists A ((all B (v4_ordinal2(B) -> (r2_hidden(B,A) <-> p1_s5_membered(B)))) & v5_membered(A))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2275 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2276 (exists A (v1_membered(A) & (all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2277 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2278 (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]. 9.07/9.14 2279 (all A all B (v3_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2280 (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]. 9.07/9.14 2281 (all A (v4_ordinal2(A) -> v2_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2282 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2283 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2284 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v2_membered(A) & v1_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2285 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2286 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2287 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_rat_1(B) & v1_int_1(B) & v1_xreal_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2288 (exists A ((all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))) & v2_membered(A))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2289 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> k4_numbers = A))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2290 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2291 (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]. 9.07/9.14 2292 (all A all B (v4_membered(A) & v4_membered(B) -> v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2293 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v4_ordinal2(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2294 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2295 (all A all B all C (v1_int_1(A) & v1_int_1(C) & v1_int_1(B) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2296 (all A all B (v2_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2297 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2298 (all A (v3_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2299 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2300 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2301 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (B = A <-> (all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2302 (all A all B (v5_membered(A) & v5_membered(B) -> v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2303 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2304 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2305 (all A (v1_xreal_0(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2306 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (r2_hidden(B,A) & v1_xcmplx_0(B))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2307 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (B = A <-> (all C (v1_int_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2308 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2309 (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]. 9.07/9.14 2310 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2311 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> k3_numbers = A))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2312 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2313 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2314 (all A all B (v4_membered(A) -> v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2315 (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]. 9.07/9.14 2316 (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]. 9.07/9.14 2317 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2318 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2319 (all A (v1_int_1(A) -> v2_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2320 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> 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]. 9.07/9.14 2321 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (A = B <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2322 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2323 (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]. 9.07/9.14 2324 (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]. 9.07/9.14 2325 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2326 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2327 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2328 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2329 (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]. 9.07/9.14 2330 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v1_membered(A) & v2_membered(A) & v3_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2331 (all A all B (v5_membered(A) -> v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2332 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v5_membered(B) & v4_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2333 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2334 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2335 (all A (-v1_xboole_0(A) & v2_membered(A) -> (exists B (v1_xreal_0(B) & r2_hidden(B,A))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2336 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2337 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t27_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2338 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-r1_xreal_0(B,A) <-> r2_hidden(k1_card_1(A),k1_card_1(B))))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2339 (all A (v3_ordinal1(A) -> k3_card_1(k1_ordinal1(A)) = k2_card_1(k3_card_1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2340 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2341 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v2_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2342 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(k1_nat_1(A,np__1)) = k2_card_1(k1_card_1(A)))) # label(t76_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2343 (all A (v1_finset_1(A) -> m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers))) # label(dt_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2344 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = k1_card_1(k5_numbers) & B = k1_ordinal2(C) & v5_ordinal1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2345 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2346 (all A r2_hidden(k1_card_1(A),k1_card_1(k1_zfmisc_1(A)))) # label(t30_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2347 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k3_card_1(A),k3_card_1(B)) <-> r2_hidden(A,B)))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2348 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> k2_card_1(B) != A)) <-> v2_card_1(A)))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2349 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_ordinal1(A) = k1_nat_1(A,np__1))) # label(t52_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2350 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2351 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2352 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2353 (all A all B (k1_card_1(A) = k1_card_1(B) -> k2_card_1(B) = k2_card_1(A))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2354 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> -r2_wellord2(A,B) & r2_hidden(k1_card_1(A),k1_card_1(B)))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2355 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2356 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2357 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> A = B))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2358 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2359 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (r1_tarski(A,k2_relat_1(C)) & B = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2360 (all A all B (v1_finset_1(A) & r2_wellord2(A,B) -> v1_finset_1(B))) # label(t68_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2361 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) & r2_wellord2(A,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2362 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2363 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s2_card_1(B)))) -> p1_s2_card_1(A)))) -> (all A (v1_card_1(A) -> p1_s2_card_1(A))) # label(s2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2364 (all A (v1_card_1(A) -> v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2365 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2366 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2367 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2368 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2369 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2370 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2371 (all A (m1_subset_1(A,k5_numbers) -> v2_ordinal1(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2372 (all A (v3_ordinal1(A) -> v2_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v3_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2373 (all A (v1_finset_1(A) & v1_card_1(A) -> (exists B (k1_card_1(B) = A & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2374 (exists A (v1_finset_1(A) & v1_card_1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2375 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2376 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2377 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2378 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k3_card_1(A),k3_card_1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2379 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2380 (all A all B (v1_card_1(B) -> (B = k1_card_1(A) <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2381 (all A k4_card_1(k1_tarski(A)) = np__1) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2382 (all A all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) & (all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2383 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2384 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2385 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> k1_xboole_0 = A | p1_s1_card_1(A)))) & (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & p1_s1_card_1(k1_xboole_0) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2386 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k1_card_1(A))) # label(t66_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2387 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2388 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2389 (all A all B all C (r1_tarski(A,B) & r2_wellord2(A,C) & r1_tarski(B,C) -> r2_wellord2(A,B) & r2_wellord2(B,C))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2390 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2391 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2392 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2393 (all A all B (v1_card_1(B) -> (r2_hidden(A,B) -> r2_hidden(k1_card_1(A),B)))) # label(t25_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2394 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_ordinal1(A,B) <-> r1_xreal_0(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2395 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2396 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (A = B <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2397 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2398 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> r2_wellord2(k3_relat_1(A),k2_wellord2(A))))) # label(t22_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2399 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2400 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k3_card_1(C)))) & A = k1_relat_1(B) -> k3_card_1(A) = k1_card_1(k8_ordinal2(B)))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2401 (all A (v1_finset_1(A) -> v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2402 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k4_card_1(A),k4_card_1(B))))))) # label(t80_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2403 (all A all B (v1_card_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_card_1(A),B)))) # label(t23_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2404 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2405 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k4_card_1(A) = B <-> k1_card_1(A) = k1_card_1(B)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2406 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2407 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.14 2408 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(A) = k3_card_1(B) -> A = B))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2409 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> -r1_tarski(B,A)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2410 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(A) = k4_card_1(B)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2411 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2412 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2413 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2414 (all A (v1_card_1(A) <-> (exists B ((all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))) & B = A & v3_ordinal1(B))))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2415 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2416 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> r1_xreal_0(A,B)))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2417 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2418 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2419 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k1_card_1(A)) & v1_finset_1(A))) # label(t69_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2420 (all A (v1_finset_1(A) -> k4_card_1(A) = k1_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2421 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2422 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2423 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2424 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2425 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r1_tarski(A,B) & B != A <-> r2_hidden(A,B)))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2426 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2427 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2428 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2429 (all A all B (r2_wellord2(A,k1_tarski(B)) <-> (exists C k1_tarski(C) = A))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2430 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2431 (all A all B all C all D (r1_xboole_0(A,B) & r1_xboole_0(C,D) & r2_wellord2(B,D) & r2_wellord2(A,C) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2432 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2433 (all A -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))) & v1_finset_1(A))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2434 (all A (r2_wellord2(A,k1_xboole_0) <-> k1_xboole_0 = A)) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2435 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2436 (all A all B (r2_wellord2(A,B) -> k2_card_1(A) = k2_card_1(B))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2437 (all A all B (k1_card_1(k1_tarski(B)) = k1_card_1(A) <-> (exists C A = k1_tarski(C)))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2438 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2439 (all A all B (r2_wellord2(A,B) <-> k1_card_1(A) = k1_card_1(B))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2440 (all A all B all C all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (np__3 = k3_finseq_1(D) & B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & A = k1_funct_1(D,np__1) <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2441 (all A (v1_relat_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2442 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2443 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2444 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> B = A))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2445 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k5_finseq_1(B) = k12_finseq_1(A,B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2446 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2447 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -((all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A))) & A != k1_xboole_0))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2448 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B))) & r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))))) -> (exists A (k2_finseq_1(f2_s5_finseq_1) = k4_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & m2_finseq_1(A,f1_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2449 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2450 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B))))) # label(t23_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2451 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2452 (all A (v4_ordinal2(A) -> k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(A))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2453 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> C = k3_finseq_1(k16_finseq_1(A,B,C))))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2454 (all A all B all C (k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C) & k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2455 (all A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2456 (all A all B all C (m1_finseq_1(B,A) & v4_ordinal2(C) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2457 (exists A all B ((exists C (v1_relat_1(C) & v1_finseq_1(C) & r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & B = C & p1_s4_finseq_1(C) & v1_funct_1(C))) <-> r2_hidden(B,A))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2458 (all A all B (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2459 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) = A)))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2460 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2461 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k3_finseq_1(B),C) -> k16_finseq_1(A,B,C) = B))))) # label(t79_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2462 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2463 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)) = A)) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2464 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(B,k2_finseq_1(A)) -> r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t81_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2465 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2466 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(B) = k2_finseq_1(A) -> B = A))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2467 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(A,C) & m2_finseq_1(B,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2468 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2469 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (k4_finseq_1(A) = k1_xboole_0 <-> k1_xboole_0 = A))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2470 (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> k1_funct_1(A,B) = f2_s2_finseq_1(B)))) & f1_s2_finseq_1 = k3_finseq_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2471 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2472 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2473 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) & p1_s3_finseq_1(k1_xboole_0) -> (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2474 (all A (v4_ordinal2(A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(k2_xcmplx_0(A,np__1))))) # label(t6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2475 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2476 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2477 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) & r2_hidden(B,k2_finseq_1(A)) | r1_xreal_0(B,np__0)))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2478 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) = k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2479 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2480 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2481 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2482 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k2_relat_1(A) & v2_funct_1(B) & v2_funct_1(A) -> k3_finseq_1(A) = k3_finseq_1(B)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2483 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2484 (all A all B (m1_finseq_1(B,A) -> v1_xboole_0(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2485 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> r2_wellord2(k2_finseq_1(A),A))) # label(t75_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2486 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k6_finseq_1(B) = A <-> np__0 = k3_finseq_1(A))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2487 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2488 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (k3_finseq_1(C) = A & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2489 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2490 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2491 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_finseq_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2492 (all A (-v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2493 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2494 (all A (v1_funct_1(k9_finseq_1(A)) & v1_relat_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2495 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2496 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> r1_xreal_0(C,k3_finseq_1(A)) | k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2497 (all A all B (m2_finseq_1(B,A) <-> m1_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2498 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) -> k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,C)))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2499 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2500 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2501 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B)))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2502 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2503 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (C = k7_relat_1(B,k2_finseq_1(A)) & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C) & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2504 (all A exists B (v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_relat_1(B) & m1_finseq_1(B,A))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2505 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2506 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k2_relat_1(k14_finseq_1(k1_relat_1(A))) = k1_relat_1(A))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2507 (all A (v4_ordinal2(A) -> k4_card_1(k2_finseq_1(A)) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2508 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_card_1(A) = A & k4_card_1(k1_card_1(A)) = A)) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2509 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k2_finseq_1(np__1) & A = k1_funct_1(B,np__1) <-> k9_finseq_1(A) = B))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2510 (all A -(v1_finset_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,k2_finseq_1(B)))))) # label(t77_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2511 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2512 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k7_finseq_1(A,k1_xboole_0) = A & k7_finseq_1(k1_xboole_0,A) = A)) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2513 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (np__1 = k3_finseq_1(B) & A = k1_funct_1(B,np__1) <-> B = k9_finseq_1(A)))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2514 (exists A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2515 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2516 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A))))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2517 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2518 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2519 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2520 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(k2_finseq_1(A)) = k1_card_1(A))) # label(t76_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2521 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2522 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2523 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) <-> C = k7_finseq_1(A,B)))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2524 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> -(r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> k7_finseq_1(A,E) != C)) & k7_finseq_1(C,D) = k7_finseq_1(A,B)))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2525 (all A all B (r1_tarski(A,B) -> r1_tarski(k13_finseq_1(A),k13_finseq_1(B)))) # label(t83_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2526 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,k3_relat_1(A)) & (exists E (v1_relat_1(E) & v1_funct_1(E) & r1_xreal_0(np__1,k3_finseq_1(E)) & k1_funct_1(E,np__1) = C & k1_funct_1(E,k3_finseq_1(E)) = D & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r1_xreal_0(k3_finseq_1(E),F) | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A)))) & v1_finseq_1(E))) & r2_hidden(D,k3_relat_1(A))))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2527 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -(r2_hidden(A,B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k4_tarski(C,k1_funct_1(B,C)) = A & r2_hidden(C,k4_finseq_1(B)))))))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2528 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_finseq_1(B)) <-> (exists C (r1_xreal_0(C,B) & r1_xreal_0(np__1,C) & A = C & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2529 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2530 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(np__1,A) & r1_xreal_0(A,B) <-> r2_hidden(A,k2_finseq_1(B))))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2531 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.15 2532 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(D = A & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B)))))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2533 (exists A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2534 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2535 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2536 (all A k6_finseq_1(A) = k1_xboole_0) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2537 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k3_finseq_1(A) = k3_finseq_1(B) -> A = B))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2538 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2539 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2540 (all A all B all C (v1_funct_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2541 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & (all B -p1_s1_finseq_1(A,B))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) -> C = B)))) -> (exists A (v1_relat_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1) & v1_funct_1(A))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2542 (all A (v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2543 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2544 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2545 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (m1_finseq_1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2546 (all A all B all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k1_funct_1(C,np__1) & k1_funct_1(C,np__2) = B & k3_finseq_1(C) = np__2 <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2547 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k7_finseq_1(A,B) -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2548 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2549 (all A (v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2550 (all A all B all C k11_finseq_1(A,B,C) = k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C))) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2551 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2552 (all A (v4_ordinal2(A) -> r2_hidden(A,k2_finseq_1(A)) | np__0 = A)) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2553 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2554 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(k7_finseq_1(A,B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2555 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_relat_1(A) = k2_finseq_1(B) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2556 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (k7_finseq_1(B,A) = k7_finseq_1(B,C) | k7_finseq_1(C,B) = k7_finseq_1(A,B) -> C = A))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2557 (all A (v1_finset_1(A) <-> (exists B (v1_funct_1(B) & A = k2_relat_1(B) & v1_finseq_1(B) & v1_relat_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2558 (all A all B (m2_finseq_1(B,A) -> v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) & v1_funct_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2559 (exists A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2560 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k9_finseq_1(A) = B <-> k2_relat_1(B) = k1_tarski(A) & k2_finseq_1(np__1) = k4_finseq_1(B)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2561 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_relat_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2562 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2563 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2564 (all A (v1_relat_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = k1_relat_1(A))) <-> v1_finseq_1(A)))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2565 (all A (v1_funct_1(A) & v1_relat_1(A) -> -((all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -r1_tarski(A,B))) & (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B))))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2566 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (k1_xboole_0 = k14_finseq_1(A) <-> A = k1_xboole_0))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2567 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2568 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2569 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> A = k1_xboole_0))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2570 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1))) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2571 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> k1_card_1(A) = k3_finseq_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2572 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> k7_finseq_1(B,C) = k8_finseq_1(A,B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2573 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2574 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k3_finseq_1(A) = np__0 <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2575 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) = k2_finseq_1(A) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2576 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2577 (all A all B k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) = k10_finseq_1(A,B)) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2578 (all A (v4_ordinal2(A) -> a_1_0_finseq_1(A) = k1_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2579 (all A (v4_ordinal2(A) -> m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2580 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2581 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2582 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2583 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2584 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (B = k9_finseq_1(A) <-> np__1 = k3_finseq_1(B) & k1_tarski(A) = k2_relat_1(B)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2585 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2586 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2587 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) = k15_finseq_1(A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2588 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> k7_relat_1(B,k2_finseq_1(C)) = k16_finseq_1(A,B,C))))) # label(d15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2589 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2590 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_finseq_1(A) -> v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2591 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k14_finseq_1(A) = B <-> k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(-r1_xreal_0(D,C) & F = k1_funct_1(B,D) & r1_xreal_0(F,E) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,C))))))))))))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2592 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2593 (all A all B ((all C (r2_hidden(C,B) <-> m2_finseq_1(C,A))) <-> k13_finseq_1(A) = B)) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2594 (exists A (v1_xboole_0(A) & v2_funct_1(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2595 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2596 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> r1_tarski(k2_finseq_1(A),k2_finseq_1(B))))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2597 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2598 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2599 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2600 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(-r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(D,k4_finseq_1(B)) & k1_nat_1(k3_finseq_1(A),D) = C))) & r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B)))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2601 (all A all B ((all C (r2_hidden(C,B) -> m2_finseq_1(C,A))) <-> m1_finseq_2(B,A))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2602 (all A (v4_ordinal2(A) -> (all B k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2603 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_finseq_2(k1_nat_1(A,np__1)) = k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,np__1))))) # label(t60_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2604 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2605 (all A all B (m2_finseq_1(B,A) -> m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)))) # label(t110_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2606 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2607 (all A all B (-v1_xboole_0(B) & v4_ordinal2(A) -> -v1_xboole_0(k4_finseq_2(A,B)))) # label(fc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2608 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_xreal_0(k3_finseq_1(B),A) -> k5_relat_1(k1_finseq_2(A),B) = B))))) # label(t64_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2609 (all A all B all C all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m2_finseq_1(F,D) -> (all G (v1_funct_1(G) & v1_funct_2(G,D,E) & m2_relset_1(G,D,E) -> (k11_finseq_1(A,B,C) = F -> k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) = k1_partfun1(k5_numbers,D,D,E,F,G)))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2610 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2611 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.07/9.16 2612 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2613 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,A) -> (all H (m2_finseq_1(H,B) -> (G = k12_finseq_1(A,D) & H = k12_finseq_1(B,E) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k3_funcop_1(F,G,H)))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2614 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_square_1(A,k3_finseq_1(C)) = k3_finseq_1(B)))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2615 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A)) & v1_relat_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2616 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B)) & v1_relat_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2617 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> k6_finseq_1(A) = B)) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2618 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funcop_1(D,B,A) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2619 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m1_subset_1(D,B) -> k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,np__1)) = D)))))))) # label(t136_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2620 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (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,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> (all J (m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_2(J,k2_zfmisc_1(A,B),C) & v1_funct_1(J) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (k11_finseq_1(D,E,F) = K & k11_finseq_1(G,H,I) = L -> k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) = k3_funcop_1(J,K,L)))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2621 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (k4_finseq_2(B,C) = k4_finseq_2(A,C) -> B = A))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2622 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(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_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,k6_finseq_1(A),F))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2623 (all A (-v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.16 2624 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -(k3_finseq_1(B) = k1_nat_1(A,np__1) & (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D k7_finseq_1(C,k9_finseq_1(D)) != B)))))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2625 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> m2_finseq_2(k10_finseq_1(B,C),A,k4_finseq_2(np__2,A)))))))) # label(t121_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2626 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (m2_finseq_1(H,B) -> (k10_finseq_1(E,F) = H -> k5_funcop_1(G,D,H) = k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F))))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2627 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2628 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> np__0 = k2_square_1(np__0,k6_xcmplx_0(A,B))))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2629 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (k1_partfun1(k5_numbers,A,A,B,D,E) = C -> k3_finseq_1(C) = k3_finseq_1(D)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2630 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> r2_hidden(A,k2_finseq_1(k1_nat_1(B,C)))))))))) # label(t9_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2631 (all A k4_finseq_2(np__0,A) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A))) # label(t112_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2632 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & v1_funct_1(H) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (I = k10_finseq_1(D,E) & k10_finseq_1(F,G) = J -> k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G))))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2633 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (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,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (k11_finseq_1(D,E,F) = I -> k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) = k4_funcop_1(H,I,G)))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2634 (all A (v4_ordinal2(A) -> (all B k4_finseq_2(A,B) = a_2_0_finseq_2(A,B)))) # label(d4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2635 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)))))))))) # label(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2636 (exists A (m2_finseq_1(A,f2_s1_finseq_2) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> k1_funct_1(A,B) = f3_s1_finseq_2(B)))) & k3_finseq_1(A) = f1_s1_finseq_2)) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2637 (all A (m1_finseq_2(k13_finseq_1(A),A) & -v1_xboole_0(k13_finseq_1(A)))) # label(t104_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2638 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k2_finseq_2(k1_nat_1(A,B),C) = k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C))))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2639 (all A m1_subset_1(k6_finseq_1(A),k4_finseq_2(np__0,A))) # label(t114_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2640 (all A (v4_ordinal2(A) -> (all B k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A)))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2641 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__3,A) = a_1_2_finseq_2(A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2642 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_2(B,k4_finseq_1(B),A) & m2_relset_1(B,k4_finseq_1(B),A) & v1_funct_1(B))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2643 (all A all B all C (v4_ordinal2(B) -> (r2_hidden(A,a_2_0_finseq_2(B,C)) <-> (exists D (m2_finseq_2(D,C,k3_finseq_2(C)) & A = D & k3_finseq_1(D) = B))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2644 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_finseq_2(B)) <-> (exists C exists D exists E (m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,B) & k11_finseq_1(C,D,E) = A))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2645 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (A != np__0 -> (all D (m1_subset_1(D,k2_finseq_1(A)) -> C = k1_funct_1(k2_finseq_2(A,C),D)))))))))) # label(t71_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2646 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (D = k9_finseq_1(A) -> k9_finseq_1(k1_funct_1(E,A)) = k1_partfun1(k5_numbers,B,B,C,D,E)))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2647 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2648 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (m2_finseq_1(H,A) -> (H = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) = k4_funcop_1(G,H,F)))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2649 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) & v1_relat_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2650 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> r1_tarski(B,k3_finseq_2(A)))) # label(t105_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2651 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> a_3_0_finseq_2(A,B,C) = k4_finseq_2(k1_nat_1(A,B),C))))))) # label(t125_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2652 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_square_1(np__0,A) = A & k4_square_1(A,np__0) = A & k3_square_1(A,np__0) = np__0 & k3_square_1(np__0,A) = np__0)) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2653 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k2_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))) & k3_finseq_1(C) = A & k3_finseq_1(B) = A -> C = B))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2654 (all A k2_finseq_2(np__0,A) = k1_xboole_0) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2655 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> m2_finseq_2(k11_finseq_1(B,C,D),A,k4_finseq_2(np__3,A)))))))))) # label(t124_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2656 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_finseq_2(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & k4_finseq_2(C,B) = A))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2657 (all A (v4_ordinal2(A) -> k3_finseq_1(k1_finseq_2(A)) = A)) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2658 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (C = k5_relat_1(D,B) & r1_xreal_0(A,k3_finseq_1(B)) -> k3_finseq_1(C) = A))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2659 (all A (v4_ordinal2(A) -> m2_finseq_1(k6_partfun1(k2_finseq_1(A)),k5_numbers))) # label(t52_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2660 p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2)) & (all A (m2_finseq_1(A,f1_s2_finseq_2) -> (all B (m1_subset_1(B,f1_s2_finseq_2) -> (p1_s2_finseq_2(A) -> p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B)))))))) -> (all A (m2_finseq_1(A,f1_s2_finseq_2) -> p1_s2_finseq_2(A))) # label(s2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2661 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2662 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k5_funcop_1(E,D,F),C))))))))))))) # label(t91_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2663 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_finseq_1(k2_finseq_2(A,C),B))))))) # label(t77_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2664 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2665 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2666 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (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) -> (all G (m2_finseq_1(G,A) -> (G = k12_finseq_1(A,D) -> k4_funcop_1(F,G,E) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t100_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2667 (all A (v4_ordinal2(A) -> v1_funct_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)) & v1_relat_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2668 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> -((all E (m2_finseq_1(E,C) -> (all F (m2_finseq_1(F,C) -> -(A = k3_finseq_1(E) & B = k3_finseq_1(F) & k8_finseq_1(C,E,F) = D))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2669 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2670 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> m2_finseq_1(k11_finseq_1(B,C,D),A))))))))) # label(t16_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2671 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(C) -> m2_finseq_1(k1_partfun1(k4_finseq_1(B),k4_finseq_1(B),k5_numbers,A,C,B),A))))))) # label(t51_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2672 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2673 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k3_funcop_1(D,E,F),C))))))))))))) # label(t84_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2674 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (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) -> k5_funcop_1(E,D,k6_finseq_1(B)) = k6_finseq_1(C))))))))))) # label(t93_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2675 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(k1_nat_1(A,np__1),B)) -> (exists D ((exists E (m1_subset_1(E,B) & C = k8_finseq_1(B,D,k12_finseq_1(B,E)))) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2676 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k5_funcop_1(C,A,B)) & v1_finseq_1(k5_funcop_1(C,A,B)) & v1_relat_1(k5_funcop_1(C,A,B))))))) # label(t80_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2677 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(B) -> v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2678 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D (r2_hidden(B,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) = k5_relat_1(k11_finseq_1(B,C,D),A))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2679 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2680 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_finseq_1(E,C) -> (all F (v1_funct_2(F,C,D) & m2_relset_1(F,C,D) & v1_funct_1(F) -> (E = k10_finseq_1(A,B) -> k1_partfun1(k5_numbers,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B))))))))))) # label(t40_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2681 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2682 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(D) -> (r1_xreal_0(B,k3_finseq_1(C)) -> np__0 = B & A != np__0 | v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C))))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2683 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(E) -> (r1_xreal_0(B,k3_finseq_1(D)) -> np__0 != A & B = np__0 | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C)))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2684 (all A (v4_ordinal2(A) -> k4_finseq_1(k1_finseq_2(A)) = k2_finseq_1(A))) # label(t54_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2685 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k3_funcop_1(D,A,B) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_square_1(k3_finseq_1(A),k3_finseq_1(B))))))))))) # label(t79_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2686 (all A (v4_ordinal2(A) -> k6_partfun1(k2_finseq_1(A)) = k1_finseq_2(A))) # label(d1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2687 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (k7_finseq_1(D,k9_finseq_1(B)) = k7_finseq_1(C,k9_finseq_1(A)) -> B = A & D = C))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2688 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers) & m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers))))) # label(t1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2689 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2690 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> A = k3_finseq_1(C))))))) # label(t109_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2691 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r2_hidden(A,k2_finseq_1(B)) & A != k1_nat_1(B,np__1) & r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2692 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_tarski(A,C) & r1_tarski(B,C) & k3_finseq_1(A) = k3_finseq_1(B) -> A = B))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2693 (all A all B (-v1_xboole_0(B) -> ((exists C (A = k12_finseq_1(B,C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2694 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,B) -> (E = k5_funcop_1(F,D,G) -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2695 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (m1_subset_1(C,A) & k12_finseq_1(A,C) = B)))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2696 (all A all B all C (m2_finseq_1(C,A) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2697 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)))))))))))) # label(t133_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2698 (all A all B (v4_ordinal2(A) -> m1_finseq_2(k4_finseq_2(A,B),B))) # label(dt_k4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2699 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (B = k5_relat_1(C,A) & k4_finseq_1(A) = k2_relat_1(C) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2700 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> A = k1_funct_1(k1_finseq_2(B),A)))))) # label(t56_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2701 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2702 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k1_funct_1(B,C) = A & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,k2_relat_1(B))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2703 (all A k10_finseq_1(A,A) = k2_finseq_2(np__2,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2704 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_finseq_2(k2_finseq_2(A,C),B,k4_finseq_2(A,B)))))))) # label(t132_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2705 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2706 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> C = k5_relat_1(k1_finseq_2(A),C))))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2707 (all A (v4_ordinal2(A) -> (all B k3_finseq_1(k2_finseq_2(A,B)) = A))) # label(t69_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2708 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_2(C,k2_finseq_1(A),B) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2709 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (B = k2_finseq_1(A) -> (all D (m2_finseq_1(D,C) -> (all E (m2_finseq_1(E,B) -> (r1_xreal_0(A,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k5_numbers,B,k5_numbers,C,E,D),C))))))))))))) # label(t35_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2710 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_finseq_2(B)) <-> (exists C exists D (m1_subset_1(C,B) & A = k10_finseq_1(C,D) & m1_subset_1(D,B)))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2711 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m1_finseq_2(C,B) & -v1_xboole_0(C) -> m1_finseq_2(C,A) & -v1_xboole_0(C))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2712 (all A all B k2_tarski(A,B) = k2_relat_1(k10_finseq_1(A,B))) # label(t147_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2713 (all A all B all C all D (-v1_xboole_0(D) & m2_subset_1(C,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_3_0_finseq_2(B,C,D)) <-> (exists E exists F (m2_finseq_2(E,D,k4_finseq_2(B,D)) & k8_finseq_1(D,E,F) = A & m2_finseq_2(F,D,k4_finseq_2(C,D))))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2714 (all A all B (v4_ordinal2(A) -> v1_finseq_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_relat_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2715 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_finseq_1(A) = k2_relat_1(D) & k5_relat_1(D,B) = C & r1_xreal_0(A,k3_finseq_1(B)) -> k3_finseq_1(C) = A))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2716 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2717 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (E = k4_funcop_1(F,G,D) -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2718 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k2_finseq_2(k1_nat_1(A,np__1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B))))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2719 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> (all D (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (r1_xreal_0(A,k3_finseq_1(C)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B)))))))))) # label(t50_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2720 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,B) -> (k11_finseq_1(E,F,G) = I -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2721 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2722 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_relat_1(C,k2_finseq_1(A)) = B & r1_xreal_0(k3_finseq_1(C),A) -> C = B))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2723 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(np__0,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> D = k8_finseq_1(B,C,D) & D = k8_finseq_1(B,D,C))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.17 2724 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k2_square_1(np__0,k6_xcmplx_0(B,A)) = k6_xcmplx_0(B,A)))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2725 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k5_numbers,B) & v1_funct_2(D,k5_numbers,B) -> (k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) = C -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2726 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,C) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,B,k4_finseq_2(A,B)) -> m2_finseq_2(k4_funcop_1(F,G,E),D,k4_finseq_2(A,D)))))))))))))))) # label(t142_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2727 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2728 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(B,C),D) & m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_1(E) -> (all F (m2_finseq_2(F,B,k4_finseq_2(A,B)) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t140_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2729 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),np__1))) # label(t19_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2730 (all A (v4_ordinal2(A) -> v1_funct_1(k1_finseq_2(A)) & v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2731 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m2_finseq_2(k12_finseq_1(A,B),A,k4_finseq_2(np__1,A)))))) # label(t118_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2732 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t129_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2733 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__1,A) = a_1_0_finseq_2(A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2734 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2735 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> (all E (m2_finseq_2(E,C,k4_finseq_2(B,C)) -> m2_finseq_2(k8_finseq_1(C,D,E),C,k4_finseq_2(k1_nat_1(A,B),C)))))))))))) # label(t127_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2736 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(A,C) = B & r1_tarski(k2_relat_1(A),k1_relat_1(C)) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2737 (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,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> m2_finseq_1(k4_funcop_1(E,F,D),C))))))))))))) # label(t97_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2738 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2739 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2740 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_finseq_1(A) = k2_relat_1(D) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B))))))))))) # label(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2741 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C (m1_subset_1(C,A) & (exists D (B = k10_finseq_1(C,D) & m1_subset_1(D,A))))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2742 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (exists C m2_finseq_2(C,A,B)))) # label(existence_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2743 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2744 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k6_finseq_1(B) = k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2745 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & (exists E (k11_finseq_1(C,D,E) = B & m1_subset_1(E,A))))))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2746 (all A all B all C k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C)) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2747 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -((all C (m2_finseq_1(C,A) -> (all D (m1_subset_1(D,A) -> B != k8_finseq_1(A,C,k12_finseq_1(A,D)))))) & np__0 != k3_finseq_1(B)))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2748 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_3_finseq_2(A)) = k3_finseq_2(A))) # label(t128_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2749 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -((all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> -(k3_finseq_1(E) = B & k7_finseq_1(D,E) = C & k3_finseq_1(D) = A))))) & k3_finseq_1(C) = k1_nat_1(A,B)))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2750 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> m2_finseq_2(k1_finseq_2(A),k5_numbers,k4_finseq_2(A,k5_numbers)))) # label(t131_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2751 (all A k9_finseq_1(A) = k2_finseq_2(np__1,A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2752 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (np__0 != A -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> k1_funct_1(k1_finseq_2(A),B) = B))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2753 (all A k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2754 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k2_finseq_1(A) = k4_finseq_1(C))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2755 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & m2_relset_1(F,k2_zfmisc_1(B,C),D) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t141_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2756 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k2_square_1(np__0,k6_xcmplx_0(A,B)),k1_numbers,k5_numbers))))) # label(t5_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2757 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funcop_1(D,A,B) = C & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2758 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k7_relat_1(B,k2_finseq_1(A)) = k5_relat_1(k1_finseq_2(A),B))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2759 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_square_1(B,C) = A -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A)))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2760 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,B) -> (G = k12_finseq_1(B,E) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k5_funcop_1(F,D,G)))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2761 (all A (-v1_xboole_0(A) -> a_1_1_finseq_2(A) = k4_finseq_2(np__2,A))) # label(t119_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2762 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G))))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2763 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_finseq_1(G) = k3_finseq_1(F) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(F) = k3_finseq_1(D) & k3_finseq_1(G) = k3_finseq_1(D)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2764 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k5_numbers,B) & v1_funct_2(C,k5_numbers,B) & v1_funct_1(C) -> m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B))))))) # label(t31_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2765 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C)) -> (exists E ((exists F (D = k8_finseq_1(C,E,F) & m2_finseq_2(F,C,k4_finseq_2(B,C)))) & m2_finseq_2(E,C,k4_finseq_2(A,C)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2766 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (m2_finseq_1(C,B) -> (r2_hidden(A,k4_finseq_1(C)) -> r2_hidden(k1_funct_1(C,A),B)))))) # label(t13_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2767 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k2_finseq_1(A)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2768 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> m2_finseq_1(k10_finseq_1(B,C),A))))))) # label(t15_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2769 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> k1_funct_1(k2_finseq_2(A,C),B) = C)))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2770 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(k2_card_3(A),B)))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2771 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C all D k4_tarski(C,D) != A) & r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2772 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k2_card_3(A) <-> k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) = k1_funct_1(B,C)))))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2773 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2774 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k4_card_3(A) = k1_xboole_0))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2775 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> np__0 = k7_card_3(A)))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2776 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) -> r2_hidden(A,B)))))) # label(t59_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2777 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2778 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_setfam_1(B) -> v1_fraenkel(k4_card_3(C)) & -v1_xboole_0(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2779 (all A (v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(A) -> -v1_xboole_0(k4_card_3(A)) & v1_fraenkel(k4_card_3(A)))) # label(fc5_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2780 (all A all B all C r1_tarski(k5_card_3(C,k3_xboole_0(A,B)),k3_xboole_0(k5_card_3(C,A),k5_card_3(C,B)))) # label(t28_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2781 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) & v1_funct_1(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2782 (all A all B all C k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B)) = k5_card_3(C,k2_xboole_0(A,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2783 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2784 (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)) -> r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) | B = A))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2785 (all A all B r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A))) # label(t31_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2786 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2787 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2788 (all A all B r1_tarski(k3_card_3(k2_funcop_1(A,B)),B)) # label(t15_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2789 (all A all B k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A))) = k2_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2790 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) <-> k1_card_3(A) = B))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2791 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2792 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2793 (all A all B k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2794 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2795 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t46_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2796 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k6_card_3(k2_funcop_1(A,B)) = k2_card_2(A,B))))) # label(t52_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2797 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2798 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2799 (all A all B (v1_card_1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2800 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_card_3(A)) & v1_relat_1(k2_card_3(A)))) # label(dt_k2_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2801 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_card_3(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_1(k1_funct_1(A,B))))))) # label(d1_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2802 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k4_classes1(A)))) # label(t57_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2803 (all A all B (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2804 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C))))))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2805 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))))) # label(t54_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2806 (all A (v1_card_1(A) -> k6_card_3(k2_funcop_1(k1_xboole_0,A)) = np__0)) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2807 (all A -(v6_ordinal1(A) & (all B -((all C -((all D -((all E (r2_hidden(E,C) -> r1_tarski(D,E))) & r2_hidden(D,C))) & k1_xboole_0 != C & r1_tarski(C,B))) & k3_tarski(A) = k3_tarski(B) & r1_tarski(B,A))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2808 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2809 (all A all B k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B))) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2810 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2811 (all A k5_card_3(A,k1_xboole_0) = k1_xboole_0) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2812 (all A all B all C (C = k5_card_3(A,B) <-> (all D ((exists E (v1_funct_1(E) & r2_hidden(E,B) & D = k1_funct_1(E,A) & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2813 (all A (v1_card_1(A) -> (all B A = k6_card_3(k2_funcop_1(k1_tarski(B),A))))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2814 (all A all B all C r1_tarski(k5_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k5_xboole_0(A,C)))) # label(t30_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2815 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)))) # label(t55_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2816 (all A (v1_card_1(A) -> (all B k7_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t51_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2817 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_tarski(k2_relat_1(A)) = k3_card_3(A))) # label(d4_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2818 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(A) -> r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t45_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2819 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2820 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r2_hidden(k6_card_3(A),k7_card_3(B))))))) # label(t56_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2821 (all A (v1_card_1(A) -> (all B (v6_ordinal1(B) & (all C (r2_hidden(C,B) -> r2_hidden(k1_card_1(C),A))) -> r1_tarski(k1_card_1(k3_tarski(B)),A))))) # label(t62_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2822 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k5_card_3(A,k2_tarski(B,C)) = k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)))))) # label(t26_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2823 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2824 (exists A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2825 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k1_card_1(k3_card_3(k2_card_3(A))) = k6_card_3(A))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2826 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k7_card_3(k2_funcop_1(A,B)) = k3_card_2(B,A))))) # label(t53_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2827 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_card_3(A,k4_card_3(B)) | k4_card_3(B) = k1_xboole_0))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2828 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k1_tarski(k1_funct_1(B,A)) = k5_card_3(A,k1_tarski(B)))) # label(t25_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2829 (all A all B (A != k1_xboole_0 -> k3_card_3(k2_funcop_1(A,B)) = B)) # label(t16_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2830 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2831 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(k2_mcart_1(A),k1_relat_1(B)) & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) <-> r2_hidden(A,k3_card_3(k2_card_3(B)))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2832 (all A all B B = k3_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2833 (all A all B all C r1_tarski(k4_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k4_xboole_0(A,C)))) # label(t29_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2834 f1_s3_card_3 != k1_xboole_0 & (all A all B all C (p1_s3_card_3(A,B) & p1_s3_card_3(B,C) -> p1_s3_card_3(A,C))) & (all A all B (p1_s3_card_3(B,A) | p1_s3_card_3(A,B))) -> (exists A (r2_hidden(A,f1_s3_card_3) & (all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2835 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_card_1(k7_card_3(A)))) # label(dt_k7_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.18 2836 (exists A (v1_relat_1(A) & v1_funct_1(A) & f1_s4_card_3 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s4_card_3) -> (all C (r2_hidden(C,f2_s4_card_3(B)) & p1_s4_card_3(B,C) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2837 (all A all B k2_zfmisc_1(B,A) = k3_card_3(k2_card_3(k2_funcop_1(A,B)))) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2838 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_card_3(A),k3_card_3(B))))))) # label(t35_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2839 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)))) # label(t58_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2840 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) & k1_relat_1(A) = f1_s1_card_3 & (all B (r2_hidden(B,f1_s1_card_3) -> f2_s1_card_3(B) = k1_funct_1(A,B))))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2841 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k4_card_3(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D (v1_relat_1(D) & C = D & (all E (r2_hidden(E,k1_relat_1(A)) -> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)))) & k1_relat_1(A) = k1_relat_1(D) & v1_funct_1(D))))))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2842 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2843 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> k7_card_3(A) = k1_card_1(k4_card_3(A)))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2844 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> A = k1_card_3(A))) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2845 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(A,B)))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2846 (all A (v3_ordinal1(A) -> (all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) -> r2_hidden(A,B)))))) # label(t60_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2847 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r2_hidden(np__0,k2_relat_1(B)) | r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t47_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2848 (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_tarski(k2_card_3(A),k2_card_3(B))))))) # label(t34_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2849 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k4_card_3(A)))) # label(fc3_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2850 (all A all B (p1_s2_card_3(A,B) & p1_s2_card_3(B,A) -> A = B)) & (all A all B all C (p1_s2_card_3(A,B) & p1_s2_card_3(B,C) -> p1_s2_card_3(A,C))) & f1_s2_card_3 != k1_xboole_0 -> (exists A (r2_hidden(A,f1_s2_card_3) & (all B -(r2_hidden(B,f1_s2_card_3) & B != A & p1_s2_card_3(B,A))))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2851 (all A (v1_card_1(A) -> k7_card_3(k2_funcop_1(k1_xboole_0,A)) = np__1)) # label(t49_card_3) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2852 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> -r2_hidden(k1_xboole_0,k2_relat_1(B)))) # label(t149_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2853 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k3_pboole(A,C,D)) -> r4_pboole(A,B,C) & r4_pboole(A,B,D)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2854 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) & p1_s2_pboole(B,C) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2855 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2856 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2857 (all A all B (m1_pboole(B,A) -> (all C (r2_hidden(C,A) -> m1_subset_1(k1_funct_1(B,C),k2_relat_1(B)))))) # label(t151_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2858 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2859 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & (all E (m1_pboole(E,A) -> (r2_pboole(A,E,D) & r2_pboole(A,E,C) -> r2_pboole(A,E,B)))) & r2_pboole(A,B,D) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2860 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k3_pboole(A,C,D)) <-> r1_pboole(A,B,C) & r1_pboole(A,B,D)))))))) # label(t8_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2861 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v3_relat_1(B) -> -v2_relat_1(B)))))) # label(cc2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2862 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) -> r6_pboole(A,B,C)))))) # label(t86_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2863 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,k4_pboole(A,C,B)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t63_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2864 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r6_pboole(A,B,C) -> r6_pboole(A,C,B)))) # label(symmetry_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2865 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B)))) & r4_pboole(A,B,C)))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2866 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k4_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2867 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) = k5_pboole(A,B,C))))) # label(d12_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2868 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r7_pboole(A,B,C)))))) # label(t130_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2869 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,B,k1_pboole(A)),B))) # label(t65_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2870 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (m4_pboole(C,A,B) <-> r2_pboole(A,C,B)))))) # label(d23_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2871 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r7_pboole(A,B,C) & r7_pboole(A,C,D) -> r7_pboole(A,B,D)))))))) # label(t132_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2872 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,D,C)),k3_pboole(A,k2_pboole(A,B,D),C))))))))) # label(t27_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2873 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) -> v1_relat_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2874 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,D) & r2_pboole(A,B,C)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2875 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2876 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2877 (all A all B all C (-v1_xboole_0(A) & v2_relat_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2878 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v2_relat_1(B) -> -v3_relat_1(B)))))) # label(cc1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2879 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)),B) -> r2_pboole(A,k3_pboole(A,C,D),B)))))))) # label(t41_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2880 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),B)))))) # label(t127_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2881 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2882 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2883 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r2_pboole(A,B,C) -> r2_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t19_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2884 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) & r1_pboole(A,B,D) -> r4_pboole(A,C,D)))))))) # label(t10_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2885 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C) & m4_pboole(C,A,B))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2886 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> v2_relat_1(C)))))) # label(t145_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2887 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v3_relat_1(B) & r2_pboole(A,C,B) -> v3_relat_1(C)))))) # label(t142_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2888 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k11_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2889 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t35_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2890 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2891 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t87_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2892 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (all D (m3_pboole(D,A,B,C) -> v1_funcop_1(D))))) # label(cc3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2893 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) & r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))))))))) # label(t45_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2894 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r4_pboole(A,B,C) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2895 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D))))))))))) # label(t61_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2896 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) | r4_pboole(A,B,D) -> r4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t106_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2897 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2898 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) & r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2899 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t126_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2900 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> k3_pboole(A,B,C) = D))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2901 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2902 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k11_pboole(A,B,C),A))) # label(dt_k11_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2903 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) -> v1_setfam_1(k2_relat_1(A))))) # label(t1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2904 (all A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) -> (k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> C = k13_pboole(A,B)))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2905 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r6_pboole(A,B,C) <-> C = B))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2906 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)))))) # label(t67_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2907 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2908 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2909 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r2_pboole(A,k3_pboole(A,B,C),k2_pboole(A,B,D)))))))) # label(t26_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2910 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,B,C),k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)) & r6_pboole(A,B,k1_pboole(A))))))) # label(t54_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2911 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r7_pboole(A,B,B))) # label(reflexivity_r7_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2912 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,C,k2_pboole(A,C,B))))))) # label(t103_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2913 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t59_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2914 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D)) & r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2915 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2916 (all A all B (m1_pboole(B,A) -> -(B != k1_pboole(A) & r5_pboole(A,B,B)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2917 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),B) <-> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2918 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2919 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (m1_pboole(B,A) <-> A = k1_relat_1(B)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2920 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (m1_pboole(C,A) & r1_pboole(A,C,B))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2921 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & v2_relat_1(B) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2922 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),B) & r6_pboole(A,k3_pboole(A,C,B),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2923 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k5_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),D))))))))) # label(t97_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2924 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k3_pboole(A,B,C),A))) # label(dt_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2925 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r2_pboole(A,B,C)))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2926 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> v1_funct_1(k6_pboole(A,B)) & -v3_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & v1_relat_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2927 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2928 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2929 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (m2_pboole(C,A,B) <-> (all D (r2_hidden(D,A) -> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D))))))))) # label(d17_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2930 (all A all B all C (-v1_xboole_0(A) & m1_pboole(C,A) & m1_pboole(B,A) -> (r3_pboole(A,B,C) <-> r1_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2931 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k5_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k4_pboole(A,C,k2_pboole(A,B,D)))))))))) # label(t96_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2932 (all A all B (m1_pboole(B,A) -> (r2_pboole(A,B,k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))) # label(t50_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2933 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,B,C) = k2_pboole(A,C,B))) # label(commutativity_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2934 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2935 (all A -(f2_s1_pboole(A) = k1_xboole_0 & r2_hidden(A,f1_s1_pboole))) -> (exists A ((all B (r2_hidden(B,f1_s1_pboole) -> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)))) & m1_pboole(A,f1_s1_pboole))) # label(s1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2936 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2937 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E))))))))))) # label(t23_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2938 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r1_pboole(A,D,C)))) <-> r7_pboole(A,B,C)))))) # label(d14_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2939 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2940 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2941 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r2_hidden(D,A) & r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2942 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t104_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2943 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)))))) # label(t129_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2944 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k3_pboole(A,B,C) = k3_pboole(A,C,B))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2945 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D)),B) -> r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t40_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2946 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k4_pboole(A,C,D)) -> r4_pboole(A,B,C)))))))) # label(t113_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2947 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2948 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,C)))))) # label(t89_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2949 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C)) = k2_finseq_2(A,C)))) # label(t152_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2950 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,B,k4_pboole(A,C,B)))))) # label(t118_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2951 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k2_pboole(A,B,B))) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2952 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,B,B),k1_pboole(A)))) # label(t64_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2953 (all A all B (m1_pboole(B,A) -> (all C (m2_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2954 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,C)))))) # label(t120_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2955 (all A -(r2_hidden(A,f1_s3_pboole) & (all B -p1_s3_pboole(A,B)))) -> (exists A (m1_pboole(A,f1_s3_pboole) & (all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2956 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),D)))))))) # label(t68_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2957 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(B = k1_pboole(A) & r4_pboole(A,B,B)))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2958 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t78_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2959 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),C),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,B,k2_pboole(A,B,C)),k2_pboole(A,B,C)))))) # label(t47_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2960 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> v1_xboole_0(k1_funct_1(B,C)))) <-> v3_relat_1(B)))) # label(d15_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2961 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r3_pboole(A,B,k1_pboole(A)))))) # label(t136_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2962 (all A all B (m1_pboole(B,A) -> v1_relat_1(B) & v1_funct_1(B))) # label(dt_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2963 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2964 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t38_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2965 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) -> (r3_pboole(A,B,C) -> -r3_pboole(A,C,B)))) # label(antisymmetry_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2966 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r2_pboole(A,C,D) & r5_pboole(A,B,D) & -r5_pboole(A,B,C)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2967 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r6_pboole(A,B,B))) # label(reflexivity_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2968 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))))))) # label(t83_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2969 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2970 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))))))))) # label(t39_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2971 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k5_pboole(A,k5_pboole(A,B,C),D),k5_pboole(A,B,k5_pboole(A,C,D))))))))) # label(t98_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.19 2972 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,B,C) <-> r2_pboole(A,B,C) & r2_pboole(A,C,B)))))) # label(d13_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2973 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,k1_pboole(A),B),k1_pboole(A)))) # label(t66_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2974 (all A all B (m1_pboole(B,A) -> ((all C -(r2_hidden(C,A) & v1_xboole_0(k1_funct_1(B,C)))) <-> v2_relat_1(B)))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2975 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,k3_pboole(A,B,C))))))) # label(t102_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2976 (all A (v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(k9_pboole(A)))) # label(dt_k9_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2977 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t88_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2978 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r7_pboole(A,B,C) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2979 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k2_pboole(A,B,C),A))) # label(dt_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2980 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)))) <-> k14_pboole(A,B,C) = D))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2981 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) & -r4_pboole(A,B,C)))))))) # label(t114_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2982 (all A all B (m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A))) <-> B = k9_pboole(A)))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2983 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r4_pboole(A,B,C) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2984 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k4_pboole(A,C,D)) -> r4_pboole(A,C,k4_pboole(A,B,D))))))))) # label(t115_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2985 (all A all B all C all D (v2_relat_1(D) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k5_relat_1(C,D) = k8_pboole(A,B,C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2986 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (exists D m3_pboole(D,A,B,C)))) # label(existence_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2987 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t79_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2988 (all A all B all C all D (v1_funct_2(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A))) # label(dt_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2989 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k1_funct_1(k5_pboole(A,B,C),D) = k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2990 (all A all B (m1_pboole(B,A) -> m1_pboole(k6_pboole(A,B),k3_finseq_2(A)))) # label(dt_k6_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2991 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C all D (m1_pboole(D,k1_tarski(C)) -> (k2_funcop_1(k1_tarski(C),A) = D -> k1_funct_2(k2_finseq_1(B),A) = k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B)))))))) # label(t153_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2992 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t94_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2993 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k3_pboole(A,k1_pboole(A),B),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,B,k1_pboole(A)),k1_pboole(A)))) # label(t55_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2994 (all A exists B (v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & m1_pboole(B,A))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2995 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r4_pboole(A,B,D) & r2_pboole(A,D,E) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2996 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k2_pboole(A,B,C))))))) # label(t105_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2997 (exists A ((all B (r2_hidden(B,f1_s4_pboole) -> k1_funct_1(A,B) = f2_s4_pboole(B))) & m1_pboole(A,f1_s4_pboole))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2998 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))) & r6_pboole(A,k3_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t46_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 2999 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(C,A,B) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k7_pboole(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3000 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),B) -> r5_pboole(A,B,C)))))) # label(t128_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3001 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k5_pboole(A,B,C) = k5_pboole(A,C,B))) # label(commutativity_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3002 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))) # label(t121_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3003 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3004 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)))))) # label(t73_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3005 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,D,C),k4_pboole(A,D,B))))))))) # label(t60_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3006 (all A all B (v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_1(k10_pboole(A,B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3007 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,C),C) & r6_pboole(A,k2_pboole(A,C,B),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3008 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,C,B))))))) # label(t100_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3009 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t80_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3010 (all A all B (m1_pboole(B,A) -> (exists C m2_pboole(C,A,B)))) # label(existence_m2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3011 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3012 (all A k2_funcop_1(A,k1_xboole_0) = k1_pboole(A)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3013 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3014 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k3_pboole(A,B,C),C) & r2_pboole(A,k3_pboole(A,B,C),B))))) # label(t17_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3015 (all A all B (m1_pboole(B,A) -> (v2_pboole(B,A) <-> v2_relat_1(B)))) # label(redefinition_v2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3016 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,C,k2_pboole(A,B,C)) & r2_pboole(A,B,k2_pboole(A,B,C)))))) # label(t16_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3017 (all A (v1_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3018 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3019 (all A all B all C (m1_pboole(B,A) & v1_funcop_1(C) & m1_pboole(C,A) -> m1_pboole(k14_pboole(A,B,C),A))) # label(dt_k14_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3020 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_pboole(A,B,C),D) -> r2_pboole(A,C,D) & r2_pboole(A,B,D)))))))) # label(t43_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3021 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3022 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3023 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),k4_pboole(A,B,C)))))) # label(t81_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3024 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r4_pboole(A,k1_pboole(A),B) & -r4_pboole(A,B,k1_pboole(A)))))) # label(t138_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3025 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) | r1_pboole(A,B,D) -> r1_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t7_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3026 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k4_pboole(A,C,D)) -> r1_pboole(A,B,C)))))))) # label(t12_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3027 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))))))))) # label(t85_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3028 (all A exists B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3029 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t95_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3030 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3031 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,C,D) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3032 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t70_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3033 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k4_pboole(A,B,C),B))))) # label(t62_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3034 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k2_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3035 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (all D (m3_pboole(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3036 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,C,k2_pboole(A,k4_pboole(A,C,B),B)) & r6_pboole(A,C,k2_pboole(A,B,k4_pboole(A,C,B)))))))) # label(t72_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3037 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A))))))) # label(t58_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3038 (all A all B (m1_pboole(B,A) -> (r6_pboole(A,B,k1_pboole(A)) <-> v3_relat_1(B)))) # label(t141_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3039 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3040 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_funct_1(B,D))) -> B = C))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3041 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t34_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3042 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,C,D)),k3_pboole(A,D,B)),k3_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,C,D)),k2_pboole(A,D,B))))))))) # label(t42_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3043 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,C,B),D) & r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3044 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_xboole_0 = k1_funct_1(B,C))) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3045 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))))))))) # label(t75_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3046 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & r5_pboole(A,B,C)))))))) # label(t135_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3047 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k12_pboole(A,B,C),A))) # label(dt_k12_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3048 (all A all B (m1_pboole(B,A) -> (exists C m4_pboole(C,A,B)))) # label(existence_m4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3049 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d4_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3050 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r5_pboole(A,E,C) & r5_pboole(A,D,B) & r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) -> r6_pboole(A,E,B) & r6_pboole(A,D,C)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3051 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> D = k12_pboole(A,B,C)))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3052 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k3_pboole(A,B,C)),k3_pboole(A,B,C)) & r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),C),k3_pboole(A,B,C)))))) # label(t48_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3053 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t82_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3054 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,C,D) & r4_pboole(A,B,C) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3055 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,B,D) & r5_pboole(A,C,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3056 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,B,B),k1_pboole(A)))) # label(t92_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3057 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3058 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) & r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))))))))) # label(t21_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3059 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)))))) # label(t119_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3060 (exists A (m1_pboole(A,f1_s5_pboole) & (all B (m1_subset_1(B,f1_s5_pboole) -> k1_funct_1(A,B) = f2_s5_pboole(B))))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3061 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),C),k4_pboole(A,B,C)))))) # label(t84_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3062 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,B) & r1_pboole(A,E,C) <-> r1_pboole(A,E,D)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3063 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3064 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) <-> r1_pboole(A,D,C)))) -> r6_pboole(A,C,B)))))) # label(t147_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3065 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) & r2_pboole(A,C,D) -> r1_pboole(A,B,D)))))))) # label(t9_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3066 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))))) # label(t139_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3067 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_relat_1(A) <-> k1_xboole_0 = A | k2_relat_1(A) = k1_tarski(k1_xboole_0)))) # label(t2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3068 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,B,C))))))) # label(t101_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3069 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r5_pboole(A,B,C) -> r5_pboole(A,C,B)))) # label(symmetry_r5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3070 (all A (m1_pboole(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3071 (all A all B all C all D (-v1_xboole_0(B) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3072 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & v1_funct_1(k1_funct_1(D,E)))) <-> m3_pboole(D,A,B,C)))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3073 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> (C = k6_pboole(A,B) <-> (all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k4_card_3(k5_relat_1(D,B)) = k1_funct_1(C,D)))))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3074 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k2_relat_1(B)) -> (exists D (C = k1_funct_1(B,D) & r2_hidden(D,A))))))))) # label(t150_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3075 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k2_pboole(A,C,D)) <-> r2_pboole(A,C,B) & (all E (m1_pboole(E,A) -> (r2_pboole(A,C,E) & r2_pboole(A,D,E) -> r2_pboole(A,B,E)))) & r2_pboole(A,D,B)))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3076 (all A all B (m1_pboole(B,A) -> (v1_pboole(B,A) <-> v3_relat_1(B)))) # label(redefinition_v1_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3077 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3078 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,B,C)),k3_pboole(A,B,C)))))) # label(t74_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3079 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3080 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k5_pboole(A,B,C),A))) # label(dt_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3081 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A))))))))) # label(t52_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3082 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r3_pboole(A,B,C) & k1_pboole(A) = k3_pboole(A,C,D) & r3_pboole(A,B,D)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3083 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3084 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3085 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B))))) # label(t71_pboole) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3086 $T # label(t4_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3087 (all A (v2_membered(A) -> v1_xreal_0(k2_seq_4(A)))) # label(dt_k2_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3088 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -((all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> -(m1_seqm_3(B,A) & v4_seq_2(B)))) & v3_seq_2(A)))) # label(t57_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3089 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> r1_xreal_0(A,np__0) | np__0 = k2_seq_2(B)))))) # label(t44_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3090 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) -> r1_xreal_0(B,k3_seq_4(A))))))) # label(t60_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3091 $T # label(t6_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3092 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,A,B) = k6_real_1(np__1,k1_nat_1(k2_nat_1(B,B),np__1)))) -> np__0 = k2_seq_2(A) & v4_seq_2(A)))) # label(t49_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3093 (all A (v1_xreal_0(A) -> k1_seq_4(A) = k1_tarski(A))) # label(redefinition_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3094 $T # label(t21_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3095 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k4_seq_4(A),k1_numbers))) # label(dt_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3096 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(B) & v5_seqm_3(A) -> k2_seq_2(k10_seq_1(A,B)) = k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) & k4_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) = k2_seq_2(k11_seq_1(A,B)) & k2_seq_2(k10_seq_1(B,A)) = k5_real_1(k2_seq_2(B),k8_funct_2(k5_numbers,k1_numbers,A,np__0)) & k3_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) = k2_seq_2(k9_seq_1(A,B))))))) # label(t59_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3097 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k2_seq_4(A) = k4_seq_4(A))) # label(redefinition_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3098 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k5_seq_4(A),k1_numbers))) # label(dt_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3099 (all A (v2_membered(A) -> -(-v1_xboole_0(A) & v2_seq_4(A) & (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(r2_hidden(D,A) & -r1_xreal_0(k2_xcmplx_0(B,C),D))))))))))))) # label(t18_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3100 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> A != k1_seqm_3(B,C)))))))) # label(t35_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3101 $T # label(t34_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3102 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v4_seq_2(A) <-> (all B (v1_xreal_0(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(B,k18_complex1(k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,D),k8_funct_2(k5_numbers,k1_numbers,A,C)))) & r1_xreal_0(C,D))))) & -r1_xreal_0(B,np__0))))))) # label(t58_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.20 3103 $T # label(t11_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3104 $T # label(t1_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3105 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> -((all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(C != B & r2_hidden(C,A) & r2_hidden(B,A)))))) & -r1_xreal_0(k4_seq_4(A),k5_seq_4(A))) & -((exists B ((exists C (r2_hidden(C,A) & C != B & r2_hidden(B,A) & v1_xreal_0(C))) & v1_xreal_0(B))) & r1_xreal_0(k4_seq_4(A),k5_seq_4(A))) | v1_xboole_0(A)))) # label(t25_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3106 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k5_numbers,k1_numbers) & v1_funct_2(C,k5_numbers,k1_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(k2_nat_1(D,D),A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> k2_seq_2(C) = np__0 & v4_seq_2(C) | r1_xreal_0(A,np__0)))))))) # label(t50_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3107 (all A (v1_xreal_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r2_hidden(k2_xcmplx_0(C,A),B)))) -> (all C (v1_xreal_0(C) -> -r2_hidden(C,B))) | (all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & -r1_xreal_0(D,C) & r2_hidden(D,B))))) | r1_xreal_0(A,np__0)))))) # label(t9_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3108 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(B) & m1_seqm_3(A,B) -> v4_seq_2(A)))))) # label(t29_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3109 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v6_seqm_3(A) & v3_seq_2(A) -> v4_seq_2(A)))) # label(t53_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3110 $T # label(t20_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3111 (all A (v1_xreal_0(A) -> A = k4_seq_4(k1_seq_4(A)) & k5_seq_4(k1_seq_4(A)) = A)) # label(t22_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3112 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) -> B = k2_seq_4(A)))))) # label(t63_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3113 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v4_seqm_3(A) & v2_seq_2(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k2_seq_2(A),k8_funct_2(k5_numbers,k1_numbers,A,B))))))) # label(t55_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3114 (all A (m1_relset_1(A,k5_numbers,k1_numbers) -> (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & v5_seqm_3(A) -> v1_funct_2(A,k5_numbers,k1_numbers) & v4_seq_2(A) & v1_seq_1(A) & v1_funct_1(A)))) # label(cc1_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3115 (all A (v1_xreal_0(A) -> -(all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(B,A))))) # label(t10_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3116 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (exists B (v1_funct_1(B) & v7_seqm_3(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v6_seqm_3(k3_seqm_3(B,A)) & v1_seqm_3(B) & v1_funct_2(B,k5_numbers,k1_numbers))))) # label(t56_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3117 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (k2_seq_2(k22_seq_1(A)) = np__0 & v4_seq_2(k22_seq_1(A)) -> k2_seq_2(A) = np__0 & v4_seq_2(A)))) # label(t28_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3118 (all A (v2_membered(A) -> -(v1_seq_4(A) & (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A)))) & -r1_xreal_0(C,np__0)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B))))))) & -v1_xboole_0(A)))) # label(t16_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3119 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v2_seq_4(A) & v1_seq_4(A) <-> v3_seq_4(A)))) # label(d3_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3120 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((exists C (k8_funct_2(k5_numbers,k1_numbers,B,C) = A & m2_subset_1(C,k1_numbers,k5_numbers))) & v5_seqm_3(B) | v5_seqm_3(B) & r2_hidden(A,k2_relat_1(B)) -> A = k2_seq_2(B)))))) # label(t40_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3121 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v2_membered(B) -> (v1_seq_4(B) & r1_tarski(A,B) -> r1_xreal_0(k2_seq_4(A),k2_seq_4(B))))))) # label(t65_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3122 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v3_seqm_3(A) & v1_seq_2(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k8_funct_2(k5_numbers,k1_numbers,A,B),k2_seq_2(A))))))) # label(t54_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3123 (all A (v1_xreal_0(A) -> m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)))) # label(dt_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3124 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(B) -> v4_seq_2(k1_seqm_3(B,A)) & k2_seq_2(k1_seqm_3(B,A)) = k2_seq_2(B)))))) # label(t33_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3125 (all A (v1_xreal_0(A) -> (all B (v2_membered(B) & -v1_xboole_0(B) -> ((all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,B) -> r1_xreal_0(C,D)))) -> r1_xreal_0(C,A)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r1_xreal_0(A,C)))) -> A = k3_seq_4(B)))))) # label(t61_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3126 $T # label(t2_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3127 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_real_1(np__1,k1_nat_1(B,np__1)) = k8_funct_2(k5_numbers,k1_numbers,A,B))) -> np__0 = k2_seq_2(A) & v4_seq_2(A)))) # label(t45_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3128 (all A (v1_xreal_0(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)))) -> r1_xreal_0(A,np__0) | v4_seq_2(B)))))) # label(t47_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3129 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> k18_complex1(k2_seq_2(A)) = k2_seq_2(k22_seq_1(A))))) # label(t27_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3130 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> r1_xreal_0(k5_seq_4(A),k4_seq_4(A)) | v1_xboole_0(A)))) # label(t24_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3131 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v5_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,A,B) = k2_seq_2(A)))))) # label(t41_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3132 (all A (v1_xreal_0(A) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> r1_xreal_0(A,np__0) | v4_seq_2(B)))))) # label(t43_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3133 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v4_seq_2(A) -> v4_seq_2(k22_seq_1(A))))) # label(t26_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3134 (all A (v2_membered(A) -> (v2_seq_4(A) -> (all B (v1_xreal_0(B) -> (B = k3_seq_4(A) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(r2_hidden(D,A) & -r1_xreal_0(k2_xcmplx_0(B,C),D)))))))))) | v1_xboole_0(A)))) # label(d5_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3135 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_numbers) & m2_relset_1(C,k5_numbers,k1_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(D,A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> k2_seq_2(C) = np__0 & v4_seq_2(C) | r1_xreal_0(A,np__0)))))))) # label(t46_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3136 (all A (v1_xreal_0(A) -> k4_seq_4(k1_seq_4(A)) = k5_seq_4(k1_seq_4(A)))) # label(t23_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3137 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(k2_seq_4(A),C)))))))) # label(t62_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3138 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v3_seqm_3(A) & v1_seq_2(A) -> v4_seq_2(A)))) # label(t51_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3139 $T # label(t3_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3140 (all A (v2_membered(A) -> v1_xreal_0(k3_seq_4(A)))) # label(dt_k3_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3141 $T # label(t5_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3142 $T # label(t13_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3143 $T # label(t7_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3144 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k3_seq_4(A) = k5_seq_4(A))) # label(redefinition_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3145 (all A (v2_membered(A) -> (v2_seq_4(A) <-> (exists B (v1_xreal_0(B) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C))))))))) # label(d2_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3146 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(A,D)))) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,np__0) & (all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(k2_xcmplx_0(B,D),E))))))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(B,D)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(k2_xcmplx_0(A,D),E)))) & -r1_xreal_0(D,np__0)))) -> A = B))))))) # label(t19_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3147 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (r1_xreal_0(C,D) & k8_funct_2(k5_numbers,k1_numbers,A,D) != k8_funct_2(k5_numbers,k1_numbers,B,D) & m2_subset_1(D,k1_numbers,k5_numbers)))))))))) # label(t31_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3148 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(E,k6_xcmplx_0(B,D))))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,B)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(-r1_xreal_0(E,k6_xcmplx_0(A,D)) & r2_hidden(E,C)))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,A)))) -> B = A))))))) # label(t17_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3149 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> (m1_seqm_3(A,B) & v4_seq_2(B) -> k2_seq_2(B) = k2_seq_2(A)))))) # label(t30_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3150 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v2_relat_1(B) & m1_seqm_3(B,A) -> k2_real_1(k2_seq_2(A)) = k2_seq_2(k18_seq_1(B))))) | np__0 = k2_seq_2(A)))) # label(t42_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3151 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) <-> (exists B (-r1_xreal_0(B,np__0) & (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r1_xreal_0(B,k18_complex1(C))))) & v1_xreal_0(B)))))) # label(t14_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3152 (all A (v2_membered(A) -> (v1_seq_4(A) -> (all B (v1_xreal_0(B) -> (B = k2_seq_4(A) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A)))))))))) | v1_xboole_0(A)))) # label(d4_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3153 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v2_seq_2(A) & v4_seqm_3(A) -> v4_seq_2(A)))) # label(t52_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3154 (all A (v1_xreal_0(A) -> v3_seq_4(k1_seq_4(A)))) # label(t15_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3155 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) & v2_seq_4(B) -> r1_xreal_0(k3_seq_4(B),k3_seq_4(A))))))) # label(t64_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3156 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -((all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> -(v2_relat_1(B) & m1_seqm_3(B,A)))) & np__0 != k2_seq_2(A) & v4_seq_2(A)))) # label(t38_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3157 (all A (v2_membered(A) -> ((exists B (v1_xreal_0(B) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))))) <-> v1_seq_4(A)))) # label(d1_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3158 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v5_seqm_3(A) -> v4_seq_2(A)))) # label(t39_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3159 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)))) -> np__0 = k2_seq_2(B) | r1_xreal_0(A,np__0)))))) # label(t48_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3160 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> k2_seq_2(A) = k2_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_seqm_3(B,C) != A))))))) # label(t36_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3161 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -v2_relat_1(k1_seqm_3(A,B)))) & k2_seq_2(A) != np__0 & v4_seq_2(A)))) # label(t37_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.21 3162 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> -((all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & (exists E (-(r1_xreal_0(C,E) & r1_xreal_0(D,C)) & r2_hidden(E,B) & r2_hidden(D,A) & v1_xreal_0(E))))))) & (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r2_hidden(C,A) & r2_hidden(D,B) & r1_xreal_0(D,C))))))))))) # label(t8_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3163 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (r1_xreal_0(C,D) & k8_funct_2(k5_numbers,k1_numbers,B,D) != k8_funct_2(k5_numbers,k1_numbers,A,D) & m2_subset_1(D,k1_numbers,k5_numbers))))) | k2_seq_2(A) = k2_seq_2(B)))))) # label(t32_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3164 $T # label(t12_seq_4) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3165 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> k3_realset1(A,B,C) = k1_realset1(C,B))))) # label(d7_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3166 (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,k1_zfmisc_1(A)) -> (m1_realset1(C,A,B) <-> (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C)))))))) # label(d2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3167 (all A (-v1_realset1(A) -> (all B (m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))))) # label(t12_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3168 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (exists C (m1_subset_1(C,k1_zfmisc_1(A)) & (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))))))) # label(t2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3169 (all A all B all C (m1_realset1(C,A,B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v1_funct_1(k2_realset1(A,B,C)) & m2_relset_1(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C) & v1_funct_2(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C))) # label(dt_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3170 (all A (-((exists B exists C (r2_hidden(B,A) & r2_hidden(C,A) & B != C)) & v1_realset1(A)) & -((all B all C -(r2_hidden(B,A) & C != B & r2_hidden(C,A))) & -v1_realset1(A)))) # label(t14_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3171 (exists A (-v1_xboole_0(A) & (all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))))) # label(t5_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3172 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_realset1(C,A,B) -> k1_realset1(B,C) = k2_realset1(A,B,C))) # label(redefinition_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3173 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (exists C m1_realset1(C,A,B)))) # label(existence_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3174 (all A (-((all B A != k1_tarski(B)) & -v1_xboole_0(A)) <-> v1_realset1(A))) # label(d4_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3175 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(v1_realset1(B) & (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & D != C & r2_hidden(D,B) & r2_hidden(C,B)))))) & -(-v1_realset1(B) & (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(C,B) & C != D & r2_hidden(D,B))))))))) # label(t15_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3176 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_2(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & m2_relset_1(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & v1_funct_1(k1_realset1(C,B)))))) # label(t9_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3177 $T # label(dt_k1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3178 (all A all B all C (m1_subset_1(B,A) & m3_realset1(C,A,B) & -v1_realset1(A) -> v1_funct_1(k4_realset1(A,B,C)) & v1_funct_2(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & m2_relset_1(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))))) # label(dt_k4_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3179 (all A all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C))))) # label(dt_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3180 (all A (-v1_xboole_0(k1_tarski(A)) & v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3181 (exists A (-v1_realset1(A) & -v1_xboole_0(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3182 (all A all B (v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)))) # label(fc1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3183 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) -> -v1_realset1(A)))) # label(t7_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3184 (all A (v1_relat_1(A) -> (all B k7_relat_1(A,k2_zfmisc_1(B,B)) = k1_realset1(A,B)))) # label(d3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3185 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3186 (all A (-v1_realset1(A) -> (exists B (m4_realset1(B,A) & -v1_xboole_0(B))))) # label(rc3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3187 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_realset1(A,B)) & v1_funct_1(k1_realset1(A,B)))) # label(fc2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3188 (all A (v1_finset_1(A) -> (v1_realset1(A) <-> -r1_xreal_0(np__2,k4_card_1(A))))) # label(t13_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3189 (all A (-v1_realset1(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) -> (r2_realset1(A,B,C) <-> v1_funct_2(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C))) & m2_relset_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C))) & v1_funct_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C))) & m1_realset1(k4_xboole_0(A,k1_tarski(C)),A,B)))))))) # label(d5_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3190 (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,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))) <-> r1_realset1(A,B,C)))))) # label(d1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3191 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_realset1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(A)))))) # label(dt_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3192 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m2_realset1(C,A,B) -> v1_funct_2(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & m2_relset_1(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & v1_funct_1(k3_realset1(A,B,C)))) # label(dt_k3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3193 (all A (-v1_xboole_0(A) -> -(v1_realset1(A) & (all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))))))) # label(t6_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3194 (all A (-v1_xboole_0(A) -> (-v1_realset1(A) <-> (all B -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))))) # label(t4_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3195 (all A all 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) -> (r2_hidden(B,k2_zfmisc_1(A,A)) -> r2_hidden(k1_funct_1(C,B),A)))) # label(t1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3196 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C m2_realset1(C,A,B)))) # label(existence_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3197 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> k1_realset1(C,k4_xboole_0(A,k1_tarski(B))) = k4_realset1(A,B,C))))))) # label(d9_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3198 (all A all B (-v1_realset1(A) & m1_subset_1(B,A) -> m4_realset1(k5_realset1(A,B),A))) # label(dt_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3199 (all A all B (-v1_realset1(A) & m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))) # label(fc4_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3200 (all A all B (-v1_realset1(A) & m1_subset_1(B,A) -> k5_realset1(A,B) = k1_tarski(B))) # label(redefinition_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3201 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & (all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(t8_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3202 (all A all B (m1_subset_1(B,A) -> (exists C m3_realset1(C,A,B)))) # label(existence_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3203 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3204 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> v1_funct_2(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & m2_relset_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & v1_funct_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B)))))))))) # label(t11_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3205 (all A (-v1_realset1(A) -> (all B (m4_realset1(B,A) <-> (exists C (m1_subset_1(C,A) & k1_tarski(C) = B)))))) # label(d10_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3206 (all A all B (m1_subset_1(B,A) -> (exists C (v1_funct_1(C) & (all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B))))) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(t10_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3207 (all A all B (m1_subset_1(B,k1_zfmisc_1(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) -> (m2_realset1(C,A,B) <-> (all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B)))))))) # label(d6_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3208 $T # label(dt_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3209 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(dt_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3210 (all A (-v1_realset1(A) -> (exists B m4_realset1(B,A)))) # label(existence_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3211 (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_realset1(C,A,B) -> m2_relset_1(k1_realset1(B,C),k2_zfmisc_1(C,C),C) & v1_funct_2(k1_realset1(B,C),k2_zfmisc_1(C,C),C) & v1_funct_1(k1_realset1(B,C)))))) # label(t3_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3212 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B))))) <-> m3_realset1(C,A,B)))))) # label(d8_realset1) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3213 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k7_funct_6(A) <-> k1_relat_1(B) = k4_card_3(k2_funct_6(A)) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -((all D (v1_relat_1(D) & v1_funct_1(D) -> -(D = k1_funct_1(B,C) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(k4_funct_5(A),k4_tarski(E,k1_funct_1(C,E))))) & k10_relat_1(A,k1_funct_6(k2_relat_1(A))) = k1_relat_1(D)))) & r2_hidden(C,k4_card_3(k2_funct_6(A))))))))))) # label(d7_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3214 (all A (A = k4_funct_6(k9_finseq_1(A)) & k3_card_3(k9_finseq_1(A)) = A)) # label(t39_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3215 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(k2_zfmisc_1(A,B),C)) -> r2_hidden(k3_funct_5(D),k1_funct_2(A,k1_funct_2(B,C))) & r2_hidden(k5_funct_5(D),k1_funct_2(B,k1_funct_2(A,C))) | k2_zfmisc_1(A,B) = k1_xboole_0))) # label(t19_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3216 (all A (v1_relat_1(A) & v1_funct_1(A) -> k4_funct_6(A) = k1_setfam_1(k2_relat_1(A)))) # label(d4_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3217 (all A (v1_relat_1(A) & v1_funct_1(A) -> k6_funct_6(A) = k3_funct_5(k7_relat_1(k6_funct_5(A),k2_zfmisc_1(k4_funct_6(k2_funct_6(A)),k1_relat_1(A)))))) # label(d6_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3218 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_funct_1(k4_funct_5(A),k4_tarski(B,C)) = k5_funct_6(A,B,C)))) # label(d5_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3219 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k5_funct_6(k11_finseq_1(C,B,D),np__2,A) = k1_funct_1(B,A) & k5_funct_6(k10_finseq_1(C,B),np__2,A) = k1_funct_1(B,A)))))))) # label(t46_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3220 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(C)))))))) # label(t52_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3221 (all A all B all C k2_funcop_1(B,k1_funct_2(A,C)) = k9_funct_6(A,k2_funcop_1(B,C))) # label(t82_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3222 $T # label(d11_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3223 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k2_funcop_1(A,k2_relat_1(B)) = k3_funct_6(k2_funcop_1(A,B)) & k2_funct_6(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_relat_1(B)))) # label(t36_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3224 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k6_funct_6(A)) & v1_relat_1(k6_funct_6(A)))) # label(dt_k6_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3225 (all A (v1_relat_1(A) & v1_funct_1(A) -> k2_funcop_1(k1_relat_1(A),k1_tarski(k1_xboole_0)) = k9_funct_6(k1_xboole_0,A))) # label(t78_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3226 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k1_relat_1(k6_funct_6(k9_finseq_1(A))) & (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(k6_funct_6(k9_finseq_1(A)),B) = k9_finseq_1(k1_funct_1(A,B)))))) # label(t61_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3227 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__1,A) = k4_card_3(k9_finseq_1(A)))) # label(t4_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3228 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_funct_6(A)) & v1_funct_1(k7_funct_6(A)))) # label(dt_k7_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3229 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) & D = k1_funct_1(C,A) -> k1_funct_1(D,B) = k5_funct_6(C,A,B)))))) # label(t44_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3230 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists E exists F exists G (m1_subset_1(G,D) & k11_finseq_1(E,F,G) = A & m1_subset_1(F,C) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_0_funct_6(B,C,D))))) # label(fraenkel_a_3_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3231 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k10_funct_6(A)) & v1_funcop_1(k10_funct_6(A)) & v1_relat_1(k10_funct_6(A)))) # label(dt_k10_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3232 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (A != k1_xboole_0 -> k1_relat_1(B) = k1_relat_1(k6_funct_6(k2_funcop_1(A,B))) & (all C (r2_hidden(C,k1_relat_1(B)) -> k2_funcop_1(A,k1_funct_1(B,C)) = k1_funct_1(k6_funct_6(k2_funcop_1(A,B)),C)))))) # label(t63_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3233 (all A all B all C (k2_funcop_1(k2_zfmisc_1(A,B),C) = k4_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))) & k6_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))) = k2_funcop_1(k2_zfmisc_1(B,A),C))) # label(t15_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3234 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(A) = k5_funct_5(k2_funct_4(A)) & k2_funct_4(k6_funct_5(A)) = k4_funct_5(A))) # label(t13_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3235 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_0_funct_6(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & A = k10_finseq_1(D,E) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3236 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__2,A) = k4_card_3(k10_finseq_1(A,A)))) # label(t6_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3237 (all A all B all C all D (r2_hidden(A,k4_card_3(k11_finseq_1(B,C,D))) <-> (exists E exists F exists G (r2_hidden(G,D) & A = k11_finseq_1(E,F,G) & r2_hidden(F,C) & r2_hidden(E,B))))) # label(t3_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3238 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k4_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & r1_tarski(k2_relat_1(k6_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & k1_relat_1(k6_funct_5(k2_funcop_1(A,B))) = k2_zfmisc_1(k1_relat_1(B),A) & k2_zfmisc_1(A,k1_relat_1(B)) = k1_relat_1(k4_funct_5(k2_funcop_1(A,B))))) # label(t17_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3239 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k8_funct_6(A,B)) & v1_relat_1(k8_funct_6(A,B)))) # label(dt_k8_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3240 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 != B -> (r2_hidden(A,k4_funct_6(B)) <-> (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(A,k1_funct_1(B,C)))))))) # label(t37_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3241 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (A = k1_relat_1(B) -> r2_wellord2(k4_card_3(B),k4_card_3(k5_relat_1(C,B)))))))) # label(t71_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3242 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k4_card_3(k10_finseq_1(k1_relat_1(A),k1_relat_1(B))) = k1_relat_1(k7_funct_6(k10_finseq_1(A,B))) & k4_card_3(k10_finseq_1(k2_relat_1(A),k2_relat_1(B))) = k2_relat_1(k7_funct_6(k10_finseq_1(A,B))) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k7_funct_6(k10_finseq_1(A,B)),k10_finseq_1(C,D)))))))) # label(t65_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3243 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> k1_xboole_0 = A | B = k1_xboole_0 | r2_hidden(k10_funct_6(D),k1_funct_2(B,k1_funct_2(A,C)))))) # label(t85_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3244 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k8_funct_6(A,B) <-> (all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k1_funct_2(k1_funct_1(A,D),B))) & k1_relat_1(C) = k1_relat_1(A)))))) # label(d8_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3245 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k1_relat_1(A),k1_relat_1(B)) & k3_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k2_relat_1(A),k2_relat_1(B)))))) # label(t34_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3246 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k11_finseq_1(k2_relat_1(A),k2_relat_1(B),k2_relat_1(C)) = k3_funct_6(k11_finseq_1(A,B,C)) & k11_finseq_1(k1_relat_1(A),k1_relat_1(B),k1_relat_1(C)) = k2_funct_6(k11_finseq_1(A,B,C)))))))) # label(t35_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3247 $T # label(d10_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3248 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> k1_xboole_0 = B | D = k10_funct_6(k10_funct_6(D)) | A = k1_xboole_0))) # label(t87_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3249 (all A all B all C (k2_xboole_0(k2_xboole_0(A,B),C) = k3_card_3(k11_finseq_1(A,B,C)) & k4_funct_6(k11_finseq_1(A,B,C)) = k3_xboole_0(k3_xboole_0(A,B),C))) # label(t41_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3250 (all A k1_xboole_0 = k8_funct_6(k1_xboole_0,A)) # label(t73_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3251 (all A (v1_relat_1(A) & v1_funct_1(A) -> k2_relat_1(k7_funct_6(k9_finseq_1(A))) = k4_card_3(k9_finseq_1(k2_relat_1(A))) & (all B (r2_hidden(B,k1_relat_1(A)) -> k9_finseq_1(k1_funct_1(A,B)) = k1_funct_1(k7_funct_6(k9_finseq_1(A)),k9_finseq_1(B)))) & k4_card_3(k9_finseq_1(k1_relat_1(A))) = k1_relat_1(k7_funct_6(k9_finseq_1(A))))) # label(t64_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3252 (all A (v1_funct_1(A) & v1_relat_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> k8_funct_6(A,k1_xboole_0) = k2_funcop_1(k1_relat_1(A),k1_xboole_0)))) # label(t72_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3253 $T # label(dt_k1_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3254 (all A (-v1_xboole_0(A) -> k4_card_3(k11_finseq_1(A,A,A)) = k4_finseq_2(np__3,A))) # label(t8_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3255 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_relat_1(k1_funct_1(C,A)) & r2_hidden(B,k1_relat_1(k6_funct_6(C))) & v1_funct_1(k1_funct_1(C,A)) & r2_hidden(A,k1_relat_1(C)) -> k5_funct_6(C,A,B) = k5_funct_6(k6_funct_6(C),B,A)))) # label(t55_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3256 (all A r1_tarski(k1_funct_6(A),A)) # label(t27_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3257 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k4_card_3(A),k1_funct_2(k1_relat_1(A),k3_card_3(A))))) # label(t10_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3258 (all A k1_xboole_0 = k9_funct_6(A,k1_xboole_0)) # label(t79_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3259 (all A (k1_xboole_0 = k4_funct_6(k2_funcop_1(k1_xboole_0,A)) & k1_xboole_0 = k3_card_3(k2_funcop_1(k1_xboole_0,A)))) # label(t42_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3260 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(k6_funct_6(C))) & E = k1_funct_1(k6_funct_6(C),B) & r2_hidden(A,k1_relat_1(C)) -> k1_funct_1(D,B) = k1_funct_1(E,A)))))))) # label(t54_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3261 (all A all B all C (k1_xboole_0 != k2_zfmisc_1(A,B) -> k2_funcop_1(B,k2_funcop_1(A,C)) = k5_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)) & k2_funcop_1(A,k2_funcop_1(B,C)) = k3_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)))) # label(t14_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3262 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) & v1_relat_1(k1_funct_1(B,A)) & v1_funct_1(k1_funct_1(B,A)) <-> r2_hidden(A,k10_relat_1(B,k1_funct_6(k2_relat_1(B))))))) # label(t28_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3263 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> r2_wellord2(k1_funct_1(A,D),k1_funct_1(C,k1_funct_1(B,D))))) & k2_relat_1(B) = k1_relat_1(C) & k1_relat_1(A) = k1_relat_1(B) -> r2_wellord2(k4_card_3(A),k4_card_3(C))))))))) # label(t70_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3264 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_6(A)) & v1_relat_1(k3_funct_6(A)))) # label(dt_k3_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3265 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,A) -> r2_wellord2(k1_funct_1(B,D),k1_funct_1(C,D)))) & k1_relat_1(C) = A & k1_relat_1(B) = A -> r2_wellord2(k4_card_3(B),k4_card_3(C))))))) # label(t69_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3266 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> v1_funct_1(k1_funct_1(k6_funct_6(B),A)) & v1_relat_1(k1_funct_1(k6_funct_6(B),A))))) # label(t50_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3267 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_funct_1(k9_funct_6(A,B)) & v1_relat_1(k9_funct_6(A,B)))) # label(dt_k9_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3268 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(k10_funct_6(A))) -> v1_relat_1(k1_funct_1(k10_funct_6(A),B)) & v1_funct_1(k1_funct_1(k10_funct_6(A),B)))))) # label(t84_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3269 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> k4_card_3(k11_finseq_1(A,B,C)) = a_3_0_funct_6(A,B,C))))))) # label(t7_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3270 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_6(k9_finseq_1(A)) = k9_finseq_1(k1_relat_1(A)) & k3_funct_6(k9_finseq_1(A)) = k9_finseq_1(k2_relat_1(A)))) # label(t33_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3271 (all A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(k2_funct_6(A)) = k1_relat_1(A))) # label(t89_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3272 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k4_partfun1(A,k4_partfun1(B,C))) -> r2_hidden(k6_funct_5(D),k4_partfun1(k2_zfmisc_1(B,A),C)) & r2_hidden(k4_funct_5(D),k4_partfun1(k2_zfmisc_1(A,B),C))))) # label(t24_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3273 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k5_funct_6(k11_finseq_1(C,D,B),np__3,A) = k1_funct_1(B,A)))))))) # label(t47_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3274 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> k1_relat_1(k3_funct_6(A)) = k1_relat_1(A))) # label(t90_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3275 (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) -> (r2_hidden(D,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(D))))) & r2_hidden(B,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(k6_funct_6(C)))))))) # label(t53_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3276 (all A all B (k2_xboole_0(A,B) = k3_card_3(k10_finseq_1(A,B)) & k3_xboole_0(A,B) = k4_funct_6(k10_finseq_1(A,B)))) # label(t40_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3277 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> r2_hidden(k4_funct_5(D),k1_funct_2(k2_zfmisc_1(A,B),C)) & r2_hidden(k6_funct_5(D),k1_funct_2(k2_zfmisc_1(B,A),C))))) # label(t20_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.22 3278 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k9_finseq_1(B),np__1,A) & k5_funct_6(k11_finseq_1(B,C,D),np__1,A) = k1_funct_1(B,A) & k5_funct_6(k10_finseq_1(B,C),np__1,A) = k1_funct_1(B,A)))))))) # label(t45_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3279 (all A all B all C k10_finseq_1(k1_funct_2(A,C),k1_funct_2(B,C)) = k8_funct_6(k10_finseq_1(A,B),C)) # label(t75_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3280 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (C = k1_funct_1(B,A) & k1_funct_1(k7_funct_6(B),D) = E & r2_hidden(D,k4_card_3(k2_funct_6(B))) & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(D,A),k1_relat_1(C)) & r2_hidden(E,k4_card_3(k3_funct_6(B))) & k1_funct_1(E,A) = k1_funct_1(C,k1_funct_1(D,A))))))))))) # label(t57_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3281 (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)) & r2_hidden(B,k4_card_3(k2_funct_6(C))) -> k5_funct_6(k7_funct_6(C),B,A) = k5_funct_6(C,A,k1_funct_1(B,A))))))) # label(t56_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3282 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(D)) & r2_hidden(A,B) -> k1_funct_1(D,C) = k5_funct_6(k2_funcop_1(B,D),A,C)))) # label(t48_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3283 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k3_funct_6(A) <-> k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A))) & (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k2_funct_5(k1_funct_1(A,C)) = k1_funct_1(B,C)))))))) # label(d3_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3284 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & C = k1_funct_1(B,A) -> r2_hidden(A,k1_relat_1(k2_funct_6(B))) & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C) & r2_hidden(A,k1_relat_1(k3_funct_6(B))) & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C)))))) # label(t31_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3285 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (A != k1_xboole_0 -> k2_relat_1(k4_funct_5(k2_funcop_1(A,B))) = k2_relat_1(B) & k2_relat_1(k6_funct_5(k2_funcop_1(A,B))) = k2_relat_1(B)))) # label(t18_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3286 (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(C)) & r2_hidden(A,k1_relat_1(B)) -> (all D all E (k1_funct_1(k13_funct_3(B,C),A) = k4_tarski(D,E) <-> k1_funct_1(k6_funct_6(k10_finseq_1(B,C)),A) = k10_finseq_1(D,E)))))))) # label(t67_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3287 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (A = k1_relat_1(F) & r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) -> -r2_hidden(k6_funct_5(F),k1_funct_2(k2_zfmisc_1(B,A),C)) & -r2_hidden(k4_funct_5(F),k1_funct_2(k2_zfmisc_1(A,B),C)) | r2_hidden(F,k1_funct_2(A,k1_funct_2(B,C)))))) # label(t22_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3288 $T # label(dt_k5_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3289 (all A all B (r2_hidden(A,k4_card_3(k9_finseq_1(B))) <-> (exists C (r2_hidden(C,B) & k9_finseq_1(C) = A)))) # label(t1_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3290 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_funct_6(k1_enumset1(A,B,C)) = k1_enumset1(A,B,C) & k1_funct_6(k2_tarski(A,B)) = k2_tarski(A,B) & k1_tarski(A) = k1_funct_6(k1_tarski(A)) & k1_funct_6(k1_xboole_0) = k1_xboole_0)))))) # label(t29_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3291 (all A all B k8_funct_6(k9_finseq_1(A),B) = k9_finseq_1(k1_funct_2(A,B))) # label(t74_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3292 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)))) # label(dt_k2_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3293 (all A all B ((all C (r2_hidden(C,B) <-> v1_relat_1(C) & v1_funct_1(C) & r2_hidden(C,A))) <-> B = k1_funct_6(A))) # label(d1_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3294 (all A all B all C k8_funct_6(k2_funcop_1(A,B),C) = k2_funcop_1(A,k1_funct_2(B,C))) # label(t76_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3295 (all A all B k9_funct_6(A,k9_finseq_1(B)) = k9_finseq_1(k1_funct_2(A,B))) # label(t80_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3296 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> -r2_hidden(k5_funct_5(F),k4_partfun1(B,k4_partfun1(A,C))) & -r2_hidden(k3_funct_5(F),k4_partfun1(A,k4_partfun1(B,C))) | r2_hidden(F,k4_partfun1(k2_zfmisc_1(A,B),C))))) # label(t25_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3297 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_card_3(k2_finseq_2(A,B)) = k4_finseq_2(A,B))))) # label(t9_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3298 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k4_partfun1(k2_zfmisc_1(A,B),C)) -> r2_hidden(k5_funct_5(D),k4_partfun1(B,k4_partfun1(A,C))) & r2_hidden(k3_funct_5(D),k4_partfun1(A,k4_partfun1(B,C)))))) # label(t23_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3299 (all A (v1_relat_1(A) & v1_funct_1(A) -> k10_funct_6(A) = k5_funct_5(k4_funct_5(A)))) # label(d12_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3300 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k1_relat_1(k7_funct_6(k2_funcop_1(A,B))) = k1_funct_2(A,k1_relat_1(B)) & (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k1_funct_2(A,k1_relat_1(B))) -> k5_relat_1(C,B) = k1_funct_1(k7_funct_6(k2_funcop_1(A,B)),C)))) & k1_funct_2(A,k2_relat_1(B)) = k2_relat_1(k7_funct_6(k2_funcop_1(A,B))))) # label(t66_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3301 (all A all B all C k10_finseq_1(k1_funct_2(A,B),k1_funct_2(A,C)) = k9_funct_6(A,k10_finseq_1(B,C))) # label(t81_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3302 (all A all B (k1_xboole_0 != A -> k4_funct_6(k2_funcop_1(A,B)) = B & B = k3_card_3(k2_funcop_1(A,B)))) # label(t43_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3303 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C all D A != k4_tarski(C,D)) & r2_hidden(A,k1_relat_1(k2_funct_4(B)))))) # label(t11_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3304 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k9_funct_6(A,B) = C <-> k1_relat_1(B) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_2(A,k1_funct_1(B,D))))))))) # label(d9_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3305 (all A (v1_funct_1(A) & v1_relat_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> ((all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(B,k2_relat_1(A)) -> v2_funct_1(B)))) <-> v2_funct_1(k7_funct_6(A)))))) # label(t59_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3306 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(B,k1_relat_1(D)) & r2_hidden(A,k1_relat_1(C)) -> (all E all F (k1_funct_1(k7_funct_6(k10_finseq_1(C,D)),k10_finseq_1(A,B)) = k10_finseq_1(E,F) <-> k1_funct_1(k15_funct_3(C,D),k4_tarski(A,B)) = k4_tarski(E,F)))))))) # label(t68_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3307 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_funct_6(A) = B <-> k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A))) & (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k1_funct_1(B,C) = k1_funct_5(k1_funct_1(A,C))))))))) # label(d2_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3308 (all A all B all C k2_funcop_1(k2_zfmisc_1(B,A),C) = k2_funct_4(k2_funcop_1(k2_zfmisc_1(A,B),C))) # label(t12_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3309 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(k6_funct_6(k10_finseq_1(A,B)),C) = k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(k6_funct_6(k10_finseq_1(A,B))) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t62_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3310 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r2_wellord2(k4_card_3(k9_funct_6(A,B)),k1_funct_2(A,k4_card_3(B))))) # label(t83_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3311 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(F),A) & r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) -> r2_hidden(F,k4_partfun1(A,k4_partfun1(B,C))) | -r2_hidden(k4_funct_5(F),k4_partfun1(k2_zfmisc_1(A,B),C)) & -r2_hidden(k6_funct_5(F),k4_partfun1(k2_zfmisc_1(B,A),C))))) # label(t26_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3312 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> k1_xboole_0 = B | (all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (all G all H (E = k1_funct_1(D,G) & F = k1_funct_1(k10_funct_6(D),H) & r2_hidden(H,B) & r2_hidden(G,A) -> B = k1_relat_1(E) & r1_tarski(k2_relat_1(F),C) & r1_tarski(k2_relat_1(E),C) & A = k1_relat_1(F) & k1_funct_1(F,G) = k1_funct_1(E,H))))))) | A = k1_xboole_0))) # label(t86_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3313 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r2_wellord2(k1_funct_2(k3_card_3(k2_card_3(B)),A),k4_card_3(k8_funct_6(B,A))))) # label(t77_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3314 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & C = k1_funct_1(B,A) -> r1_tarski(k2_relat_1(C),k2_relat_1(k6_funct_5(B))) & r1_tarski(k2_relat_1(C),k2_relat_1(k4_funct_5(B)))))))) # label(t16_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3315 (all A all B (r1_tarski(A,k1_funct_6(B)) -> k1_funct_6(A) = A)) # label(t30_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3316 (all A all B all C ((exists D exists E (r2_hidden(D,B) & r2_hidden(E,C) & k10_finseq_1(D,E) = A)) <-> r2_hidden(A,k4_card_3(k10_finseq_1(B,C))))) # label(t2_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3317 (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(k6_funct_6(B))) & C = k1_funct_1(k6_funct_6(B),A) -> k10_relat_1(B,k1_funct_6(k2_relat_1(B))) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(k4_funct_5(B),k4_tarski(D,A)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(D,A),k1_relat_1(k4_funct_5(B)))))))))) # label(t51_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3318 $T # label(dt_k4_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3319 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_relat_1(k7_funct_6(A)) = k4_card_3(k3_funct_6(A)))) # label(t58_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3320 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k4_card_3(k10_finseq_1(A,B)) = a_2_0_funct_6(A,B))))) # label(t5_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3321 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k6_funct_6(A)),k4_card_3(k3_funct_6(A))) & k1_relat_1(k6_funct_6(A)) = k4_funct_6(k2_funct_6(A)))) # label(t49_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3322 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> r2_hidden(F,k1_funct_2(k2_zfmisc_1(A,B),C)) | -r2_hidden(k5_funct_5(F),k1_funct_2(B,k1_funct_2(A,C))) & -r2_hidden(k3_funct_5(F),k1_funct_2(A,k1_funct_2(B,C)))))) # label(t21_funct_6) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3323 (all A all B all C (v1_trees_1(B) & m1_trees_1(C,B) & v1_finset_1(B) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_1_pre_circ(B,C)) <-> (exists D (D = A & -r1_tarski(C,D) & m1_trees_1(D,B)))))) # label(fraenkel_a_2_1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3324 (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(A,B) -> r1_tarski(k1_funct_4(A,C),k1_funct_4(B,C))))))))) # label(t3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3325 (all A all B m1_pboole(k2_pre_circ(A,B),A)) # label(dt_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3326 (exists A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,f1_s3_pre_circ) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(B,np__1)) = f3_s3_pre_circ(B,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,B)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0))) # label(s3_pre_circ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3327 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) & v1_funct_2(A,k5_numbers,f1_s3_pre_circ) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,f1_s3_pre_circ) & m2_relset_1(B,k5_numbers,f1_s3_pre_circ) -> (f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,C)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(C,np__1)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,B,C)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,k1_nat_1(C,np__1)))) -> A = B))))) # label(s3_pre_circ_AndRHS) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3328 $T # label(t1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3329 (all A np__1 = k4_card_1(k1_trees_4(A))) # label(t24_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3330 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_pboole(B,A) -> k3_pre_circ(A,B,C) = k7_relat_1(B,C))) # label(redefinition_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3331 (all A all B all C (v1_finset_1(B) & v1_trees_1(B) & m1_trees_1(C,B) & -v1_xboole_0(B) -> ((exists D (r1_tarski(C,D) & A = D & m1_trees_1(D,B))) <-> r2_hidden(A,a_2_0_pre_circ(B,C))))) # label(fraenkel_a_2_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3332 (all A all B (v1_funct_1(A) & v1_finset_1(A) & m1_subset_1(B,k1_relat_1(A)) & v3_trees_2(A) & v1_relat_1(A) -> v1_relat_1(k5_trees_2(A,B)) & v1_finset_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)))) # label(fc4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3333 (all A (v4_trees_3(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> k1_funct_1(A,k1_nat_1(B,np__1)) = k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B))))))) # label(t16_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3334 (all A (v1_funct_1(A) & v3_trees_2(A) & v1_finset_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v3_trees_2(B) & v1_finset_1(B) & v1_funct_1(B) -> (all C all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v6_trees_3(E) & v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> -(r2_hidden(k12_finseq_1(k5_numbers,D),k1_relat_1(A)) & k4_trees_4(C,E) = A & (all F (v6_trees_3(F) & v1_finseq_1(F) & v1_funct_1(F) & v1_relat_1(F) -> -(B = k1_funct_1(F,k1_nat_1(D,np__1)) & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r2_hidden(G,k4_finseq_1(E)) -> k1_funct_1(E,G) = k1_funct_1(F,G) | k1_nat_1(D,np__1) = G))) & k3_finseq_1(F) = k3_finseq_1(E) & k8_trees_2(A,k12_finseq_1(k5_numbers,D),B) = k4_trees_4(C,F))))))))))))) # label(t19_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3335 (all A all B k2_funcop_1(A,B) = k2_pre_circ(A,B)) # label(redefinition_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3336 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(B,A) <-> (all C (r2_hidden(C,A) -> v1_finset_1(k1_funct_1(B,C))))))) # label(d3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3337 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_pboole(k3_pre_circ(A,B,C),C))) # label(dt_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3338 $T # label(d2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3339 (all A (m1_subset_1(A,f1_s4_pre_circ) -> (r2_hidden(A,f2_s4_pre_circ) -> v1_funct_1(f5_s4_pre_circ(A)) & m2_relset_1(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) & v1_funct_2(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A))))) -> (exists A ((all B (m1_subset_1(B,f1_s4_pre_circ) -> (r2_hidden(B,f2_s4_pre_circ) -> f5_s4_pre_circ(B) = k1_funct_1(A,B)))) & m3_pboole(A,f2_s4_pre_circ,f3_s4_pre_circ,f4_s4_pre_circ))) # label(s4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3340 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k1_tarski(C) = k2_relat_1(A) & k1_relat_1(A) = k1_tarski(B) -> A = k1_tarski(k4_tarski(B,C)))))) # label(t2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3341 (all A (v4_trees_3(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v4_trees_3(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(B,D) = k1_funct_1(A,D) | k1_nat_1(C,np__1) = D))) & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) & k3_finseq_1(A) = k3_finseq_1(B) -> (all D (v1_trees_1(D) & -v1_xboole_0(D) -> (k1_funct_1(B,k1_nat_1(C,np__1)) = D -> k5_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,C),D) = k13_trees_3(B))))))))))) # label(t18_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3342 (all A (-v1_xboole_0(A) -> (all B all C (v2_relat_1(C) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> k1_relat_1(k10_funct_6(D)) = B)))))) # label(t8_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3343 (all A (v1_relat_1(A) & v1_funct_1(A) & v6_trees_3(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> r2_hidden(k12_finseq_1(k5_numbers,B),k13_trees_3(k2_funct_6(A)))))))) # label(t17_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3344 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> -v1_xboole_0(k3_tarski(k2_relat_1(B))))))) # label(t6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3345 (all A all B all C all D (v1_finset_1(B) & v1_trees_1(B) & v1_finset_1(C) & m1_trees_1(D,B) & v1_trees_1(C) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_pre_circ(B,C,D)) <-> (exists E (k8_finseq_1(k5_numbers,D,E) = A & m1_trees_1(E,C)))))) # label(fraenkel_a_3_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3346 (all A (r2_hidden(A,a_0_0_pre_circ) <-> (exists B (p1_s1_pre_circ(B) & A = f2_s1_pre_circ(B) & m1_subset_1(B,f1_s1_pre_circ))))) # label(fraenkel_a_0_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3347 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k4_card_3(k2_finseq_2(A,k1_tarski(B))) = k1_tarski(k2_finseq_2(A,B))))) # label(t12_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3348 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> r2_tarski(k4_trees_1(A,B),a_2_0_pre_circ(A,B)))))) # label(t13_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3349 (all A all B (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v2_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3350 (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) -> (r1_tarski(A,B) & r1_xboole_0(k1_relat_1(A),k1_relat_1(C)) -> r1_tarski(A,k1_funct_4(B,C))))))))) # label(t4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3351 (exists A ((all B (m1_subset_1(B,f1_s2_pre_circ) -> (r2_hidden(B,f1_s2_pre_circ) -> (p1_s2_pre_circ(B) -> f2_s2_pre_circ(B) = k1_funct_1(A,B)) & (-p1_s2_pre_circ(B) -> f3_s2_pre_circ(B) = k1_funct_1(A,B))))) & m1_pboole(A,f1_s2_pre_circ))) # label(s2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3352 (all A (v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v1_finset_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & v1_finset_1(B) -> (all C (m1_trees_1(C,k1_relat_1(A)) -> k1_nat_1(k4_card_1(A),k4_card_1(B)) = k1_nat_1(k4_card_1(k8_trees_2(A,C,B)),k4_card_1(k5_trees_2(A,C))))))))) # label(t23_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3353 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k4_card_3(B)) -> r2_hidden(k5_relat_1(D,C),k4_card_3(k5_relat_1(D,B)))))))))) # label(t11_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3354 (all A (v1_finset_1(A) & v1_trees_1(A) & -v1_xboole_0(A) -> (all B (v1_finset_1(B) & v1_trees_1(B) & -v1_xboole_0(B) -> (all C (m1_trees_1(C,A) -> k1_nat_1(k4_card_1(A),k4_card_1(B)) = k1_nat_1(k4_card_1(k5_trees_1(A,C,B)),k4_card_1(k4_trees_1(A,C))))))))) # label(t22_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3355 (all A k4_funct_5(k2_pre_circ(A,k1_xboole_0)) = k1_xboole_0) # label(t7_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3356 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_card_1(A) = k1_card_1(k1_relat_1(A)))) # label(t21_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3357 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_trees_1(B) & v1_finset_1(B) -> (all C (m1_trees_1(C,A) -> (all D (m2_finseq_1(D,k5_numbers) -> -(r2_hidden(D,k5_trees_1(A,C,B)) & (all E (m1_trees_1(E,B) -> D != k8_finseq_1(k5_numbers,C,E))) & r1_tarski(C,D)))))))))) # label(t15_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3358 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_trees_3(A)) -> v1_finset_1(B))))) # label(cc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3359 (exists A (-v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A))) # label(rc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3360 (all A exists B (m1_pboole(B,A) & v2_relat_1(B) & v1_pre_circ(B,A) & v1_funct_1(B) & v1_relat_1(B))) # label(rc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3361 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) -> (all C (m1_trees_1(C,A) -> k2_xboole_0(a_2_1_pre_circ(A,C),a_3_0_pre_circ(A,B,C)) = k5_trees_1(A,C,B))))))) # label(t14_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3362 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (m1_trees_1(B,A) -> -(B != k1_xboole_0 & r1_xreal_0(k4_card_1(A),k4_card_1(k4_trees_1(A,B)))))))) # label(t20_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3363 (all A (-v1_xboole_0(A) & v5_membered(A) & v1_finset_1(A) -> v4_ordinal2(k2_seq_4(A)) & v1_xcmplx_0(k2_seq_4(A)) & v1_xreal_0(k2_seq_4(A)))) # label(fc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3364 (all A all B all C (v1_relat_1(A) & v1_finset_1(A) & v3_trees_2(A) & v1_relat_1(C) & v1_finset_1(C) & v3_trees_2(C) & v1_funct_1(C) & m1_subset_1(B,k1_relat_1(A)) & v1_funct_1(A) -> v1_funct_1(k8_trees_2(A,B,C)) & v1_finset_1(k8_trees_2(A,B,C)) & v3_trees_2(k8_trees_2(A,B,C)) & v1_relat_1(k8_trees_2(A,B,C)))) # label(fc5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3365 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v2_membered(A) -> v1_xreal_0(k1_pre_circ(A)))) # label(dt_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3366 (all A all B (m1_pboole(B,A) -> k1_funct_1(k6_pboole(A,B),k6_finseq_1(A)) = k1_tarski(k1_xboole_0))) # label(t5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.23 3367 (all A (v1_finset_1(A) & v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & r2_hidden(B,A) <-> k1_pre_circ(A) = B))))) # label(d1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3368 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> (all E (m1_subset_1(E,B) -> (exists F (m1_pboole(F,A) & k1_funct_1(k10_funct_6(D),E) = F & r3_pboole(A,F,C))))))))))))) # label(t10_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3369 (all A (v1_funct_1(k1_trees_4(A)) & v1_finset_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) & v1_relat_1(k1_trees_4(A)))) # label(fc6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3370 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v2_membered(A) -> k2_seq_4(A) = k1_pre_circ(A))) # label(redefinition_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3371 (all A all B (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v2_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3372 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (m1_subset_1(D,k4_card_3(B)) -> ((all E (r2_hidden(E,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,E),k1_funct_1(B,E)))) & r1_tarski(k1_relat_1(C),k1_relat_1(B)) -> m1_subset_1(k1_funct_4(D,C),k4_card_3(B))))))))) # label(t9_pre_circ) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3373 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) | r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,B,D),C)))))))) # label(t15_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3374 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> r2_pboole(A,k5_pboole(A,B,D),C)))))))) # label(t17_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3375 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k5_pboole(A,C,D)) <-> r2_pboole(A,B,k2_pboole(A,C,D)) & r5_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t13_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3376 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((exists D (r1_pboole(A,D,C) & r1_pboole(A,B,D) & m1_pboole(D,A))) <-> r1_pboole(A,B,k2_mboolean(A,C))))))) # label(t21_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3377 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r6_pboole(A,k3_pboole(A,D,B),k1_pboole(A))))) -> r6_pboole(A,k3_pboole(A,k2_mboolean(A,C),B),k1_pboole(A))))))) # label(t34_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3378 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k1_mboolean(A,k4_pboole(A,C,B))),k1_mboolean(A,k5_pboole(A,B,C))))))) # label(t12_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3379 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,B))) # label(t24_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3380 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k2_pboole(A,k2_pre_circ(A,k1_tarski(k1_xboole_0)),k4_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)))))))) # label(t10_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3381 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t5_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3382 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (k1_mboolean(A,B) = C <-> (all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_zfmisc_1(k1_funct_1(B,D))))))))) # label(d1_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3383 (all A all B (m1_pboole(B,A) -> m1_pboole(k1_mboolean(A,B),A))) # label(dt_k1_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3384 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k1_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t9_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3385 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))) -> (all D (r2_hidden(D,A) -> r3_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(t8_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3386 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k11_pboole(A,B,C),k1_mboolean(A,k1_mboolean(A,k2_pboole(A,B,C)))))))) # label(t18_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3387 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> r2_pboole(A,B,k2_mboolean(A,C))))))) # label(t26_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3388 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r5_pboole(A,B,D) & r2_pboole(A,B,C) <-> r2_pboole(A,B,k4_pboole(A,C,D))))))))) # label(t11_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3389 (all A r6_pboole(A,k2_mboolean(A,k1_pboole(A)),k1_pboole(A))) # label(t22_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3390 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_mboolean(A,k2_pboole(A,B,C)),k2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t28_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3391 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k3_tarski(B)))) # label(t23_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3392 (all A all B (m1_pboole(B,A) -> r2_pboole(A,B,k1_mboolean(A,k2_mboolean(A,B))))) # label(t31_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3393 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_mboolean(A,k1_mboolean(A,B)),B))) # label(t30_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3394 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) & v2_relat_1(D) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r6_pboole(A,k3_pboole(A,E,C),k1_pboole(A))))) & r2_pboole(A,C,k2_mboolean(A,k2_pboole(A,B,D))) -> r2_pboole(A,C,k2_mboolean(A,B))))))))) # label(t36_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3395 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t6_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3396 (all A all B all C r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k2_tarski(k1_tarski(B),k1_tarski(C)))),k2_pre_circ(A,k2_tarski(B,C)))) # label(t25_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3397 $T # label(t14_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3398 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k12_pboole(A,B,C),k1_mboolean(A,k11_pboole(A,B,C))))))) # label(t20_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3399 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))))))) # label(t7_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3400 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) & v2_relat_1(B) -> ((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & r1_pboole(A,D,B) & -r2_pboole(A,D,C) & -r2_pboole(A,C,D)))))) -> r1_pboole(A,k2_mboolean(A,B),B)))) # label(t37_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3401 (all A all B (m1_pboole(B,A) -> v2_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)) & v1_relat_1(k1_mboolean(A,B)))) # label(fc1_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3402 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) & r2_pboole(A,k2_mboolean(A,B),C) -> r2_pboole(A,D,C)))))))) # label(t32_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3403 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t27_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3404 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k3_tarski(k1_funct_1(B,D)))) <-> C = k2_mboolean(A,B)))))) # label(d2_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3405 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t29_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3406 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r2_pboole(A,D,B)))) -> r2_pboole(A,k2_mboolean(A,C),B)))))) # label(t33_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3407 (all A all B (m1_pboole(B,A) -> m1_pboole(k2_mboolean(A,B),A))) # label(dt_k2_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3408 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,B,k1_mboolean(A,C)) <-> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) <-> r1_pboole(A,D,B))))))))) # label(t1_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3409 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t16_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3410 (all A r6_pboole(A,k1_mboolean(A,k1_pboole(A)),k2_pre_circ(A,k1_tarski(k1_xboole_0)))) # label(t2_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3411 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,k2_tarski(k1_xboole_0,k1_tarski(B))))) # label(t4_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3412 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k1_zfmisc_1(B)))) # label(t3_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3413 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(k2_pboole(A,B,C)) & (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,k2_pboole(A,B,C)) & r1_pboole(A,D,k2_pboole(A,B,C)) -> D = E | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A))))))) -> r6_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C)))))))) # label(t35_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3414 (all A (v1_relat_1(k2_mboolean(A,k1_pboole(A))) & v1_funct_1(k2_mboolean(A,k1_pboole(A))) & v3_relat_1(k2_mboolean(A,k1_pboole(A))))) # label(fc2_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3415 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,k1_mboolean(A,C)) <-> r2_pboole(A,B,C)))))) # label(t19_mboolean) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3416 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) & v2_relat_1(D) -> (r1_pboole(A,B,C) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,B,E)))) -> r1_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t53_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3417 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C))))) # label(rc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3418 (all A all B (v2_relat_1(B) & m1_pboole(B,A) & v1_pre_circ(B,A) -> -((all C (m1_pboole(C,A) -> -(r1_pboole(A,C,B) & (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,D,C))))))) & (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,D,B) & -r2_pboole(A,C,D) & -r2_pboole(A,D,C) & r1_pboole(A,C,B))))))))) # label(t29_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3419 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> m4_pboole(k2_pzfmisc1(A,B,D),A,k1_mboolean(A,C))))))))) # label(t39_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3420 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) & v2_relat_1(B) -> -((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & r1_pboole(A,D,B) & -r2_pboole(A,C,D) & -r2_pboole(A,D,C)))))) & (all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,C,D)))) & r1_pboole(A,C,B))))))) # label(t28_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3421 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (m3_pboole(C,A,B,k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)))))) # label(t16_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3422 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(v1_pre_circ(B,A) & (all E (m1_pboole(E,A) -> (all F (m1_pboole(F,A) -> -(v1_pre_circ(F,A) & r2_pboole(A,B,k11_pboole(A,E,F)) & r2_pboole(A,F,D) & r2_pboole(A,E,C) & v1_pre_circ(E,A)))))) & r2_pboole(A,B,k11_pboole(A,C,D))))))))) # label(t26_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3423 (all A (r2_hidden(A,f1_s1_mssubfam) -> (all B -((all C -(p1_s1_mssubfam(C,B,A) & r2_hidden(C,k1_funct_1(f3_s1_mssubfam,A)))) & r2_hidden(B,k1_funct_1(f2_s1_mssubfam,A)))))) -> (exists A ((all B -(r2_hidden(B,f1_s1_mssubfam) & (all C (v1_funct_1(C) & v1_funct_2(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & m2_relset_1(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) -> -(k1_funct_1(A,B) = C & (all D (r2_hidden(D,k1_funct_1(f2_s1_mssubfam,B)) -> p1_s1_mssubfam(k1_funct_1(C,D),D,B)))))))) & m3_pboole(A,f1_s1_mssubfam,f2_s1_mssubfam,f3_s1_mssubfam))) # label(s1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3424 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_pre_circ(k4_pboole(A,C,B),A) & v1_funct_1(k4_pboole(A,C,B)) & v1_relat_1(k4_pboole(A,C,B)))) # label(fc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3425 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v2_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v1_relat_1(C))))) # label(rc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3426 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> m4_pboole(k4_pboole(A,D,B),A,k1_mboolean(A,C)))))))) # label(t36_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3427 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k2_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t34_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3428 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,C) & r1_pboole(A,D,C) -> r1_pboole(A,k2_pboole(A,D,E),C)))))) <-> v1_mssubfam(C,A,B)))))) # label(d3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3429 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (v1_pre_circ(k1_mssubfam(A,B),A) -> v1_pre_circ(k2_mssubfam(A,B),A)))) # label(t24_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3430 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> ((all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A)))) & v1_pre_circ(B,A) -> v1_pre_circ(k2_mboolean(A,B),A)))) # label(t22_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3431 (all A all B (m1_pboole(B,A) -> v1_mssubfam(k7_mssubfam(A,B),A,B) & v3_mssubfam(k7_mssubfam(A,B),A,B) & v4_mssubfam(k7_mssubfam(A,B),A,B) & v6_mssubfam(k7_mssubfam(A,B),A,B) & m4_pboole(k7_mssubfam(A,B),A,k1_mboolean(A,B)) & v5_mssubfam(k7_mssubfam(A,B),A,B) & v2_mssubfam(k7_mssubfam(A,B),A,B))) # label(dt_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3432 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -((all E (m1_pboole(E,A) -> -(v1_pre_circ(E,A) & r2_pboole(A,B,k11_pboole(A,E,C)) & r2_pboole(A,E,D)))) & r2_pboole(A,B,k11_pboole(A,D,C)) & v1_pre_circ(C,A) & v1_pre_circ(B,A)))))))) # label(t27_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3433 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v5_mssubfam(C,A,B)))))) # label(cc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3434 (all A all B (m1_pboole(B,A) -> m4_pboole(k3_mssubfam(A,B),A,k1_mboolean(A,B)))) # label(dt_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3435 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> v1_funcop_1(k13_pboole(B,C)) & m1_pboole(k13_pboole(B,C),A))))) # label(t15_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3436 $T # label(d1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3437 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) <-> v6_mssubfam(C,A,B)))))) # label(d8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3438 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> ((all D all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(D,A) & k1_funct_1(C,D) = E -> v1_finset_1(k10_relat_1(E,k1_funct_1(B,D)))))) & r2_pboole(A,B,k2_mssubfam(A,C)) -> v1_pre_circ(B,A)))))) # label(t25_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3439 (all A all B all C (v1_funcop_1(B) & m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) -> v1_relat_1(k14_pboole(A,C,B)) & v1_pre_circ(k14_pboole(A,C,B),A) & v1_funct_1(k14_pboole(A,C,B)))) # label(fc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3440 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,B) -> r1_tarski(C,D))) -> r1_tarski(C,k8_setfam_1(A,B))))))) # label(t4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3441 (all A all B (m1_pboole(B,A) -> k1_mboolean(A,B) = k7_mssubfam(A,B))) # label(redefinition_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3442 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v1_pre_circ(k11_pboole(A,B,C),A) & v2_relat_1(B) -> v1_pre_circ(C,A)))))) # label(t20_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3443 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,k6_mssubfam(A,B,D)) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,C,E))))))))))) # label(t52_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3444 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,C) & r1_pboole(A,E,C) -> r1_pboole(A,k3_pboole(A,D,E),C)))))) <-> v3_mssubfam(C,A,B)))))) # label(d5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3445 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m4_pboole(D,A,k1_mboolean(A,C)) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r2_pboole(A,B,E)))) -> r2_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t45_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3446 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_xboole_0(B,C) & r2_hidden(B,D) -> r1_xboole_0(k8_setfam_1(A,D),C)))) # label(t7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3447 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k6_mssubfam(A,B,C),k2_mboolean(A,C)))))) # label(t42_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3448 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m4_pboole(k6_mssubfam(A,B,C),A,B))) # label(dt_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3449 (all A all B all C (v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_funct_1(k3_pboole(A,C,B)) & v1_pre_circ(k3_pboole(A,C,B),A) & v1_relat_1(k3_pboole(A,C,B)))) # label(fc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3450 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (k1_tarski(C) = B -> C = k8_setfam_1(A,B)))))) # label(t9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3451 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) -> r6_pboole(A,k6_mssubfam(A,B,C),k1_pboole(A))))))) # label(t44_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3452 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & v1_pre_circ(B,A) -> v1_funct_1(k12_pboole(A,B,C)) & v1_pre_circ(k12_pboole(A,B,C),A) & v1_relat_1(k12_pboole(A,B,C)))) # label(fc9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3453 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> m4_pboole(k1_pzfmisc1(A,B),A,k1_mboolean(A,C))))))) # label(t38_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3454 (all A all B all C (m1_pboole(C,A) & v1_pre_circ(C,A) & m1_pboole(B,A) & v1_pre_circ(B,A) -> v1_pre_circ(k2_pboole(A,B,C),A) & v1_funct_1(k2_pboole(A,B,C)) & v1_relat_1(k2_pboole(A,B,C)))) # label(fc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3455 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v6_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3456 (all A all B all C (v1_funcop_1(C) & m1_pboole(C,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (D = k1_funct_1(C,A) & r2_hidden(A,B) -> k1_relat_1(D) = k1_funct_1(k1_mssubfam(B,C),A)))))) # label(t14_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3457 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r1_pboole(A,C,E) -> r6_pboole(A,k3_pboole(A,k6_mssubfam(A,B,E),D),k1_pboole(A))))))))))) # label(t48_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3458 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> k1_mssubfam(A,B) = k2_funct_6(B))) # label(redefinition_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3459 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (r2_hidden(D,C) -> r1_tarski(B,D))) -> r1_tarski(B,k8_setfam_1(A,C)) | C = k1_xboole_0))) # label(t5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3460 (all A all B all C all D (m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> k4_mssubfam(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3461 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (all E (m4_pboole(E,A,B) -> (r6_pboole(A,C,k2_pzfmisc1(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,D,E))))))))))) # label(t51_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3462 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> m1_pboole(k1_mssubfam(A,B),A))) # label(dt_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3463 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> (all C (m4_pboole(C,A,B) -> v1_pre_circ(C,A))))) # label(cc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3464 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) & r1_pboole(A,C,E) -> r2_pboole(A,k6_mssubfam(A,B,E),D)))))))))) # label(t47_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3465 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m1_pboole(k5_mssubfam(A,B,C),A))) # label(dt_k5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3466 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k2_mboolean(A,C),B))))) # label(t40_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3467 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> k3_funct_6(B) = k2_mssubfam(A,B))) # label(redefinition_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3468 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k1_pboole(A)) -> r6_pboole(A,k6_mssubfam(A,B,C),B)))))) # label(t41_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3469 (all A all B all C (v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_relat_1(k11_pboole(A,B,C)) & v1_funct_1(k11_pboole(A,B,C)) & v1_pre_circ(k11_pboole(A,B,C),A))) # label(fc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3470 (all A all B (m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v2_relat_1(C) & v1_mssubfam(C,A,B) & v3_mssubfam(C,A,B) & v6_mssubfam(C,A,B) & v5_mssubfam(C,A,B) & v4_mssubfam(C,A,B) & v2_mssubfam(C,A,B) & v1_funct_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3471 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(k1_xboole_0,B) -> k1_xboole_0 = k8_setfam_1(A,B)))) # label(t3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3472 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v1_mssubfam(C,A,B)))))) # label(cc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3473 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (r6_pboole(A,C,k1_pzfmisc1(A,D)) -> r6_pboole(A,k6_mssubfam(A,B,C),D)))))))) # label(t50_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3474 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> (m2_pboole(B,A,C) -> r1_pboole(A,B,C)))))) # label(t12_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3475 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m1_pboole(D,A) -> ((all E -(r2_hidden(E,A) & (all F (m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E)))) -> -(k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F) & F = k1_funct_1(C,E)))))) <-> D = k5_mssubfam(A,B,C)))))))) # label(d2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3476 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,D) & r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,D),C)))) # label(t6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3477 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> r1_tarski(k8_setfam_1(A,B),k5_setfam_1(A,B))))) # label(t1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3478 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k3_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t35_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3479 (all A all B (m1_pboole(B,A) -> k1_mboolean(A,B) = k3_mssubfam(A,B))) # label(redefinition_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3480 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & v1_pre_circ(k11_pboole(A,C,B),A) -> v1_pre_circ(C,A)))))) # label(t19_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3481 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & D = k1_funct_1(C,A) -> k1_funct_1(k2_mssubfam(B,C),A) = k2_relat_1(D)))))) # label(t13_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3482 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v5_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3483 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) -> v1_pre_circ(B,A)))) # label(cc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3484 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> m1_pboole(k2_mssubfam(A,B),A))) # label(dt_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.24 3485 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) <-> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k6_mssubfam(A,B,D),C))))))))) # label(d6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3486 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_funct_1(k3_pboole(A,B,C)) & v1_pre_circ(k3_pboole(A,B,C),A) & v1_relat_1(k3_pboole(A,B,C)))) # label(fc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3487 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> v2_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)) & v1_pre_circ(k1_mboolean(A,B),A) & v1_relat_1(k1_mboolean(A,B)))) # label(fc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3488 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v5_mssubfam(C,A,B) <-> r1_pboole(A,B,C)))))) # label(d7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3489 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(k2_mboolean(A,B),A) -> v1_pre_circ(B,A) & (all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A))))))) # label(t23_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3490 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v1_funcop_1(D) & m1_pboole(D,A) -> (m3_pboole(D,A,B,C) & r1_pzfmisc1(A,B,C) -> r6_pboole(A,k1_mssubfam(A,D),B) & r2_pboole(A,k2_mssubfam(A,D),C)))))))) # label(t17_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3491 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v3_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v1_relat_1(C))))) # label(rc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3492 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),C)))))))) # label(t43_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3493 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k2_pboole(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,E)))))))))))) # label(t49_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3494 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v1_pre_circ(C,A) & r2_pboole(A,B,C) -> v1_pre_circ(B,A)))))) # label(t18_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3495 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k5_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t37_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3496 (all A all B all C (m1_pboole(C,B) -> (all D (m4_pboole(D,B,k1_mboolean(B,C)) -> (r2_hidden(A,B) -> m1_subset_1(k1_funct_1(D,A),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(C,A))))))))) # label(t32_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3497 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,B) & v1_relat_1(C) & v3_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A))))) # label(rc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3498 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> m2_pboole(B,A,C)))))) # label(t11_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3499 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(v1_pre_circ(C,A) & (all D (m1_pboole(D,A) -> -(r6_pboole(A,k14_pboole(A,D,B),C) & v1_pre_circ(D,A) & r2_pboole(A,D,k1_mssubfam(A,B))))) & r2_pboole(A,C,k2_mssubfam(A,B))))))) # label(t30_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3500 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (B = k2_tarski(C,D) -> k5_subset_1(A,C,D) = k8_setfam_1(A,B)))))))) # label(t10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3501 (all A all B all C (m4_pboole(C,A,k1_mboolean(A,B)) & m1_pboole(B,A) -> k5_mssubfam(A,B,C) = k6_mssubfam(A,B,C))) # label(redefinition_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3502 (all A all B all C all D (-v1_xboole_0(A) & m1_pboole(B,A) & m1_subset_1(D,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m1_subset_1(k4_mssubfam(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,D)))))) # label(dt_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3503 (all A all B (m1_pboole(B,A) -> v1_pre_circ(k1_pboole(A),A) & m4_pboole(k1_pboole(A),A,k1_mboolean(A,B)) & v3_relat_1(k1_pboole(A)))) # label(t31_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3504 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,C))))))))) # label(t46_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3505 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v6_mssubfam(C,A,B)))))) # label(cc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3506 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k2_mboolean(A,D),C)))) <-> v2_mssubfam(C,A,B)))))) # label(d4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3507 (all A (v1_relat_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A) & v1_funct_1(k1_pboole(A)))) # label(fc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3508 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> (r1_pboole(A,B,D) -> m4_pboole(B,A,C)))))))) # label(t33_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3509 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v3_mssubfam(C,A,B)))))) # label(cc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3510 (all A all B all C (v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_funct_1(k5_pboole(A,B,C)) & v1_pre_circ(k5_pboole(A,B,C),A) & v1_relat_1(k5_pboole(A,B,C)))) # label(fc10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3511 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(B,A) <-> v1_pre_circ(k1_mboolean(A,B),A)))) # label(t21_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3512 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k4_subset_1(k1_zfmisc_1(A),C,D) = B -> k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D)) = k8_setfam_1(A,B)))))))) # label(t8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3513 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,C) -> r1_tarski(k8_setfam_1(A,C),B)))) # label(t2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3514 (all A (l1_struct_0(A) -> (v1_xboole_0(u1_struct_0(A)) <-> v3_struct_0(A)))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3515 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (all C (m1_subset_1(C,B) <-> m1_struct_0(C,A,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3516 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_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]. 9.12/9.25 3517 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3518 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3519 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3520 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3521 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3522 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3523 (exists A (-v3_struct_0(A) & l1_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3524 (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]. 9.12/9.25 3525 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3526 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3527 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> g1_struct_0(u1_struct_0(A)) = A))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3528 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3529 (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]. 9.12/9.25 3530 (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]. 9.12/9.25 3531 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3532 (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]. 9.12/9.25 3533 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> 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]. 9.12/9.25 3534 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3535 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3536 (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]. 9.12/9.25 3537 (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]. 9.12/9.25 3538 (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]. 9.12/9.25 3539 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k1_struct_0(A,B) = k1_tarski(B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3540 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(A,B) = g2_struct_0(C,D) -> C = A & D = B)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3541 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3542 (all A all B all C (v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k3_lattices(A,B,C) = k1_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3543 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(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)) -> k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k3_lattices(A,B,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3544 (all A (l1_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,C) & k2_lattices(A,C,B) = B)) <-> B = k5_lattices(A))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3545 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3546 (all A all B all C (v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) & -v3_struct_0(A) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3547 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_lattices(A) -> k3_lattices(A,B,C) = k3_lattices(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3548 (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) -> v2_lattices(g2_lattices(A,B)) & l2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3549 (all A (l1_lattices(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_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3550 (exists A (l1_lattices(A) & -v3_struct_0(A) & v1_lattices(A) & v7_lattices(A) & v6_lattices(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3551 (all A (-v3_struct_0(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v6_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_lattices(A,B,B) = B)))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3552 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v15_lattices(A) <-> v13_lattices(A) & v14_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3553 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,k7_lattices(A,C)) <-> k4_lattices(A,B,C) = k5_lattices(A)))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3554 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> k2_lattices(A,B,C) = k4_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3555 (all A (l3_lattices(A) & v10_lattices(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,u1_struct_0(A)) -> k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)) = k4_lattices(A,B,k3_lattices(A,C,D)))))))) <-> (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)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t19_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3556 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3557 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)))))))) <-> v11_lattices(A)))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3558 (exists A (-v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v2_lattices(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3559 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 9.12/9.25 3560 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & v16_lattices(A) & l3_lattices(A) & v11_lattices(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,C,B) <-> k7_lattices(A,B) = C)))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3561 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3562 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> v3_lattices(g3_lattices(A,B,C)) & l3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3563 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3564 (all A (l2_lattices(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_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = k1_lattices(A,B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3565 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v8_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_lattices(A,k2_lattices(A,B,C),C)))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3566 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3567 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v11_lattices(A) & v13_lattices(A) & v15_lattices(A) & v17_lattices(A) & v16_lattices(A) & v14_lattices(A) & v10_lattices(A) & v9_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3568 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_lattices(A,B,C) = k5_lattices(A) & k2_lattices(A,C,B) = k5_lattices(A) & k6_lattices(A) = k1_lattices(A,C,B) & k1_lattices(A,B,C) = k6_lattices(A) <-> r2_lattices(A,B,C)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3569 (all A (l1_lattices(A) -> (v1_lattices(A) -> g1_lattices(u1_struct_0(A),u1_lattices(A)) = A))) # label(abstractness_v1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3570 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3571 (all A (l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k1_lattices(A,B,C) <-> r1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3572 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3573 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3574 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3575 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3576 (all A (v4_lattices(A) & l2_lattices(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_lattices(A,C,B) & r1_lattices(A,B,C) -> C = B))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3577 (all A all B (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v2_lattices(g2_lattices(A,B)) & -v3_struct_0(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3578 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_lattices(A,C,B))))) <-> v6_lattices(A)))) # label(d6_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3579 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_lattices(A) = k4_lattices(A,k7_lattices(A,B),B))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3580 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattices(A,C,B))))) <-> v16_lattices(A)))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3581 (all A (l1_lattices(A) -> m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3582 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3583 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3584 (all A (l2_lattices(A) & v5_lattices(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,u1_struct_0(A)) -> (r1_lattices(A,C,D) & r1_lattices(A,B,C) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3585 (exists A (-v3_struct_0(A) & v3_lattices(A) & l3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3586 (all A (-v3_struct_0(A) & v8_lattices(A) & l3_lattices(A) & v9_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> k2_lattices(A,B,C) = B))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3587 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_lattices(A,C,B) & k1_lattices(A,B,C) = B)) <-> B = k6_lattices(A))))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3588 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3589 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = B & k2_lattices(A,C,B) = B)) & m1_subset_1(B,u1_struct_0(A)))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3590 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3591 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3592 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3593 (exists A (l3_lattices(A) & v3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3594 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v9_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,k1_lattices(A,B,C))))))))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3595 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3596 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3597 (all A (l3_lattices(A) & v8_lattices(A) & v6_lattices(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_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3598 (exists A (l1_lattices(A) & v1_lattices(A) & -v3_struct_0(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3599 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g2_lattices(A,B) = g2_lattices(C,D) -> D = B & C = A)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3600 (exists A (-v3_struct_0(A) & v3_lattices(A) & v6_lattices(A) & v7_lattices(A) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v12_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A) & v4_lattices(A) & l3_lattices(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3601 (all A (l2_lattices(A) -> v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3602 (all A (l3_lattices(A) -> (v11_lattices(A) & v15_lattices(A) & v16_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3603 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A) <-> v17_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3604 (all A (l3_lattices(A) -> (v17_lattices(A) & -v3_struct_0(A) -> v11_lattices(A) & v13_lattices(A) & v15_lattices(A) & v16_lattices(A) & v14_lattices(A) & -v3_struct_0(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3605 (exists A (l2_lattices(A) & v2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3606 (all A (-v3_struct_0(A) & l1_lattices(A) -> m1_subset_1(k5_lattices(A),u1_struct_0(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3607 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3608 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) -> -v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3609 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3610 (all A (l3_lattices(A) -> (v3_lattices(A) -> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3611 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> v1_lattices(g1_lattices(A,B)) & -v3_struct_0(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3612 (all A (-v3_struct_0(A) & l2_lattices(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)) -> k1_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k1_lattices(A,B,C),D))))))) <-> v5_lattices(A)))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3613 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A) -> -v3_struct_0(A) & v10_lattices(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3614 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k5_lattices(A),B) = B)))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3615 (all A all B all C (l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3616 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k6_lattices(A),B) = k6_lattices(A))))) # label(t44_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3617 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3618 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v4_lattices(A) & v5_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & v8_lattices(A) <-> v10_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3619 (all A all B all C (v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v6_lattices(A) & -v3_struct_0(A) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3620 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3621 (all A (-v3_struct_0(A) & l3_lattices(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_lattices(A,B,D) -> k2_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k2_lattices(A,C,D))))))))) <-> v12_lattices(A)))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3622 (all A (l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,B,B))))) # label(t18_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3623 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v15_lattices(A) -> v14_lattices(A) & v13_lattices(A) & -v3_struct_0(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3624 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3625 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B))))))))) # label(t53_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3626 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,k5_lattices(A),B))))) # label(t41_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3627 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3628 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_lattices(A) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3629 (all A (v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(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_lattices(A,B,k1_lattices(A,B,C)))))))) # label(t22_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3630 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v11_lattices(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)) -> k3_lattices(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)))))))))) # label(t31_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3631 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v13_lattices(A) & v14_lattices(A) -> -v3_struct_0(A) & v15_lattices(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3632 (all A (l2_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.25 3633 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all D all E all F (g3_lattices(D,E,F) = g3_lattices(A,B,C) -> C = F & E = B & D = A)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3634 (all A (v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v7_lattices(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,u1_struct_0(A)) -> (r1_lattices(A,B,C) -> r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D))))))))))) # label(t27_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3635 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3636 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B)) & m1_subset_1(B,u1_struct_0(A))))))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3637 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> -v3_struct_0(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3638 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3639 (all A (v11_lattices(A) & l3_lattices(A) & v10_lattices(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,u1_struct_0(A)) -> k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3640 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> l1_lattices(g1_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3641 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3642 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3643 (all A (l1_lattices(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,u1_struct_0(A)) -> k2_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k2_lattices(A,B,C),D))))))) <-> v7_lattices(A)))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3644 (exists A (l3_lattices(A) & v5_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3645 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3646 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3647 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3648 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,k6_lattices(A),B))))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3649 (exists A (-v3_struct_0(A) & v3_lattices(A) & v7_lattices(A) & v9_lattices(A) & v13_lattices(A) & v15_lattices(A) & v14_lattices(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3650 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3651 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3652 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3653 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3654 (all A (l2_lattices(A) -> (v2_lattices(A) -> g2_lattices(u1_struct_0(A),u2_lattices(A)) = A))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3655 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v4_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k1_lattices(A,C,B)))))))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3656 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3657 (all A (l3_lattices(A) -> (v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v8_lattices(A) & v9_lattices(A) & v12_lattices(A) & v10_lattices(A) & v7_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3658 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3659 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3660 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_lattices(A) = k4_lattices(A,k5_lattices(A),B))))) # label(t40_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3661 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k4_lattices(A,B,C)))))))) # label(t50_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3662 (exists A (-v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v13_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & l3_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3663 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3664 (all A (v10_lattices(A) & l3_lattices(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,u1_struct_0(A)) -> k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)))))))) -> v11_lattices(A)))) # label(t29_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3665 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3666 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_lattices(A,B) = g1_lattices(C,D) -> D = B & C = A)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3667 (all A (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(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)) -> (k4_lattices(A,B,C) = k4_lattices(A,B,D) & k3_lattices(A,B,D) = k3_lattices(A,B,C) -> D = C))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3668 $T # label(t1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3669 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(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)) -> (k5_rlvect_1(A,C) = k5_rlvect_1(A,B) -> B = C))))))) # label(t31_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3670 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k5_rlvect_1(A,B)) = B)))) # label(t30_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 9.22/9.26 3671 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k7_rlvect_1(A,B,C) = k10_finseq_1(B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3672 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))))))))) # label(t77_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3673 (all A (l1_rlvect_1(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_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3674 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k2_rlvect_1(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t20_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3675 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,B)) & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A))))) # label(t16_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3676 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) & k1_rlvect_1(A) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)))))) # label(t76_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3677 (all A (l2_rlvect_1(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,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (k1_rlvect_1(A) = k2_rlvect_1(A,B,C) & m1_subset_1(C,u1_struct_0(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)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_rlvect_1(A,B,np__1))) & (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)) -> k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) = k3_rlvect_1(A,D,k4_real_1(B,C)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k2_rlvect_1(A,C,D),B))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k2_rlvect_1(A,B,k1_rlvect_1(A)))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))) -> v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3678 (exists A (l1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v1_rlvect_1(A) & -v3_struct_0(A))) # label(rc5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3679 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k1_rlvect_1(A))) # label(t60_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3680 (all A all B all C all D (m1_subset_1(B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> l2_rlvect_1(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(dt_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3681 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) -> (all D all E all F (g1_rlvect_1(D,E,F) = g1_rlvect_1(A,B,C) -> E = B & F = C & D = A)))) # label(free_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3682 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3683 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3684 $T # label(t12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3685 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (v2_funct_1(C) & v2_funct_1(B) & k2_relat_1(B) = k2_relat_1(C) -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3686 (exists A (l1_rlvect_1(A) & v1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3687 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_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)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,D,B,C)))))))))) # label(t89_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3688 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(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_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t62_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3689 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(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,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t82_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3690 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(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_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)) = k5_rlvect_1(A,k2_rlvect_1(A,B,C)))))))) # label(t45_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3691 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v8_rlvect_1(B,A) <-> B != k1_rlvect_1(A)))))) # label(d13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3692 (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)) -> m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3693 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3694 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (np__0 = k3_finseq_1(B) -> k9_rlvect_1(A,B) = k1_rlvect_1(A)))))) # label(t94_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3695 (all A (l2_rlvect_1(A) -> v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3696 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> B = C))))))) # label(t35_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3697 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,k1_rlvect_1(A),B) = B & B = k2_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3698 $T # label(t65_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3699 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,k1_rlvect_1(A)) = B)))) # label(t26_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3700 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)) & B = k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))))))) # label(t91_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3701 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))) = k5_rlvect_1(A,k2_rlvect_1(A,C,B)))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3702 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(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,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t81_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3703 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (k1_funct_1(B,k1_nat_1(E,np__1)) = F -> k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) | r1_xreal_0(k3_finseq_1(B),E)))))) & k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) = k1_rlvect_1(A) & C = k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & v1_funct_1(D))) <-> k9_rlvect_1(A,B) = C))))))) # label(d12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3704 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3705 (all A all B all C all D (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)))) # label(dt_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3706 (exists A (l2_rlvect_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3707 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v3_rlvect_1(A) & -v3_struct_0(A) -> k2_rlvect_1(A,B,C) = k4_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3708 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3709 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k5_rlvect_1(A,B) -> B = k1_rlvect_1(A)))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.36/174.80 3710 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1) & D = k1_funct_1(B,k3_finseq_1(B)) & k7_relat_1(B,k4_finseq_1(C)) = C -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D)))))))))) # label(t55_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3711 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (E = k1_funct_1(C,D) & r2_hidden(D,k4_finseq_1(B)) -> k5_rlvect_1(A,E) = k1_funct_1(B,D)))))) & k3_finseq_1(B) = k3_finseq_1(C) -> k9_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,C))))))))) # label(t57_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3712 (all A all B all C all D (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k8_rlvect_1(A,B,C,D) = k11_finseq_1(B,C,D))) # label(redefinition_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3713 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k3_rlvect_1(A,B,np__2))))) # label(t79_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3714 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k1_rlvect_1(A))) # label(t68_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3715 (all A (l1_rlvect_1(A) -> v1_funct_1(u1_rlvect_1(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3716 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,k1_real_1(np__1)) = k5_rlvect_1(A,B))))) # label(t29_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3717 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3718 $T # label(t6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3719 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)) = k3_rlvect_1(A,B,np__3))))) # label(t93_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3720 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) -> m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3721 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(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,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t63_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3722 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(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_rlvect_1(A,B,C) = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) & k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) = k2_rlvect_1(A,B,C) & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)) = k2_rlvect_1(A,B,C))))))) # label(t92_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3723 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_rlvect_1(A) -> k4_rlvect_1(A,C,B) = k4_rlvect_1(A,B,C))) # label(commutativity_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3724 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_numbers) & l2_rlvect_1(A) -> m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3725 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,B) = k1_rlvect_1(A))))) # label(t28_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3726 (all A (l1_rlvect_1(A) -> (v1_rlvect_1(A) -> A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))))) # label(abstractness_v1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3727 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(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)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)))))))) # label(t47_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3728 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) = k2_rlvect_1(A,B,C))))))) # label(t5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3729 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_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)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (C = k1_funct_1(B,np__1) & k1_funct_1(B,np__2) = D & E = k1_funct_1(B,np__3) & k3_finseq_1(B) = np__3 -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E)))))))))))) # label(t97_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3730 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (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,u1_struct_0(A)) -> k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B))))))))))) # label(t67_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3731 (exists A (l2_rlvect_1(A) & -v3_struct_0(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3732 $T # label(t17_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3733 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_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)) -> (k1_funct_1(B,np__2) = D & k1_funct_1(B,np__1) = C & np__2 = k3_finseq_1(B) -> k2_rlvect_1(A,C,D) = k9_rlvect_1(A,B)))))))))) # label(t96_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3734 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(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)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,C) -> B = k5_rlvect_1(A,C)))))))) # label(t19_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3735 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(C,k2_finseq_1(D)) & D = k3_finseq_1(B) -> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A))))))))))) # label(t54_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3736 (all A all B all C (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3737 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v4_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))))))))))) # label(d6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3738 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))) <-> v6_rlvect_1(A)))) # label(d8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3739 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(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)) -> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k6_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t44_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3740 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k3_rlvect_1(C,D,k5_real_1(A,B)) = k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)))))))))) # label(t49_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3741 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) = k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)))))))) # label(t58_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3742 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_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)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3743 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))))))) # label(t69_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3744 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k5_rlvect_1(A,k1_rlvect_1(A)))) # label(t25_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3745 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (k3_finseq_1(B) = np__1 -> k1_funct_1(B,np__1) = k9_rlvect_1(A,B)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3746 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) = B & B = k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)))))) # label(t75_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3747 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,C,A) = k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)))))))) # label(t40_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3748 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> -(A != np__0 & k1_rlvect_1(B) != C & k1_rlvect_1(B) = k3_rlvect_1(B,C,A)))))))) # label(t24_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3749 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))))))))) # label(t73_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3750 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_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)) -> k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t84_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3751 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(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,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t85_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3752 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(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,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t86_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3753 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3754 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))))))))) # label(t70_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3755 (exists A (v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3756 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_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)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E) | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) -> E = D))))))))))) # label(t21_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3757 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k6_rlvect_1(A,B,C))))))) # label(d11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3758 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k6_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t46_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3759 $T # label(t32_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3760 (all A (l2_struct_0(A) -> k1_rlvect_1(A) = u2_struct_0(A))) # label(d2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3761 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B)) <-> v5_rlvect_1(A)))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3762 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k2_rlvect_1(A,C,D),B))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__1) = B)) & (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)) -> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B))))))) & (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)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) <-> v7_rlvect_1(A)))) # label(d9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3763 (all A (v4_rlvect_1(A) & l1_rlvect_1(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,u1_struct_0(A)) -> k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t42_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3764 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3765 (all A all B all C all D (m1_subset_1(B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all E all F all G all H (g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H) -> A = E & D = H & C = G & B = F)))) # label(free_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3766 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & -v3_struct_0(g2_rlvect_1(A,B,C,D)))) # label(fc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3767 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B)))) # label(t61_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3768 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k3_rlvect_1(B,k6_rlvect_1(B,C,D),A) = k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3769 (all A all B all C (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v3_rlvect_1(A) -> m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3770 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k2_rlvect_1(A,B,C) = k1_rlvect_1(A))))))))) # label(d10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3771 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3772 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3773 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))))) # label(t74_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3774 $T # label(t9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3775 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = A))) # label(abstractness_v2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3776 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3777 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3778 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))) = k3_rlvect_1(A,B,k1_real_1(np__2)))))) # label(t80_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.80 3779 (all A (l2_struct_0(A) -> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)))) # label(dt_k1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3780 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)))))))) # label(t38_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3781 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) = k4_rlvect_1(A,B,B) -> B = k1_rlvect_1(A)))))) # label(t34_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3782 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l1_rlvect_1(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(dt_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3783 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k3_rlvect_1(C,D,B) = k3_rlvect_1(C,D,A) -> k1_rlvect_1(C) = D | A = B))))))))) # label(t51_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3784 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_rlvect_1(A,B))))) # label(t3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3785 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3786 $T # label(t18_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3787 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3788 (all A (l1_struct_0(A) -> (all B (r1_rlvect_1(A,B) <-> r2_hidden(B,u1_struct_0(A)))))) # label(d1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3789 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A))))) # label(t64_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3790 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_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)) -> (k6_rlvect_1(A,B,D) = k6_rlvect_1(A,B,C) -> D = C))))))))) # label(t37_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3791 (all A (m1_subset_1(A,k1_numbers) -> (all B (v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k1_rlvect_1(B) = C | np__0 = A -> k3_rlvect_1(B,C,A) = k1_rlvect_1(B)))))))) # label(t23_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3792 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_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)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,D)),C))))))))) # label(t83_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3793 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t66_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3794 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(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)) -> k9_rlvect_1(A,k7_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t72_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3795 (all A (l1_rlvect_1(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_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C))))) <-> v3_rlvect_1(A)))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3796 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_rlvect_1(A,B,C) = B | k2_rlvect_1(A,C,B) = B -> C = k1_rlvect_1(A)))))))) # label(t22_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3797 (exists A (l1_rlvect_1(A) & v1_rlvect_1(A) & -v3_struct_0(A))) # label(rc4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3798 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t90_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3799 (all A (l1_rlvect_1(A) -> l2_struct_0(A))) # label(dt_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3800 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k3_rlvect_1(B,D,A) = k3_rlvect_1(B,C,A) -> C = D | A = np__0))))))))) # label(t50_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3801 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3802 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)))))))) # label(t39_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3803 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(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)) -> (exists D (B = k6_rlvect_1(A,C,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t36_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3804 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(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,u1_struct_0(A)) -> k4_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3805 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)))))))) # label(d4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3806 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(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,u1_struct_0(A)) -> k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))) = k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D))))))))) # label(t71_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3807 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r2_hidden(E,k4_finseq_1(C)) & F = k1_funct_1(D,E) -> k3_rlvect_1(B,F,A) = k1_funct_1(C,E)))))) & k3_finseq_1(C) = k3_finseq_1(D) -> k9_rlvect_1(B,C) = k3_rlvect_1(B,k9_rlvect_1(B,D),A)))))))))) # label(t56_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3808 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(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,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) = k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))))) # label(t41_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3809 $T # label(t52_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3810 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_group_1(A) = k3_group_1(A,B) -> k2_group_1(A) = B))))) # label(t18_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3811 $T # label(t39_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3812 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k1_group_1(A,D,B))) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,B,D) = C)))))) & (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)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) -> v4_group_1(A) & v3_group_1(A)))) # label(t6_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3813 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(np__0,A) -> k6_group_1(B,A,C) = k6_group_1(B,k1_int_2(A),C)))))))) # label(t55_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3814 (all A (-v3_struct_0(A) & l1_group_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)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,B,C) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,C,D) = B & k1_group_1(A,D,C) = B)) & C = k1_group_1(A,C,B))))) | l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A)))) # label(t5_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3815 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,B))))))) # label(d10_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3816 $T # label(t4_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3817 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3818 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (A = np__0 -> k2_group_1(B) = k6_group_1(B,A,C)))))))) # label(t59_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3819 $T # label(t89_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3820 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k4_xcmplx_0(A),C) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t70_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3821 (all A (l1_group_1(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,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)))))))) <-> v4_group_1(A)))) # label(d4_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3822 $T # label(t11_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3823 $T # label(t57_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3824 (all A (-v3_struct_0(A) & l1_group_1(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3825 (all A (l1_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k5_group_1(A)) & m2_relset_1(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)))) # label(dt_k5_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3826 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D)) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E))))))))))))) # label(t53_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3827 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) & k2_group_1(A) = k1_group_1(A,C,B) <-> k3_group_1(A,B) = C))))))) # label(d6_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3828 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k6_group_1(B,A,C) = k2_group_1(B) -> r1_nat_1(k7_group_1(B,C),A)))))))) # label(t86_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3829 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) -> v2_group_1(A) & -v3_struct_0(A)))) # label(cc1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3830 (all A (l1_struct_0(A) -> (v6_group_1(A) <-> v1_finset_1(u1_struct_0(A))))) # label(d14_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3831 (all A (l1_group_1(A) -> v1_funct_1(u1_group_1(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3832 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k2_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = C & k1_group_1(A,C,B) = C)))))))) # label(d5_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3833 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_group_1(C,k6_group_1(C,B,D),k6_group_1(C,A,D)) = k6_group_1(C,k2_xcmplx_0(B,A),D))))))))) # label(t65_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3834 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> -v3_struct_0(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(fc2_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3835 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> np__1 = k7_group_1(A,k2_group_1(A)))) # label(t84_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3836 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (B = k4_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d7_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3837 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(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)) -> (exists D (k1_group_1(A,B,D) = C & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t23_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3838 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> v1_group_1(g1_group_1(A,B)) & -v3_struct_0(g1_group_1(A,B)))) # label(fc1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3839 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,D,E) = k1_group_1(C,E,D) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t75_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3840 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k4_group_1(A)) & v1_funct_2(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k4_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3841 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k1_nat_1(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t48_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3842 (all A (l1_group_1(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)) -> k1_group_1(A,C,B) = k1_group_1(A,B,C))))) <-> v7_group_1(A)))) # label(d16_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3843 $T # label(t9_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3844 $T # label(t88_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3845 $T # label(t83_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3846 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k8_group_1(A) = k1_card_1(u1_struct_0(A)))) # label(d13_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3847 (all A (l1_group_1(A) -> (v1_group_1(A) -> A = g1_group_1(u1_struct_0(A),u1_group_1(A))))) # label(abstractness_v1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3848 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,k10_group_1(A,B,C)) = k10_group_1(A,k3_group_1(A,B),k3_group_1(A,C)))))))) # label(t94_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3849 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_card_1(k8_group_1(A)))) # label(dt_k8_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3850 $T # label(t93_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3851 $T # label(t78_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3852 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_nat_1(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t50_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3853 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v7_group_1(A) -> k10_group_1(A,B,C) = k1_group_1(A,B,C))) # label(redefinition_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3854 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(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)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C))))))))) # label(t27_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3855 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_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)) -> (k1_group_1(A,C,B) = k1_group_1(A,D,B) | k1_group_1(A,B,D) = k1_group_1(A,B,C) -> D = C))))))))) # label(t14_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3856 (all A all B (v3_group_1(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)))) # label(dt_k3_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3857 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,C,B) -> C = np__0))) <-> v5_group_1(B,A)))))) # label(d11_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3858 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (v5_group_1(B,A) -> (C = k7_group_1(A,B) <-> C = np__0)) & (-v5_group_1(B,A) -> (C != np__0 & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,D,B) -> r1_xreal_0(C,D) | D = np__0))) & k6_group_1(A,C,B) = k2_group_1(A) <-> C = k7_group_1(A,B))))))))) # label(d12_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3859 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C all D (g1_group_1(C,D) = g1_group_1(A,B) -> C = A & D = B)))) # label(free_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3860 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(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)) -> (k3_group_1(A,B) = k3_group_1(A,C) -> C = B))))))) # label(t17_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3861 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_group_1(A,B,C) | B = k1_group_1(A,C,B) -> k2_group_1(A) = C))))))) # label(t15_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3862 $T # label(t81_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3863 $T # label(t3_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3864 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k2_xcmplx_0(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)) & k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k2_xcmplx_0(A,np__1),C))))))) # label(t66_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3865 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) -> (k5_group_1(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,k1_nat_1(D,np__1)) = k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,D),C)))))))))) # label(d8_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3866 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) -> v2_binop_1(u1_group_1(A),u1_struct_0(A)))) # label(t31_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3867 $T # label(t80_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3868 $T # label(t76_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3869 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,B,C) & k2_group_1(A) = k1_group_1(A,C,B) -> C = k3_group_1(A,B)))))))) # label(t12_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3870 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,k7_binop_2(np__1),B) = k3_group_1(A,B))))) # label(t62_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3871 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v1_finseqop(u1_group_1(A),u1_struct_0(A)))) # label(t36_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3872 (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) -> l1_group_1(g1_group_1(A,B)) & v1_group_1(g1_group_1(A,B)))) # label(dt_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3873 $T # label(t1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3874 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__0,B) = k2_group_1(A))))) # label(t43_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3875 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(A,np__0) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t60_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3876 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,B) = k6_group_1(A,np__2,B))))) # label(t45_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3877 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v7_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t96_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3878 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,A,D),C)))))))))) # label(t77_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3879 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t74_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3880 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(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)) -> (k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)) <-> k1_group_1(A,B,C) = k1_group_1(A,C,B)))))))) # label(t26_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3881 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)) = k6_group_1(B,A,k1_group_1(B,C,D))))))))))) # label(t54_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3882 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_group_1(A,k3_group_1(A,B)))))) # label(t19_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3883 (exists A (l1_group_1(A) & -v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v2_group_1(A) & v1_group_1(A))) # label(rc3_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3884 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t68_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3885 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & C = k1_group_1(A,B,C))))) <-> v2_group_1(A)))) # label(d2_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3886 $T # label(t41_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3887 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t95_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3888 (all A (l1_group_1(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)) -> k1_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C))))))) # label(d1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3889 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> k2_group_1(B) = k6_group_1(B,A,k2_group_1(B)))))) # label(t61_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3890 (all A (v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> v4_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v6_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v5_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v3_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))))) # label(t97_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3891 (exists A (v1_group_1(A) & l1_group_1(A))) # label(rc1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3892 $T # label(t38_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3893 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_group_1(A,k2_group_1(A)))) # label(t16_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3894 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & v3_group_1(A) -> m2_subset_1(k7_group_1(A,B),k1_numbers,k5_numbers))) # label(dt_k7_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3895 $T # label(t8_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3896 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k3_group_1(A,B) <-> k2_group_1(A) = k6_group_1(A,np__2,B)))))) # label(t47_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3897 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k6_group_1(A,k7_group_1(A,B),B))))) # label(t82_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3898 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(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,u1_struct_0(A)) -> (D = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,B),D) = C))))))))) # label(t21_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3899 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t73_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3900 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k3_group_1(A,k1_group_1(A,B,C)))))))) # label(t25_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3901 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3902 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3903 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(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)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,C),B) = k1_group_1(A,B,k3_group_1(A,C))))))))) # label(t28_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3904 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> k2_group_1(B) = k6_group_1(B,A,k2_group_1(B)))))) # label(t42_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3905 (exists A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A))) # label(rc2_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3906 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (np__1 = k7_group_1(A,B) -> k2_group_1(A) = B))))) # label(t85_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3907 $T # label(t87_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3908 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (v1_int_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k3_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B)))) & (r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B))))))))) # label(d9_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3909 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -v5_group_1(k2_group_1(A),A))) # label(t79_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3910 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,B,C) & k1_group_1(A,C,B) = C)) -> B = k2_group_1(A)))))) # label(t10_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3911 (all A (l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)))) # label(t32_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3912 $T # label(t58_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3913 $T # label(t29_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3914 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v3_group_1(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & (exists D (B = k1_group_1(A,C,D) & B = k1_group_1(A,D,C) & m1_subset_1(D,u1_struct_0(A)))) & k1_group_1(A,B,C) = C))))))) # label(d3_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3915 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t64_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3916 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t63_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3917 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(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_group_1(A) = k1_group_1(A,B,C) | k1_group_1(A,C,B) = k2_group_1(A) -> B = k3_group_1(A,C) & C = k3_group_1(A,B)))))))) # label(t20_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3918 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (v1_finset_1(C) & C = u1_struct_0(A) & k4_card_1(C) = B)) <-> k9_group_1(A) = B)))))) # label(d15_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3919 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__3,B) = k1_group_1(A,k1_group_1(A,B,B),B))))) # label(t46_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3920 $T # label(t30_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3921 (all A (l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_binop_1(u1_struct_0(A),u1_group_1(A)))) # label(t33_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3922 $T # label(t13_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3923 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,A,k3_group_1(B,C)) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t51_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3924 (all A all B all C (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & v1_int_1(B) & -v3_struct_0(A) -> m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3925 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> m2_subset_1(k9_group_1(A),k1_numbers,k5_numbers))) # label(dt_k9_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3926 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_group_1(A) -> v1_setwiseo(u1_group_1(A),u1_struct_0(A)))) # label(t34_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3927 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k6_group_1(A,np__1,B))))) # label(t44_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3928 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k3_xcmplx_0(A,B),D))))))))) # label(t67_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3929 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (-r1_xreal_0(np__0,A) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t56_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3930 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k1_nat_1(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)) & k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k1_nat_1(A,np__1),C))))))) # label(t49_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3931 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k7_binop_2(A),C))))))) # label(t71_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3932 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> r1_finseqop(u1_struct_0(A),k4_group_1(A),u1_group_1(A)))) # label(t35_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3933 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_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 = k1_group_1(A,D,k3_group_1(A,C)) <-> k1_group_1(A,B,C) = D))))))))) # label(t22_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3934 $T # label(t91_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3935 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k1_group_1(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,A,D),C)))))))))) # label(t52_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3936 (all A all B all C (v7_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & -v3_struct_0(A) -> k10_group_1(A,B,C) = k10_group_1(A,C,B))) # label(commutativity_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3937 (exists A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & v2_group_1(A) & v1_group_1(A) & l1_group_1(A))) # label(rc4_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3938 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k6_finseqop(u1_struct_0(A),u1_group_1(A)) = k4_group_1(A))) # label(t37_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3939 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(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)) -> (exists D (C = k1_group_1(A,D,B) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t24_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3940 $T # label(t2_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3941 $T # label(t40_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3942 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> r1_xreal_0(np__1,k9_group_1(A))))) # label(t90_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3943 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,A,k3_group_1(B,C)))))))) # label(t72_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3944 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v7_group_1(A) -> m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3945 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,A,k6_group_1(C,B,D)) = k6_group_1(C,k3_xcmplx_0(B,A),D))))))))) # label(t69_group_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3946 (all A (l1_vectsp_1(A) -> (v2_group_1(A) & -v3_struct_0(A) -> v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A)))) # label(cc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3947 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v5_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B)))))))))) # label(d12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3948 $T # label(t16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3949 (all A all B all C (m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l1_vectsp_1(g1_vectsp_1(A,B,C)) & v1_vectsp_1(g1_vectsp_1(A,B,C)))) # label(dt_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3950 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(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,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,C,D)) = k2_rlvect_1(A,D,k5_rlvect_1(A,C)) & k6_rlvect_1(A,B,k2_rlvect_1(A,D,C)) = k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) & k5_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,C),D)) = k2_rlvect_1(A,D,C) & k6_rlvect_1(A,C,D) = k5_rlvect_1(A,k2_rlvect_1(A,D,k5_rlvect_1(A,C))) & k5_rlvect_1(A,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k5_rlvect_1(A,D),C))))))))) # label(t64_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3951 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k10_group_1(A,B,C) <-> C = k4_vectsp_1(A,B))))))))) # label(d22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3952 $T # label(d4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3953 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k5_rlvect_1(A,B),C))))))) # label(t41_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3954 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (exists B (l4_vectsp_1(B,A) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B))))) # label(rc13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3955 $T # label(t83_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3956 $T # label(t71_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3957 $T # label(t24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3958 $T # label(t31_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3959 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & v1_funct_1(u2_vectsp_1(A,B)))) # label(dt_u2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3960 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & -v3_struct_0(B) & v11_vectsp_1(B,A))))) # label(rc12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3961 $T # label(d10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3962 (exists A l2_vectsp_1(A)) # label(existence_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3963 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & v11_vectsp_1(B,A))))) # label(rc11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3964 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C) & k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) & (exists E (k2_rlvect_1(A,B,E) = k1_rlvect_1(A) & m1_subset_1(E,u1_struct_0(A)))) & B = k2_rlvect_1(A,B,k1_rlvect_1(A)))))))) <-> v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3965 $T # label(t76_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3966 $T # label(t55_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3967 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(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_rlvect_1(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,B),C)))))))) # label(t92_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3968 $T # label(t2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3969 $T # label(t11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3970 $T # label(t1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.81 3971 $T # label(t17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3972 $T # label(t9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3973 $T # label(t75_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3974 $T # label(t91_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3975 $T # label(d1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3976 (all A all B (v8_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)))) # label(dt_k4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3977 (all A (l1_struct_0(A) -> (all B (l4_vectsp_1(B,A) -> l1_rlvect_1(B))))) # label(dt_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3978 $T # label(t8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3979 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v7_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(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,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B) & -(B != k1_rlvect_1(A) & (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_group_1(A,B,E) != k2_group_1(A))))))))))))) # label(t22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3980 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k6_rlvect_1(A,C,B))))))) # label(t81_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3981 $T # label(t37_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3982 (all A all B all C all D all E (l1_struct_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) -> -v3_struct_0(g4_vectsp_1(A,B,C,D,E)) & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(fc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3983 $T # label(t35_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3984 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,k1_rlvect_1(A),B))))) # label(t39_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3985 (all A (l1_vectsp_1(A) -> m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)))) # label(dt_u1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3986 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (all B (-v3_struct_0(B) & l4_vectsp_1(B,A) -> (v12_vectsp_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,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> E = k6_vectsp_1(A,B,k2_group_1(A),E) & k6_vectsp_1(A,B,C,k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k1_group_1(A,C,D),E) & k6_vectsp_1(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E)) & k6_vectsp_1(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,C,F))))))))))))))) # label(d26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3987 (exists A (l1_vectsp_1(A) & -v3_struct_0(A) & v1_vectsp_1(A))) # label(rc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3988 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all F all G all H all I all J (g4_vectsp_1(A,B,C,D,E) = g4_vectsp_1(F,G,H,I,J) -> C = H & J = E & D = I & B = G & F = A)))) # label(free_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3989 $T # label(t10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3990 $T # label(t27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3991 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> -(B != k1_rlvect_1(A) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) != k2_group_1(A)))))) <-> v9_vectsp_1(A)))) # label(d20_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3992 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,B,k5_rlvect_1(A,C)))))))) # label(t40_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3993 $T # label(t15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3994 $T # label(t53_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3995 $T # label(d7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3996 $T # label(t56_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3997 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_vectsp_1(A,B,k5_rlvect_1(A,C),D) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) & k6_rlvect_1(B,E,k6_vectsp_1(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)))))))))))) # label(t68_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3998 $T # label(t82_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 3999 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_rlvect_1(A) != k4_vectsp_1(A,B) & k1_rlvect_1(A) != k5_rlvect_1(A,k4_vectsp_1(A,B))))))) # label(t74_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4000 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l4_vectsp_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(B)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) = k6_vectsp_1(A,B,C,D))))))))) # label(d24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4001 $T # label(t18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4002 (all A (l3_vectsp_1(A) -> (-v3_struct_0(A) & v5_vectsp_1(A) & v4_vectsp_1(A) -> v7_vectsp_1(A) & -v3_struct_0(A)))) # label(cc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4003 $T # label(d5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4004 (all A (l2_vectsp_1(A) -> l1_vectsp_1(A) & l2_struct_0(A))) # label(dt_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4005 $T # label(t29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4006 (all A (l3_vectsp_1(A) -> l2_vectsp_1(A) & l1_rlvect_1(A))) # label(dt_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4007 (all A all B all C all D all E (v1_funct_1(B) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)))) # label(dt_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4008 (all A (v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> B = k4_vectsp_1(A,k4_vectsp_1(A,B))))))) # label(t73_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4009 $T # label(t32_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4010 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) -> (all D all E all F (g1_vectsp_1(D,E,F) = g1_vectsp_1(A,B,C) -> A = D & E = B & C = F)))) # label(free_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4011 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(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)) -> (B = k1_rlvect_1(A) | C = k1_rlvect_1(A) <-> k10_group_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t44_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4012 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(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,u1_struct_0(A)) -> k1_group_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k1_group_1(A,B,D),k1_group_1(A,C,D)))))))))) # label(t45_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4013 (exists A (l2_vectsp_1(A) & -v3_struct_0(A) & v2_vectsp_1(A))) # label(rc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4014 $T # label(t48_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4015 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) -> B = C) & (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> B = C) & (C = B -> k6_rlvect_1(A,B,C) = k1_rlvect_1(A)) & (C = B -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k1_rlvect_1(A)))))))) # label(t66_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4016 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)))))))))) # label(t69_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4017 (all A (v4_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(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,u1_struct_0(A)) -> k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t43_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4018 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_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)) -> k6_rlvect_1(A,k2_rlvect_1(A,C,B),k2_rlvect_1(A,D,B)) = k6_rlvect_1(A,C,D))))))))) # label(t90_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4019 $T # label(t19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4020 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = k1_group_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)))))))) # label(t42_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4021 (all A (l1_vectsp_1(A) -> (v7_group_1(A) & v8_vectsp_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_vectsp_1(A)))) # label(cc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4022 (all A (l1_vectsp_1(A) -> m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)))) # label(dt_k2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4023 (all A all B all C (-v3_struct_0(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l3_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) -> m1_subset_1(k5_vectsp_1(A,B,C),u1_struct_0(A)))) # label(dt_k5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4024 (exists A (-v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v2_group_1(A) & l1_vectsp_1(A))) # label(rc9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4025 $T # label(t26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4026 $T # label(t54_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4027 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) -> v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(dt_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4028 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v4_vectsp_1(A)))) # label(d11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4029 $T # label(t38_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4030 (all A (l1_vectsp_1(A) -> (v1_vectsp_1(A) -> g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A)) = A))) # label(abstractness_v1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4031 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> (v11_vectsp_1(B,A) -> g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B)) = B))) # label(abstractness_v11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4032 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k7_vectsp_1(A)))) # label(dt_k7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4033 $T # label(t77_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4034 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k2_group_1(A)) = B)) <-> v6_vectsp_1(A)))) # label(d13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4035 $T # label(d17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4036 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> -v3_struct_0(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v4_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & l1_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v7_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v3_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))))) # label(t94_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4037 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B != k1_rlvect_1(A) -> k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D))))))))) # label(t67_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4038 (all A (l1_vectsp_1(A) -> u1_vectsp_1(A) = k2_vectsp_1(A))) # label(d9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4039 (exists A (v1_vectsp_1(A) & l1_vectsp_1(A))) # label(rc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4040 $T # label(t47_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4041 $T # label(d3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4042 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> B = k7_vectsp_1(A)))))) # label(d25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4043 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> (v8_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,k2_group_1(A),B)))))) # label(d19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4044 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B))))))))) # label(t89_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4045 $T # label(t14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4046 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (k2_rlvect_1(A,k2_group_1(A),k2_group_1(A)) != k1_rlvect_1(A) <-> v13_vectsp_1(A)))) # label(d29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4047 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(A) = B | k1_rlvect_1(C) = D <-> k1_rlvect_1(C) = k6_vectsp_1(A,C,B,D)))))))))) # label(t60_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4048 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) -> B = k1_rlvect_1(A)))))) # label(t86_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4049 $T # label(t85_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4050 (all A (v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(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)) -> k5_vectsp_1(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)))))))) # label(d23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4051 (exists A l1_vectsp_1(A)) # label(existence_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4052 (all A (l3_vectsp_1(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,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)) & k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B))))))) <-> v7_vectsp_1(A)))) # label(d18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4053 $T # label(t30_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4054 (all A (l3_vectsp_1(A) -> (v3_vectsp_1(A) -> A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A))))) # label(abstractness_v3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4055 (all A (m1_subset_1(A,u1_struct_0(k3_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k3_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k3_vectsp_1)) -> k4_rlvect_1(k3_vectsp_1,A,B) = k4_rlvect_1(k3_vectsp_1,B,A) & k4_rlvect_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,A,B),C) & k4_rlvect_1(k3_vectsp_1,A,k1_rlvect_1(k3_vectsp_1)) = A & k1_rlvect_1(k3_vectsp_1) = k4_rlvect_1(k3_vectsp_1,A,k5_rlvect_1(k3_vectsp_1,A)) & -(A != k1_rlvect_1(k3_vectsp_1) & (all D (m1_subset_1(D,u1_struct_0(k3_vectsp_1)) -> k10_group_1(k3_vectsp_1,A,D) != k2_group_1(k3_vectsp_1)))) & k10_group_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,B,C),A) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,B,A),k10_group_1(k3_vectsp_1,C,A)) & k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),k10_group_1(k3_vectsp_1,A,C)) = k10_group_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) & k10_group_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),A) = A & k10_group_1(k3_vectsp_1,A,k10_group_1(k3_vectsp_1,B,C)) = k10_group_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),C) & k10_group_1(k3_vectsp_1,B,A) = k10_group_1(k3_vectsp_1,A,B))))))) # label(t21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4056 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v8_vectsp_1(A) & v6_vectsp_1(A) -> -v3_struct_0(A) & v2_group_1(A)))) # label(cc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4057 (exists A (l3_vectsp_1(A) & v3_vectsp_1(A))) # label(rc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4058 (exists A (l2_vectsp_1(A) & v2_vectsp_1(A))) # label(rc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4059 (all A (m1_subset_1(A,u1_struct_0(k1_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k1_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_1)) -> k4_rlvect_1(k1_vectsp_1,B,A) = k4_rlvect_1(k1_vectsp_1,A,B) & k1_rlvect_1(k1_vectsp_1) = k4_rlvect_1(k1_vectsp_1,A,k5_rlvect_1(k1_vectsp_1,A)) & A = k4_rlvect_1(k1_vectsp_1,A,k1_rlvect_1(k1_vectsp_1)) & k4_rlvect_1(k1_vectsp_1,A,k4_rlvect_1(k1_vectsp_1,B,C)) = k4_rlvect_1(k1_vectsp_1,k4_rlvect_1(k1_vectsp_1,A,B),C))))))) # label(t6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4060 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (v13_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_rlvect_1(A,B,B) = k1_rlvect_1(A) -> k1_rlvect_1(A) = B)))))) # label(d28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4061 $T # label(t51_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4062 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v13_vectsp_1(A))) # label(rc14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4063 $T # label(t62_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4064 $T # label(t58_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4065 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_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)) -> (k6_rlvect_1(A,C,k10_group_1(A,D,B)) = k1_rlvect_1(A) -> B = k1_rlvect_1(A) | k10_group_1(A,C,k4_vectsp_1(A,B)) = D) & (k6_rlvect_1(A,k10_group_1(A,B,D),C) = k1_rlvect_1(A) -> B = k1_rlvect_1(A) | k10_group_1(A,C,k4_vectsp_1(A,B)) = D))))))))) # label(t88_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4066 $T # label(t13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4067 $T # label(d8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4068 $T # label(t28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4069 (exists A (l1_group_1(A) & -v3_struct_0(A) & v4_group_1(A) & v7_group_1(A))) # label(rc8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4070 $T # label(t4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4071 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> k1_rlvect_1(A) = k6_rlvect_1(A,C,B)))))))) # label(t87_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4072 $T # label(t49_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4073 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_rlvect_1(C) = k6_vectsp_1(A,C,k1_rlvect_1(A),D) & k6_vectsp_1(A,C,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(C,D) & k1_rlvect_1(C) = k6_vectsp_1(A,C,B,k1_rlvect_1(C)))))))))) # label(t59_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4074 $T # label(t50_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4075 $T # label(t3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4076 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k6_rlvect_1(A,k1_rlvect_1(A),B) & B = k6_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t65_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4077 (all A (l1_vectsp_1(A) -> l1_group_1(A))) # label(dt_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4078 $T # label(d27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4079 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & l4_vectsp_1(B,A) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(B) -> m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4080 $T # label(t25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4081 (exists A l3_vectsp_1(A)) # label(existence_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4082 (all A (l2_vectsp_1(A) -> (v2_vectsp_1(A) -> A = g2_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A))))) # label(abstractness_v2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4083 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l2_vectsp_1(g2_vectsp_1(A,B,C,D)) & v2_vectsp_1(g2_vectsp_1(A,B,C,D)))) # label(dt_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4084 $T # label(d14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4085 $T # label(t57_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4086 $T # label(d2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4087 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(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,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t93_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4088 $T # label(t12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4089 $T # label(t46_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4090 (all A (l2_vectsp_1(A) & -v3_struct_0(A) -> (k1_rlvect_1(A) = k2_group_1(A) <-> v10_vectsp_1(A)))) # label(d21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4091 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A))) # label(rc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4092 (all A (l1_struct_0(A) -> (exists B l4_vectsp_1(B,A)))) # label(existence_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4093 $T # label(d16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4094 $T # label(t79_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4095 $T # label(t52_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4096 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,B,k1_rlvect_1(A)))))) # label(t36_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4097 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all F all G all H all I all J (g3_vectsp_1(F,G,H,I,J) = g3_vectsp_1(A,B,C,D,E) -> G = B & I = D & E = J & C = H & A = F)))) # label(free_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4098 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(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)) -> (k5_rlvect_1(A,B) = C <-> k1_rlvect_1(A) = k2_rlvect_1(A,B,C)))))))) # label(t63_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4099 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all E all F all G all H (g2_vectsp_1(E,F,G,H) = g2_vectsp_1(A,B,C,D) -> F = B & C = G & D = H & E = A)))) # label(free_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4100 (exists A (l3_vectsp_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4101 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(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)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> B = C))))))) # label(t84_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4102 $T # label(t34_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4103 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)) = k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)))))))))))) # label(t70_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4104 $T # label(t5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4105 $T # label(t23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4106 (exists A (v3_vectsp_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4107 (all A (v4_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(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,u1_struct_0(A)) -> (k10_group_1(A,B,D) = k10_group_1(A,B,C) -> D = C | B = k1_rlvect_1(A)))))))))) # label(t33_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4108 $T # label(t80_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4109 $T # label(t72_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4110 $T # label(t61_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4111 (all A (l3_vectsp_1(A) -> (-v3_struct_0(A) & v7_vectsp_1(A) -> v4_vectsp_1(A) & v5_vectsp_1(A) & -v3_struct_0(A)))) # label(cc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4112 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v5_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & v13_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A))) # label(rc15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4113 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v4_rlvect_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)) -> k1_binop_1(u1_rlvect_1(A),B,k1_binop_1(u1_rlvect_1(A),C,D)) = k1_binop_1(u1_rlvect_1(A),k1_binop_1(u1_rlvect_1(A),B,C),D)))))))))) # label(d3_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4114 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k1_funct_1(k5_realset2(A),k4_tarski(C,B)) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)))))))) # label(t9_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4115 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m3_realset1(B,k2_realset2(A),k4_realset2(A)) -> (B = k5_realset2(A) <-> (exists C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & k1_realset2(k2_realset2(A),k3_realset2(A),B,k4_realset2(A),C) = A))))))) # label(d12_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4116 (exists A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_realset2(A) & v1_realset2(A) & v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4117 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_realset2(A),k2_realset2(A)) & m2_relset_1(B,k2_realset2(A),k2_realset2(A)) -> ((all C (m1_subset_1(C,k2_realset2(A)) -> k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),B,C))) = k4_realset2(A))) <-> B = k7_realset2(A)))))) # label(d14_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4118 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> (k1_funct_1(k5_realset2(A),k4_tarski(B,D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)) -> C = D))))))))) # label(t30_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4119 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,B) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C))))))) # label(t5_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4120 (all A all B all C all D all E (-v1_realset1(A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,k4_xboole_0(A,k5_realset1(A,D))) & m1_subset_1(D,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_realset2(k1_realset2(A,B,C,D,E)) & l3_vectsp_1(k1_realset2(A,B,C,D,E)) & v3_vectsp_1(k1_realset2(A,B,C,D,E)))) # label(dt_k1_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4121 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k4_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(B,k4_realset2(A))))))) # label(t17_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4122 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k5_realset2(A),k4_tarski(B,D)))) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k3_realset2(A),k4_tarski(C,D)))) & k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k5_realset2(A),k4_tarski(C,D)))))))))))) # label(t3_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4123 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k4_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(k4_realset2(A),B)))))) # label(t18_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4124 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))))))))))) # label(t23_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4125 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,D)),k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(C,D))))) = k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k3_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C))),D)))))))))) # label(t16_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4126 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),B)) = B & B = k1_funct_1(k5_realset2(A),k4_tarski(B,k6_realset2(A))))))) # label(t25_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4127 (all A (-v1_realset1(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_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,k4_xboole_0(A,k5_realset1(A,D))) -> (all F (-v3_realset2(F) & l3_vectsp_1(F) & v3_vectsp_1(F) -> (u1_struct_0(F) = A & u1_rlvect_1(F) = B & u1_group_1(F) = C & E = u1_vectsp_1(F) & D = u2_struct_0(F) <-> k1_realset2(A,B,C,D,E) = F))))))))))))) # label(d6_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4128 (all A (v4_realset2(A) & l3_vectsp_1(A) -> m1_subset_1(k4_realset2(A),k2_realset2(A)))) # label(dt_k4_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4129 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (-v1_realset1(B) -> (k2_realset2(A) = B <-> (exists C (v1_funct_1(C) & (exists D (m1_subset_1(D,B) & (exists E ((exists F (A = k1_realset2(B,C,E,D,F) & m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D))))) & m3_realset1(E,B,D))))) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B)))))))) # label(d9_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4130 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C),D) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,D)))))))))) # label(t4_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4131 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k2_realset2(A)))))))) # label(t22_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4132 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> B = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),k4_realset2(A),B) & B = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,k4_realset2(A)))))) # label(t6_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4133 (exists A (v3_vectsp_1(A) & v4_realset2(A) & l3_vectsp_1(A))) # label(rc4_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4134 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & m1_subset_1(k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))))))) # label(t28_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4135 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> B = k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B)))))) # label(t27_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4136 (all A (l1_rlvect_1(A) -> (v2_realset2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_binop_1(u1_rlvect_1(A),B,C) = u2_struct_0(A) & u2_struct_0(A) = k1_binop_1(u1_rlvect_1(A),C,B)))))))) # label(d2_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4137 (all A (v4_realset2(A) & l3_vectsp_1(A) -> m2_relset_1(k8_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & v1_funct_2(k8_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & v1_funct_1(k8_realset2(A)))) # label(dt_k8_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4138 (all A (l3_vectsp_1(A) & v4_realset2(A) -> k4_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),k4_realset2(A))))) # label(t20_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4139 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (k4_realset2(A) = B <-> (exists C (m3_realset1(C,k2_realset2(A),B) & (exists D (m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),B))) & A = k1_realset2(k2_realset2(A),k3_realset2(A),C,B,D)))))))))) # label(d11_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4140 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (A = k1_realset2(k2_realset2(A),k3_realset2(A),k5_realset2(A),k4_realset2(A),B) <-> k6_realset2(A) = B))))) # label(d13_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4141 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,B) -> (k6_realset2(A) = D & C = k4_realset1(k2_realset2(A),k4_realset2(A),k5_realset2(A)) & B = k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))) -> v3_rlvect_1(g1_rlvect_1(B,C,D)) & v1_realset2(g1_rlvect_1(B,C,D)) & l1_rlvect_1(g1_rlvect_1(B,C,D)) & v2_realset2(g1_rlvect_1(B,C,D)) & v4_rlvect_1(g1_rlvect_1(B,C,D)) & -v3_struct_0(g1_rlvect_1(B,C,D))))))))))) # label(t2_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4142 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (exists C (k1_funct_1(k5_realset2(A),k4_tarski(B,C)) = k6_realset2(A) & k1_funct_1(k5_realset2(A),k4_tarski(C,B)) = k6_realset2(A) & m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))))))) # label(t11_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4143 (all A (l3_vectsp_1(A) & v4_realset2(A) -> v1_funct_2(k7_realset2(A),k2_realset2(A),k2_realset2(A)) & m2_relset_1(k7_realset2(A),k2_realset2(A),k2_realset2(A)) & v1_funct_1(k7_realset2(A)))) # label(dt_k7_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.82 4144 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (k6_realset2(A) = k1_funct_1(k5_realset2(A),k4_tarski(B,C)) -> C = k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k8_realset2(A),B)))))))) # label(t26_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4145 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> m1_subset_1(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k2_realset2(A)) & m1_subset_1(k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B),k2_realset2(A)) & m1_subset_1(k1_funct_1(k3_realset2(A),k4_tarski(B,C)),k2_realset2(A)))))))) # label(t14_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4146 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k3_realset2(A),k4_tarski(C,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),D))))) = k1_funct_1(k3_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,D))))))))))))) # label(t15_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4147 (all A (l3_vectsp_1(A) & v4_realset2(A) -> -v1_realset1(k2_realset2(A)))) # label(dt_k2_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4148 (all A (l1_rlvect_1(A) -> (v1_realset2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_binop_1(u1_rlvect_1(A),u2_struct_0(A),B) & k1_binop_1(u1_rlvect_1(A),B,u2_struct_0(A)) = B))))) # label(d1_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4149 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> (all D (m1_subset_1(D,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k1_funct_1(k5_realset2(A),k4_tarski(k1_funct_1(k5_realset2(A),k4_tarski(B,C)),D)) = k1_funct_1(k5_realset2(A),k4_tarski(B,k1_funct_1(k5_realset2(A),k4_tarski(C,D)))))))))))) # label(t8_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4150 (all A (l1_struct_0(A) -> (v3_realset2(A) <-> v1_realset1(u1_struct_0(A))))) # label(d5_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4151 (all A (l3_vectsp_1(A) & v4_realset2(A) -> k1_funct_1(k5_realset2(A),k4_tarski(k4_realset2(A),k6_realset2(A))) = k4_realset2(A))) # label(t21_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4152 (all A (l3_vectsp_1(A) & v4_realset2(A) -> m1_subset_1(k6_realset2(A),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))))) # label(dt_k6_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4153 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (all D (m1_subset_1(D,k2_realset2(A)) -> (k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,D) -> D = C))))))))) # label(t29_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4154 (all A (l3_vectsp_1(A) -> (v4_realset2(A) <-> (exists B ((exists C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & (exists D ((exists E (m3_realset1(E,B,D) & (exists F (A = k1_realset2(B,C,E,D,F) & v4_rlvect_1(g1_rlvect_1(B,C,D)) & v1_realset2(g1_rlvect_1(B,C,D)) & v2_realset2(g1_rlvect_1(B,C,D)) & (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,I)),k1_funct_1(E,k4_tarski(H,I)))) = k1_funct_1(E,k4_tarski(k1_funct_1(C,k4_tarski(G,H)),I)) & k1_funct_1(C,k4_tarski(k1_funct_1(E,k4_tarski(G,H)),k1_funct_1(E,k4_tarski(G,I)))) = k1_funct_1(E,k4_tarski(G,k1_funct_1(C,k4_tarski(H,I)))))))))) & (all G (-v1_xboole_0(G) -> (all H (v1_funct_2(H,k2_zfmisc_1(G,G),G) & m2_relset_1(H,k2_zfmisc_1(G,G),G) & v1_funct_1(H) -> (all I (m1_subset_1(I,G) -> (I = F & H = k4_realset1(B,D,E) & k4_xboole_0(B,k5_realset1(B,D)) = G -> v1_realset2(g1_rlvect_1(G,H,I)) & l1_rlvect_1(g1_rlvect_1(G,H,I)) & v2_realset2(g1_rlvect_1(G,H,I)) & v4_rlvect_1(g1_rlvect_1(G,H,I)) & v3_rlvect_1(g1_rlvect_1(G,H,I)) & -v3_struct_0(g1_rlvect_1(G,H,I))))))))) & l1_rlvect_1(g1_rlvect_1(B,C,D)) & v3_rlvect_1(g1_rlvect_1(B,C,D)) & -v3_struct_0(g1_rlvect_1(B,C,D)) & m1_subset_1(F,k4_xboole_0(B,k5_realset1(B,D))))))) & m1_subset_1(D,B))))) & -v1_realset1(B)))))) # label(d8_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4155 (all A (l3_vectsp_1(A) & v4_realset2(A) -> m3_realset1(k5_realset2(A),k2_realset2(A),k4_realset2(A)))) # label(dt_k5_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4156 (all A (v4_realset2(A) & l3_vectsp_1(A) -> m2_relset_1(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) & v1_funct_2(k3_realset2(A),k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) & v1_funct_1(k3_realset2(A)))) # label(dt_k3_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4157 (all A (v4_realset2(A) & l3_vectsp_1(A) -> v2_realset2(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & l1_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v1_realset2(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v4_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & v3_rlvect_1(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))) & -v3_struct_0(g1_rlvect_1(k2_realset2(A),k3_realset2(A),k4_realset2(A))))) # label(t1_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4158 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_binop_1(u1_rlvect_1(A),B,C) = k1_binop_1(u1_rlvect_1(A),C,B))))) <-> v3_rlvect_1(A)))) # label(d4_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4159 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> k1_funct_1(k5_realset2(A),k4_tarski(B,C)) = k1_funct_1(k5_realset2(A),k4_tarski(C,B)))))))) # label(t24_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4160 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> B = k1_funct_1(k5_realset2(A),k4_tarski(k6_realset2(A),B)) & k1_funct_1(k5_realset2(A),k4_tarski(B,k6_realset2(A))) = B)))) # label(t10_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4161 (all A (l1_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = C)))) <-> v3_realset2(A)))) # label(d7_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4162 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> B = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B)))))) # label(t13_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4163 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (v1_funct_2(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & m2_relset_1(B,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) & v1_funct_1(B) -> ((all C (m1_subset_1(C,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A)))) -> k1_funct_1(k5_realset2(A),k4_tarski(C,k8_funct_2(k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),k4_realset2(A))),B,C))) = k6_realset2(A))) <-> k8_realset2(A) = B))))) # label(d15_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4164 (all A (v4_realset2(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> k1_funct_1(k7_realset2(A),k1_funct_1(k5_realset2(A),k4_tarski(B,C))) = k1_funct_1(k5_realset2(A),k4_tarski(B,k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),C))))))))) # label(t19_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4165 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (all C (m1_subset_1(C,k2_realset2(A)) -> (k4_realset2(A) = k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) -> C = k8_funct_2(k2_realset2(A),k2_realset2(A),k7_realset2(A),B)))))))) # label(t12_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4166 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (m1_subset_1(B,k2_realset2(A)) -> (exists C (k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),B,C) = k4_realset2(A) & k2_binop_1(k2_realset2(A),k2_realset2(A),k2_realset2(A),k3_realset2(A),C,B) = k4_realset2(A) & m1_subset_1(C,k2_realset2(A)))))))) # label(t7_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4167 (all A (l3_vectsp_1(A) & v4_realset2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) & m2_relset_1(B,k2_zfmisc_1(k2_realset2(A),k2_realset2(A)),k2_realset2(A)) -> (k3_realset2(A) = B <-> (exists C (m1_subset_1(C,k2_realset2(A)) & (exists D (m3_realset1(D,k2_realset2(A),C) & (exists E (A = k1_realset2(k2_realset2(A),B,D,C,E) & m1_subset_1(E,k4_xboole_0(k2_realset2(A),k5_realset1(k2_realset2(A),C)))))))))))))) # label(d10_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4168 (exists A (l3_vectsp_1(A) & -v3_realset2(A) & v3_vectsp_1(A))) # label(rc3_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4169 (exists A (l1_struct_0(A) & v3_realset2(A))) # label(rc2_realset2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4170 (all A all B (m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> m2_finseq_1(k1_unialg_1(A,B),k4_partfun1(k13_finseq_1(A),A)))) # label(dt_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4171 (exists A (-v3_struct_0(A) & v7_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) & v3_unialg_1(A) & l1_unialg_1(A))) # label(rc5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4172 (exists A (v3_unialg_1(A) & -v3_struct_0(A) & l1_unialg_1(A))) # label(rc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4173 (exists A l1_unialg_1(A)) # label(existence_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4174 (all A (l1_unialg_1(A) -> (v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) <-> v6_unialg_1(A)))) # label(d7_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4175 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> m2_finseq_1(k3_unialg_1(A),k5_numbers))) # label(dt_k3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4176 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(u1_unialg_1(A))) -> v1_funct_1(k1_funct_1(u1_unialg_1(A),B)) & m2_relset_1(k1_funct_1(u1_unialg_1(A),B),k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))))))) # label(t5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4177 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> v3_unialg_1(g1_unialg_1(A,B)) & -v3_struct_0(g1_unialg_1(A,B)))) # label(fc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4178 $T # label(d6_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4179 (all A all B (v1_funct_1(B) & m2_relset_1(B,k13_finseq_1(A),A) -> ((all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(C,k1_relat_1(B)) & k3_finseq_1(D) = k3_finseq_1(C) -> r2_hidden(D,k1_relat_1(B))))))) <-> v2_unialg_1(B,A)))) # label(d2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4180 (all A (v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (v1_unialg_1(D,u1_struct_0(A)) & m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(D) & -v1_xboole_0(D) -> (D = k1_funct_1(u1_unialg_1(A),C) -> k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D))))))) <-> B = k3_unialg_1(A)))))) # label(d11_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4181 (exists A (v3_unialg_1(A) & l1_unialg_1(A))) # label(rc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4182 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v2_unialg_1(B,A) & v1_unialg_1(B,A) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,k13_finseq_1(A),A))))) # label(rc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4183 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> v2_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & m2_relset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k13_finseq_1(A),A) & v1_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & v1_funct_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)) & -v1_xboole_0(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)))))) # label(t2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4184 (all A (l1_unialg_1(A) -> l1_struct_0(A))) # label(dt_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4185 (all A (v6_unialg_1(A) & l1_unialg_1(A) -> v1_relat_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_finseq_1(u1_unialg_1(A)))) # label(fc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4186 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> l1_unialg_1(g1_unialg_1(A,B)) & v3_unialg_1(g1_unialg_1(A,B)))) # label(dt_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4187 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (v5_unialg_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_relset_1(D,k13_finseq_1(A),A) & v1_funct_1(D) -> (r2_hidden(C,k4_finseq_1(B)) & D = k1_funct_1(B,C) -> v2_unialg_1(D,A))))))))) # label(d5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4188 (all A (l1_unialg_1(A) -> m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))))) # label(dt_u1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4189 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k13_finseq_1(A),A) & v1_unialg_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> ((all D (m2_finseq_1(D,A) -> (r2_hidden(D,k1_relat_1(B)) -> k3_finseq_1(D) = C))) <-> C = k2_unialg_1(A,B)))))))) # label(d10_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4190 (all A (l1_unialg_1(A) & v7_unialg_1(A) -> v1_funct_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_relat_1(u1_unialg_1(A)))) # label(fc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4191 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> (v1_unialg_1(B,A) <-> (all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(C,k1_relat_1(B)) & r2_hidden(D,k1_relat_1(B)) -> k3_finseq_1(D) = k3_finseq_1(C))))))))) # label(d1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4192 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (all C all D (g1_unialg_1(C,D) = g1_unialg_1(A,B) -> A = C & D = B)))) # label(free_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4193 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(B,k13_finseq_1(A),A) & v1_unialg_1(B,A) & v1_funct_1(B) -> m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers))) # label(dt_k2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4194 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (v4_unialg_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_1(D) & m2_relset_1(D,k13_finseq_1(A),A) -> (D = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)) -> v1_unialg_1(D,A))))))))) # label(d4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4195 (all A (l1_unialg_1(A) -> (v3_unialg_1(A) -> A = g1_unialg_1(u1_struct_0(A),u1_unialg_1(A))))) # label(abstractness_v3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4196 (all A (l1_unialg_1(A) -> (v2_relat_1(u1_unialg_1(A)) & k1_xboole_0 != u1_unialg_1(A) <-> v8_unialg_1(A)))) # label(d9_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4197 (all A all B (m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> k1_unialg_1(A,B) = k5_finseq_1(B))) # label(redefinition_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4198 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m1_subset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k4_partfun1(k13_finseq_1(A),A)))))) # label(t3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4199 $T # label(d3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4200 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,k4_partfun1(k13_finseq_1(A),A)) -> (C = k2_funcop_1(k1_tarski(k6_finseq_1(A)),B) -> v2_relat_1(k1_unialg_1(A,C)) & v5_unialg_1(k1_unialg_1(A,C),A) & v4_unialg_1(k1_unialg_1(A,C),A)))))))) # label(t4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4201 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> -(-v1_xboole_0(B) & k1_xboole_0 = k1_relat_1(B)) & -(v1_xboole_0(B) & k1_xboole_0 != k1_relat_1(B)))) # label(t1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4202 (all A (l1_unialg_1(A) & v8_unialg_1(A) -> -v1_xboole_0(u1_unialg_1(A)) & v2_relat_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & v1_relat_1(u1_unialg_1(A)))) # label(fc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4203 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v5_unialg_1(B,A) & v4_unialg_1(B,A) & v1_finseq_1(B) & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)))))) # label(rc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4204 (all A (l1_unialg_1(A) -> (v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) <-> v7_unialg_1(A)))) # label(d8_unialg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4205 $T # label(t5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4206 (all A (-v3_struct_0(A) & v3_unialg_1(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) -> A = k13_msualg_1(k7_msualg_1(A),k10_msualg_1(A)))) # label(t15_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4207 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (exists B l3_msualg_1(B,A)))) # label(existence_l3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4208 (all A all B (v6_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & v3_realset2(A) & -v3_struct_0(A) -> v3_unialg_1(k13_msualg_1(A,B)) & v6_unialg_1(k13_msualg_1(A,B)) & v7_unialg_1(k13_msualg_1(A,B)) & l1_unialg_1(k13_msualg_1(A,B)) & v8_unialg_1(k13_msualg_1(A,B)) & -v3_struct_0(k13_msualg_1(A,B)))) # label(dt_k13_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4209 (all A (v3_realset2(A) & l1_msualg_1(A) & v6_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> m2_finseq_1(u5_msualg_1(A,B),k4_partfun1(k3_finseq_2(k11_msualg_1(A,B)),k11_msualg_1(A,B))))))) # label(t14_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4210 (all A all B (l1_struct_0(A) & m1_pboole(B,u1_struct_0(A)) -> l2_msualg_1(g2_msualg_1(A,B),A) & v3_msualg_1(g2_msualg_1(A,B),A))) # label(dt_g2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4211 (exists A (l1_msualg_1(A) & v1_msualg_1(A))) # label(rc1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4212 (all A (l1_msualg_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = u1_msualg_1(A))) <-> v6_msualg_1(A)))) # label(d12_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4213 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B))))))) # label(d11_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4214 (all A all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) -> -v1_xboole_0(C))))) # label(cc2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4215 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B))))) # label(d7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4216 (all A all B all C (m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) & m1_pboole(B,u1_struct_0(A)) & l1_msualg_1(A) & -v3_struct_0(A) -> (all D all E all F (g3_msualg_1(D,E,F) = g3_msualg_1(A,B,C) -> A = D & F = C & B = E)))) # label(free_g3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4217 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (v5_msualg_1(C,A) & l3_msualg_1(C,A) -> -v1_xboole_0(k5_msualg_1(A,B,C)))))))) # label(t6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4218 (exists A (l1_msualg_1(A) & v2_msualg_1(A) & v1_msualg_1(A) & -v3_struct_0(A))) # label(rc2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4219 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (v3_realset2(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) -> (all D (m1_subset_1(D,k2_relat_1(u4_msualg_1(A,B))) -> C = D))))))))) # label(t10_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4220 (all A (-v2_msualg_1(A) & v6_msualg_1(A) & l1_msualg_1(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> k13_msualg_1(A,B) = g1_unialg_1(k11_msualg_1(A,B),k12_msualg_1(A,B)))))) # label(d19_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4221 $T # label(d3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4222 (all A (l1_msualg_1(A) -> l1_struct_0(A))) # label(dt_l1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4223 (exists A (l1_msualg_1(A) & -v3_struct_0(A) & -v2_msualg_1(A) & v1_msualg_1(A))) # label(rc3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4224 $T # label(t1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4225 (all A (l1_msualg_1(A) & v6_msualg_1(A) & -v2_msualg_1(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (v5_msualg_1(C,A) & l3_msualg_1(C,A) -> r1_tarski(k3_msualg_1(A,B,C),k3_finseq_2(k11_msualg_1(A,C))))))))) # label(t13_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4226 (all A (l1_struct_0(A) -> (exists B (l2_msualg_1(B,A) & v3_msualg_1(B,A))))) # label(rc4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4227 (all A all B (l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & v3_realset2(A) & -v3_struct_0(A) -> -v1_xboole_0(k11_msualg_1(A,B)))) # label(fc4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4228 (all A all B (m1_pboole(B,u1_struct_0(A)) & l1_struct_0(A) -> (all C all D (g2_msualg_1(C,D) = g2_msualg_1(A,B) -> D = B & C = A)))) # label(free_g2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4229 (all A (v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> u1_unialg_1(A) = k9_msualg_1(A))) # label(d15_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4230 (all A all B all C (-v3_struct_0(A) & -v2_msualg_1(A) & l3_msualg_1(C,A) & m1_subset_1(B,u1_msualg_1(A)) & l1_msualg_1(A) -> m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))))) # label(dt_k4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4231 (all A (v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & -v3_struct_0(A) -> v5_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) & v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A)))) # label(fc3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4232 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B))))))) # label(d10_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4233 (all A (l1_msualg_1(A) -> (u1_msualg_1(A) = k1_xboole_0 <-> v2_msualg_1(A)))) # label(d5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4234 (all A (-v3_struct_0(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) -> (all B (v3_realset2(B) & v1_msualg_1(B) & -v2_msualg_1(B) & l1_msualg_1(B) & v6_msualg_1(B) -> (k1_tarski(np__0) = u1_struct_0(B) & u2_msualg_1(B) = k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0)) & u3_msualg_1(B) = k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0) & u1_msualg_1(B) = k4_finseq_1(k6_msualg_1(A)) <-> k7_msualg_1(A) = B))))) # label(d13_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4235 (all A (v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(A) -> v4_msualg_1(k10_msualg_1(A),k7_msualg_1(A)) & l3_msualg_1(k10_msualg_1(A),k7_msualg_1(A)))) # label(dt_k10_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4236 (all A all B all C all D (m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_1(D) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,B,k3_finseq_2(A)) & v1_funct_1(C) -> (all E all F all G all H (g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H) -> B = F & D = H & C = G & A = E)))) # label(free_g1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4237 (all A all B (-v3_struct_0(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & l1_msualg_1(A) -> (all C (m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) -> -v1_xboole_0(C))))) # label(cc1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4238 (all A all B all C (-v2_msualg_1(A) & l3_msualg_1(C,A) & m1_subset_1(B,u1_msualg_1(A)) & l1_msualg_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))))) # label(dt_k3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4239 (all A all B (l2_msualg_1(B,A) & l1_struct_0(A) -> (v3_msualg_1(B,A) -> g2_msualg_1(A,u4_msualg_1(A,B)) = B))) # label(abstractness_v3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4240 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) -> v3_realset2(k7_msualg_1(A)) & -v2_msualg_1(k7_msualg_1(A)) & v6_msualg_1(k7_msualg_1(A)) & v1_msualg_1(k7_msualg_1(A)) & -v3_struct_0(k7_msualg_1(A)))) # label(fc2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4241 (exists A l1_msualg_1(A)) # label(existence_l1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4242 (all A (l1_struct_0(A) -> (all B (l2_msualg_1(B,A) -> (v5_msualg_1(B,A) <-> v2_relat_1(u4_msualg_1(A,B))))))) # label(d8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4243 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)))))) # label(t12_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4244 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> m2_finseq_1(k6_msualg_1(A),k5_numbers))) # label(dt_k6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4245 $T # label(d2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4246 (all A all B all C (-v2_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) & l1_msualg_1(A) & -v3_struct_0(A) -> v1_funct_1(k5_msualg_1(A,B,C)) & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)))) # label(dt_k5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4247 (all A all B (l1_struct_0(A) & l2_msualg_1(B,A) -> m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)))) # label(dt_u4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4248 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) -> m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))))) # label(dt_k1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4249 (all A (l1_struct_0(A) -> (exists B (l2_msualg_1(B,A) & v5_msualg_1(B,A) & v3_msualg_1(B,A))))) # label(rc7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4250 (all A (l1_msualg_1(A) -> v1_funct_1(u2_msualg_1(A)) & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))))) # label(dt_u2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4251 $T # label(t4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4252 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> l2_msualg_1(B,A))))) # label(dt_l3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4253 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> k8_msualg_1(A) = k10_pboole(k1_tarski(np__0),u1_struct_0(A)))) # label(d14_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4254 $T # label(dt_l2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4255 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),k1_relat_1(D),C) & v1_funct_1(k1_partfun1(A,B,B,C,D,E)))))))))) # label(t7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4256 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> k1_funct_1(u2_msualg_1(A),B) = k1_msualg_1(A,B))))) # label(d6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4257 (all A (l1_msualg_1(A) -> v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & v1_funct_1(u3_msualg_1(A)))) # label(dt_u3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4258 $T # label(t3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4259 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (exists B (l3_msualg_1(B,A) & v4_msualg_1(B,A))))) # label(rc5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4260 (all A (v3_realset2(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (k11_msualg_1(A,B) = C <-> m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))))))))) # label(d17_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4261 (all A all B all C all D (v1_funct_1(C) & v1_funct_1(D) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_2(C,B,k3_finseq_2(A)) -> v1_msualg_1(g1_msualg_1(A,B,C,D)) & l1_msualg_1(g1_msualg_1(A,B,C,D)))) # label(dt_g1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4262 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & l1_msualg_1(A) -> m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))))) # label(dt_u5_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4263 (all A (v6_msualg_1(A) & l1_msualg_1(A) & -v2_msualg_1(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) & v5_msualg_1(C,A) -> k4_finseq_2(k3_finseq_1(k1_msualg_1(A,B)),k11_msualg_1(A,C)) = k3_msualg_1(A,B,C))))))) # label(t11_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4264 (all A all B (-v3_struct_0(A) & v3_realset2(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & v6_msualg_1(A) & -v2_msualg_1(A) -> m2_finseq_1(k12_msualg_1(A,B),k4_partfun1(k13_finseq_1(k11_msualg_1(A,B)),k11_msualg_1(A,B))))) # label(dt_k12_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4265 $T # label(d1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4266 (all A (v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & -v3_struct_0(A) -> g3_msualg_1(k7_msualg_1(A),k8_msualg_1(A),k9_msualg_1(A)) = k10_msualg_1(A))) # label(d16_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4267 $T # label(t2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4268 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l1_msualg_1(A) -> m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)))) # label(dt_k2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4269 (all A (l1_struct_0(A) -> (exists B l2_msualg_1(B,A)))) # label(existence_l2_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4270 $T # label(dt_k11_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4271 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & v6_msualg_1(A) & v3_realset2(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> k12_msualg_1(A,B) = u5_msualg_1(A,B))))) # label(d18_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4272 (all A all B (l1_struct_0(A) & l2_msualg_1(B,A) & v5_msualg_1(B,A) -> v1_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)))) # label(fc1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4273 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> k3_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B))))))) # label(d9_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4274 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> -v1_xboole_0(k3_unialg_1(A)))) # label(t9_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4275 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> v2_relat_1(k8_msualg_1(A)) & m1_pboole(k8_msualg_1(A),u1_struct_0(k7_msualg_1(A))))) # label(dt_k8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4276 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> k3_unialg_1(A) = k6_msualg_1(A))) # label(redefinition_k6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4277 (all A (v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0))) & m2_relset_1(B,k4_finseq_1(k6_msualg_1(A)),k3_finseq_2(k1_tarski(np__0))) & v1_funct_1(B) -> (k1_partfun1(k5_numbers,k5_numbers,k5_numbers,k3_finseq_2(k1_tarski(np__0)),k6_msualg_1(A),k9_pboole(np__0)) = B -> g1_msualg_1(k1_tarski(np__0),k4_finseq_1(k6_msualg_1(A)),B,k10_pboole(k4_finseq_1(k6_msualg_1(A)),np__0)) = k7_msualg_1(A)))))) # label(t16_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4278 (all A (l1_msualg_1(A) -> (v1_msualg_1(A) -> g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) = A))) # label(abstractness_v1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4279 $T # label(d4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4280 (exists A (-v3_struct_0(A) & v3_realset2(A) & -v2_msualg_1(A) & v6_msualg_1(A) & v1_msualg_1(A) & l1_msualg_1(A))) # label(rc8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4281 (all A (-v1_xboole_0(A) -> (all B (v1_unialg_1(B,A) & m2_relset_1(B,k3_finseq_2(A),A) & v2_unialg_1(B,A) & -v1_xboole_0(B) & v1_funct_1(B) -> k1_relat_1(B) = k1_funct_2(k2_finseq_1(k2_unialg_1(A,B)),A))))) # label(t8_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4282 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (exists B (l3_msualg_1(B,A) & v5_msualg_1(B,A) & v4_msualg_1(B,A))))) # label(rc6_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4283 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> m3_pboole(k9_msualg_1(A),u1_msualg_1(k7_msualg_1(A)),k8_pboole(u1_msualg_1(k7_msualg_1(A)),k3_finseq_2(u1_struct_0(k7_msualg_1(A))),u2_msualg_1(k7_msualg_1(A)),k6_pboole(u1_struct_0(k7_msualg_1(A)),k8_msualg_1(A))),k8_pboole(u1_msualg_1(k7_msualg_1(A)),u1_struct_0(k7_msualg_1(A)),u3_msualg_1(k7_msualg_1(A)),k8_msualg_1(A))))) # label(dt_k9_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4284 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> v3_realset2(k7_msualg_1(A)) & l1_msualg_1(k7_msualg_1(A)) & v6_msualg_1(k7_msualg_1(A)) & -v2_msualg_1(k7_msualg_1(A)) & v1_msualg_1(k7_msualg_1(A)))) # label(dt_k7_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4285 $T # label(dt_u1_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4286 (all A all B (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) -> (v4_msualg_1(B,A) -> B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B))))) # label(abstractness_v4_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4287 (all A all B all C (l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) & -v3_struct_0(A) -> l3_msualg_1(g3_msualg_1(A,B,C),A) & v4_msualg_1(g3_msualg_1(A,B,C),A))) # label(dt_g3_msualg_1) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4288 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(C,B,k3_finseq_2(A)) -> -v3_struct_0(g1_msualg_1(A,B,C,D)) & v1_msualg_1(g1_msualg_1(A,B,C,D)))) # label(fc3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4289 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all C (m1_msualg_2(C,A,B) -> l3_msualg_1(C,A))))) # label(dt_m1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4290 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v2_relat_1(k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C)) -> v2_relat_1(k9_msualg_2(A,B,C))))))))) # label(t17_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4291 (all A all B (l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k14_msualg_2(A,B)))) # label(fc11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4292 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> m1_msualg_2(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A,B))))) # label(t38_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4293 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v2_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t33_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4294 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A) -> (all D (v4_msualg_1(D,A) & m1_msualg_2(D,A,B) -> C = k11_msualg_2(A,B,C,k13_msualg_2(A,B,C,D)))))))))) # label(t28_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4295 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) -> (r2_hidden(E,k5_msualg_2(A,C,D)) -> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B))))))))))))) # label(t18_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.83 4296 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> k12_msualg_2(A,B,k2_msualg_2(A,B)) = k11_msualg_2(A,B,k12_msualg_2(A,B,k2_msualg_2(A,B)),C))))))) # label(t24_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4297 (all A all B all C (v2_msualg_2(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k1_msualg_2(A,B,C)))) # label(fc4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4298 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> m1_msualg_2(B,A,B))))) # label(t6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4299 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v4_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> B = k12_msualg_2(A,B,C)))))))) # label(t22_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4300 (all A all B all C all D (-v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & m1_msualg_2(C,A,B) & m1_msualg_2(D,A,B) & l3_msualg_1(B,A) & -v3_struct_0(A) -> m1_msualg_2(k13_msualg_2(A,B,C,D),A,B) & v4_msualg_1(k13_msualg_2(A,B,C,D),A))) # label(dt_k13_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4301 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> r6_pboole(u1_msualg_1(A),k4_msualg_2(A,B,C),u5_msualg_1(A,B))))))))) # label(t5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4302 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m3_pboole(D,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)) -> (D = k4_msualg_2(A,B,C) <-> (all E (m1_subset_1(E,u1_msualg_1(A)) -> k3_msualg_2(A,B,E,C) = k1_funct_1(D,E)))))))))))) # label(d9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4303 (all A all B (v2_msualg_2(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> v2_relat_1(k2_msualg_2(A,B)) & v1_funct_1(k2_msualg_2(A,B)) & -v3_relat_1(k2_msualg_2(A,B)) & v1_relat_1(k2_msualg_2(A,B)))) # label(fc5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4304 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C ((all D (r2_hidden(D,C) <-> v4_msualg_1(D,A) & m1_msualg_2(D,A,B))) <-> C = k14_msualg_2(A,B))))))) # label(d20_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4305 (all A (v2_msualg_2(A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v5_msualg_1(C,A) -> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)) & v2_relat_1(k2_msualg_2(A,B)))))))) # label(t12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4306 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> r1_tarski(k5_msualg_2(A,B,C),k6_msualg_2(A,B)))))))) # label(t41_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4307 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (exists C (v4_msualg_1(C,A) & m1_msualg_2(C,A,B))))) # label(rc2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4308 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> (all D (m1_subset_1(D,u1_msualg_1(A)) -> k5_msualg_1(A,D,B) = k3_msualg_2(A,B,D,C))) & v3_msualg_2(C,A,B)))))))) # label(t4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4309 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) & v4_msualg_1(B,A) -> B = k6_lattices(k17_msualg_2(A,B)))))) # label(t37_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4310 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E ((all F ((exists G (F = k1_funct_1(G,D) & r2_hidden(G,k5_msualg_2(A,B,C)) & m4_pboole(G,u1_struct_0(A),u4_msualg_1(A,B)))) <-> r2_hidden(F,E))) <-> k8_msualg_2(A,B,C,D) = E)))))))))) # label(d14_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4311 (all A all B all C all D (l3_msualg_1(B,A) & m1_msualg_2(D,A,B) & m1_msualg_2(C,A,B) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> v4_msualg_1(k11_msualg_2(A,B,C,D),A) & m1_msualg_2(k11_msualg_2(A,B,C,D),A,B))) # label(dt_k11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4312 $T # label(dt_k8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4313 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v15_lattices(k17_msualg_2(A,B)))))) # label(t34_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4314 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,k6_msualg_2(A,B)) -> C = k7_msualg_2(A,B,C))))))) # label(d13_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4315 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) -> -v3_struct_0(k17_msualg_2(A,B)) & v3_lattices(k17_msualg_2(A,B)) & v5_lattices(k17_msualg_2(A,B)) & v6_lattices(k17_msualg_2(A,B)) & v7_lattices(k17_msualg_2(A,B)) & v15_lattices(k17_msualg_2(A,B)) & v14_lattices(k17_msualg_2(A,B)) & v13_lattices(k17_msualg_2(A,B)) & v10_lattices(k17_msualg_2(A,B)) & v9_lattices(k17_msualg_2(A,B)) & v8_lattices(k17_msualg_2(A,B)) & v4_lattices(k17_msualg_2(A,B)))) # label(fc12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4316 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> v3_msualg_2(k9_msualg_2(A,B,C),A,B) & r2_pboole(u1_struct_0(A),C,k9_msualg_2(A,B,C)))))))) # label(t21_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4317 $T # label(d1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4318 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v4_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A))) # label(fc6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4319 (all A all B all C (-v3_struct_0(A) & l1_msualg_1(A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l3_msualg_1(B,A) & -v2_msualg_1(A) -> m3_pboole(k4_msualg_2(A,B,C),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),C)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),C)))) # label(dt_k4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4320 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k9_msualg_2(A,C,D)),B)))))))))) # label(t20_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4321 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) -> ((all D (m1_subset_1(D,k14_msualg_2(A,B)) -> (all E (m1_subset_1(E,k14_msualg_2(A,B)) -> (all F (v4_msualg_1(F,A) & m1_msualg_2(F,A,B) -> (all G (v4_msualg_1(G,A) & m1_msualg_2(G,A,B) -> (F = D & G = E -> k11_msualg_2(A,B,F,G) = k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E)))))))))) <-> C = k16_msualg_2(A,B)))))))) # label(d22_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4322 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> v1_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t30_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4323 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> (r2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)) -> m1_msualg_2(C,A,D)))))))))) # label(t9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4324 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (l3_msualg_1(C,A) -> (all D (l3_msualg_1(D,A) -> (m1_msualg_2(C,A,D) & m1_msualg_2(B,A,C) -> m1_msualg_2(B,A,D)))))))))) # label(t7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4325 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)) -> k12_msualg_2(A,B,D) = C))))))))) # label(t23_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4326 (all A all B all C (-v2_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l1_msualg_1(A) & -v3_struct_0(A) -> v4_msualg_1(k10_msualg_2(A,B,C),A) & m1_msualg_2(k10_msualg_2(A,B,C),A,B))) # label(dt_k10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4327 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> g3_lattices(k14_msualg_2(A,B),k15_msualg_2(A,B),k16_msualg_2(A,B)) = k17_msualg_2(A,B))))) # label(d23_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4328 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(C,A,B) <-> (all D (m1_subset_1(D,u1_msualg_1(A)) -> r1_msualg_2(A,B,D,C)))))))))) # label(d7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4329 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) -> (k1_funct_1(u4_msualg_1(A,B),C) != k1_xboole_0 -> (k1_msualg_2(A,B,C) = D <-> (exists E (-v1_xboole_0(E) & a_4_0_msualg_2(A,B,C,E) = D & k1_funct_1(u4_msualg_1(A,B),C) = E)))) & (k1_xboole_0 = k1_funct_1(u4_msualg_1(A,B),C) -> (k1_xboole_0 = D <-> k1_msualg_2(A,B,C) = D)))))))))) # label(d4_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4330 (all A all B (l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & -v2_msualg_1(A) & -v3_struct_0(A) -> m2_relset_1(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_2(k16_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_1(k16_msualg_2(A,B)))) # label(dt_k16_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4331 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (exists C m1_msualg_2(C,A,B)))) # label(existence_m1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4332 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> (all E (v4_msualg_1(E,A) & m1_msualg_2(E,A,B) -> (E = k13_msualg_2(A,B,C,D) <-> (all F (m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),F,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))) -> k12_msualg_2(A,B,F) = E)))))))))))))) # label(d19_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4333 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v1_msualg_2(B,A) <-> (exists C (m1_subset_1(C,u1_msualg_1(A)) & k1_funct_1(u2_msualg_1(A),C) = k1_xboole_0 & k1_funct_1(u3_msualg_1(A),C) = B))))))) # label(d2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4334 (all A all B (l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,B)))) # label(dt_k2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4335 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> (all E (v4_msualg_1(E,A) & m1_msualg_2(E,A,B) -> (E = k11_msualg_2(A,B,C,D) <-> r6_pboole(u1_struct_0(A),u4_msualg_1(A,E),k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))) & (all F (m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),F,u4_msualg_1(A,E)) -> v3_msualg_2(F,A,B) & r6_pboole(u1_msualg_1(A),u5_msualg_1(A,E),k4_msualg_2(A,B,F)))))))))))))))) # label(d17_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4336 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v1_msualg_2(B,A))) <-> v2_msualg_2(A)))) # label(d3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4337 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_2(C,k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_1(C) -> (C = k15_msualg_2(A,B) <-> (all D (m1_subset_1(D,k14_msualg_2(A,B)) -> (all E (m1_subset_1(E,k14_msualg_2(A,B)) -> (all F (v4_msualg_1(F,A) & m1_msualg_2(F,A,B) -> (all G (m1_msualg_2(G,A,B) & v4_msualg_1(G,A) -> (F = D & G = E -> k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),C,D,E) = k13_msualg_2(A,B,F,G))))))))))))))))) # label(d21_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4338 (exists A (l1_msualg_1(A) & -v3_struct_0(A) & v1_msualg_1(A) & -v2_msualg_1(A) & v2_msualg_2(A))) # label(rc1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4339 $T # label(dt_k5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4340 (all A all B all C (-v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & -v2_msualg_1(A) -> m1_subset_1(k1_msualg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))))) # label(dt_k1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4341 (all A all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (exists C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A) & v5_msualg_1(C,A))))) # label(rc3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4342 (all A all B all C all D (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_msualg_1(A)) & m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> v1_funct_1(k3_msualg_2(A,B,C,D)) & m2_relset_1(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) & v1_funct_2(k3_msualg_2(A,B,C,D),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)))) # label(dt_k3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4343 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (v4_msualg_1(D,A) & m1_msualg_2(D,A,B) -> (D = k12_msualg_2(A,B,C) <-> (all E (m1_msualg_2(E,A,B) -> (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,E)) -> m1_msualg_2(D,A,E)))) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,D))))))))))) # label(d18_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4344 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r1_msualg_2(A,B,C,D) -> k3_msualg_2(A,B,C,D) = k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C))))))))))) # label(d8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4345 $T # label(t39_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4346 (all A (v2_msualg_2(A) & l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v5_msualg_1(C,A) -> (all D (v5_msualg_1(D,A) & m1_msualg_2(D,A,B) -> v2_relat_1(k3_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D))))))))))) # label(t13_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4347 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) -> (r2_pboole(u1_struct_0(A),D,E) -> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),B))))))))))))) # label(t3_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4348 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,B)) -> k13_msualg_2(A,B,k12_msualg_2(A,B,D),C) = k12_msualg_2(A,B,D)))))))))) # label(t26_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4349 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l3_msualg_1(B,A) & l1_msualg_1(A) -> -v1_xboole_0(k6_msualg_2(A,B)))) # label(fc8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4350 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> k5_lattices(k17_msualg_2(A,B)) = k12_msualg_2(A,B,k2_msualg_2(A,B)))))) # label(t35_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4351 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (v4_msualg_1(C,A) & m1_msualg_2(C,A,B) -> (all D (v4_msualg_1(D,A) & m1_msualg_2(D,A,B) -> D = k13_msualg_2(A,B,k11_msualg_2(A,B,C,D),D))))))))) # label(t29_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4352 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (D = k9_msualg_2(A,B,C) <-> (all E (m1_subset_1(E,u1_struct_0(A)) -> k1_setfam_1(k8_msualg_2(A,B,C,E)) = k1_funct_1(D,E)))))))))))) # label(d15_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4353 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(C,A,B) -> k10_msualg_2(A,B,C) = g3_msualg_1(A,C,k4_msualg_2(A,B,C))))))))) # label(d16_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4354 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (m1_subset_1(B,u1_msualg_1(A)) -> (all C (l3_msualg_1(C,A) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,C)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,C)) -> (r2_hidden(E,k5_msualg_2(A,C,D)) -> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,B,C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_msualg_2(A,C,D))),B))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),E),B))))))))))))) # label(t19_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4355 (all A all B all C (-v2_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l1_msualg_1(A) & -v3_struct_0(A) -> m4_pboole(k9_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)))) # label(dt_k9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4356 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> v2_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t31_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4357 (all A all B (-v3_struct_0(A) & -v2_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) -> v1_funct_1(k15_msualg_2(A,B)) & m2_relset_1(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)) & v1_funct_2(k15_msualg_2(A,B),k2_zfmisc_1(k14_msualg_2(A,B),k14_msualg_2(A,B)),k14_msualg_2(A,B)))) # label(dt_k15_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4358 (all A all B all C (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> v4_msualg_1(k12_msualg_2(A,B,C),A) & m1_msualg_2(k12_msualg_2(A,B,C),A,B))) # label(dt_k12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4359 (all A all B all C (m1_pboole(B,A) & v2_relat_1(C) & m1_pboole(C,A) -> v1_funct_1(k2_pboole(A,B,C)) & v2_relat_1(k2_pboole(A,B,C)) & v1_relat_1(k2_pboole(A,B,C)))) # label(fc1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4360 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> r2_pboole(u1_struct_0(A),k2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C),k9_msualg_2(A,B,C)))))))) # label(t16_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4361 $T # label(dt_k6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4362 (all A all B all C (-v3_struct_0(A) & -v2_msualg_1(A) & m1_subset_1(C,k6_msualg_2(A,B)) & l3_msualg_1(B,A) & l1_msualg_1(A) -> m4_pboole(k7_msualg_2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B)))) # label(dt_k7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4363 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (l3_msualg_1(C,A) -> ((all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)) -> r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) & v3_msualg_2(D,A,B)))) & m4_pboole(u4_msualg_1(A,C),u1_struct_0(A),u4_msualg_1(A,B)) <-> m1_msualg_2(C,A,B)))))))) # label(d10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4364 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B)) -> k12_msualg_2(A,B,C) = k6_lattices(k17_msualg_2(A,B))))))))) # label(t36_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4365 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D ((all E (r2_hidden(E,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B))))) & m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B)) & (all F (m4_pboole(F,u1_struct_0(A),u4_msualg_1(A,B)) -> (F = E -> r2_pboole(u1_struct_0(A),C,F) & r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),F) & v3_msualg_2(F,A,B)))) <-> r2_hidden(E,D))) <-> k5_msualg_2(A,B,C) = D)))))))) # label(d11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4366 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (k2_msualg_2(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_funct_1(C,D) = k1_msualg_2(A,B,D)))))))))) # label(d5_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4367 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> r2_hidden(u4_msualg_1(A,B),k5_msualg_2(A,B,C)))))))) # label(t40_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4368 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m1_msualg_2(D,A,B) -> k13_msualg_2(A,B,D,C) = k13_msualg_2(A,B,C,D))))))))) # label(t27_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4369 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> v1_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)))))) # label(t32_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4370 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r2_hidden(D,k5_msualg_2(A,B,C)) <-> r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),D) & r2_pboole(u1_struct_0(A),C,D) & v3_msualg_2(D,A,B)))))))))) # label(t14_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4371 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (l3_msualg_1(C,A) -> (v4_msualg_1(C,A) & m1_msualg_2(C,A,B) & m1_msualg_2(B,A,C) & v4_msualg_1(B,A) -> B = C))))))) # label(t8_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4372 (all A all B all C all D all E (-v2_msualg_1(B) & -v1_xboole_0(E) & m1_subset_1(D,u1_struct_0(B)) & l3_msualg_1(C,B) & l1_msualg_1(B) & -v3_struct_0(B) -> ((exists F (m1_subset_1(F,E) & (exists G (m1_subset_1(G,u1_msualg_1(B)) & r2_hidden(F,k2_relat_1(k5_msualg_1(B,G,C))) & D = k1_funct_1(u3_msualg_1(B),G) & k1_xboole_0 = k1_funct_1(u2_msualg_1(B),G))) & F = A)) <-> r2_hidden(A,a_4_0_msualg_2(B,C,D,E))))) # label(fraenkel_a_4_0_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4373 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (v5_msualg_1(B,A) & l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),E,k2_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))) -> k13_msualg_2(A,B,k12_msualg_2(A,B,D),C) = k12_msualg_2(A,B,E)))))))))))) # label(t25_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4374 (all A all B all C (v2_relat_1(C) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_relat_1(k2_pboole(A,C,B)) & v1_funct_1(k2_pboole(A,C,B)) & v2_relat_1(k2_pboole(A,C,B)))) # label(fc2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4375 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k3_xboole_0(k4_card_3(k5_relat_1(D,B)),k4_card_3(k5_relat_1(D,C))) = k4_card_3(k5_relat_1(D,k3_pboole(A,B,C))))))))))) # label(t2_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4376 (all A all B all C all D (-v3_struct_0(A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) & l3_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> -v1_xboole_0(k8_msualg_2(A,B,C,D)))) # label(fc9_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4377 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) & v4_msualg_1(C,A) -> (all D (v4_msualg_1(D,A) & m1_msualg_2(D,A,B) -> (r6_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)) -> D = C))))))))) # label(t10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4378 $T # label(t1_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4379 (all A (-v2_msualg_1(A) & l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_msualg_2(C,A,B) -> m4_pboole(k2_msualg_2(A,B),u1_struct_0(A),u4_msualg_1(A,C)))))))) # label(t11_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4380 (all A all B (-v3_struct_0(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & l1_msualg_1(A) & -v2_msualg_1(A) -> -v3_struct_0(k17_msualg_2(A,B)) & v3_lattices(k17_msualg_2(A,B)) & l3_lattices(k17_msualg_2(A,B)) & v10_lattices(k17_msualg_2(A,B)))) # label(dt_k17_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4381 (all A all B all C (-v3_struct_0(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v2_relat_1(C) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l1_msualg_1(A) & -v2_msualg_1(A) -> v4_msualg_1(k12_msualg_2(A,B,C),A) & v5_msualg_1(k12_msualg_2(A,B,C),A))) # label(fc10_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4382 $T # label(dt_k14_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4383 (all A all B all C (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l3_msualg_1(B,A) -> -v1_xboole_0(k5_msualg_2(A,B,C)))) # label(fc7_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4384 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),D)),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),D),C)) <-> r1_msualg_2(A,B,C,D)))))))))) # label(d6_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4385 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (v3_msualg_2(C,A,B) <-> r2_hidden(C,k6_msualg_2(A,B))))))))) # label(t15_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4386 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> (all C ((all D (r2_hidden(D,k1_funct_2(u1_struct_0(A),k1_zfmisc_1(k3_card_3(u4_msualg_1(A,B))))) & (all E (m4_pboole(E,u1_struct_0(A),u4_msualg_1(A,B)) -> (D = E -> v3_msualg_2(E,A,B)))) & m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) <-> r2_hidden(D,C))) <-> C = k6_msualg_2(A,B))))))) # label(d12_msualg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4387 (all A (-v1_xboole_0(A) -> (all B (l1_msualg_1(B) & -v2_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k2_funct_6(k13_pralg_2(A,B,C,D)),E) = k3_msualg_1(B,D,k6_pralg_2(A,B,C,E)))) & k1_relat_1(k2_funct_6(k13_pralg_2(A,B,C,D))) = A)))))))) # label(t18_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4388 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> v1_fraenkel(k4_card_3(B)) & v1_pralg_2(k4_card_3(B)) & -v1_xboole_0(k4_card_3(B)))) # label(fc1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4389 $T # label(t19_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4390 (all A all B all C (-v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & -v2_msualg_1(B) -> v4_msualg_1(k15_pralg_2(A,B,C),B))) # label(fc8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4391 $T # label(dt_k8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4392 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k2_pralg_2(A) <-> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_relat_1(B)) -> k1_funct_1(B,C) = k1_funct_1(A,k10_funct_6(C))))) & (all C ((exists D (v1_funct_1(D) & r2_hidden(D,k1_relat_1(A)) & k10_funct_6(D) = C & v1_relat_1(D))) <-> r2_hidden(C,k1_relat_1(B))))))))) # label(d6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4393 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> k1_relat_1(k4_funct_5(k12_pralg_2(A,B,C))) = k2_zfmisc_1(A,u1_msualg_1(B)))))) # label(t12_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4394 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k2_pralg_2(A)) & v1_relat_1(k2_pralg_2(A)))) # label(dt_k2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4395 $T # label(dt_k1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4396 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> m1_pboole(C,A))))) # label(dt_m2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4397 $T # label(t7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4398 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) & v2_relat_1(C) -> (all D (m1_pboole(D,A) & v2_relat_1(D) -> (all E (m2_relset_1(E,B,k3_finseq_2(A)) & v1_funct_2(E,B,k3_finseq_2(A)) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,A) & v1_funct_2(F,B,A) -> (all G (m3_pboole(G,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),k8_pboole(B,A,F,C)) -> (all H (m3_pboole(H,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),k8_pboole(B,A,F,D)) -> (all I (m3_pboole(I,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),k8_pboole(B,A,F,k11_pboole(A,C,D))) -> (I = k5_pralg_2(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,B) -> (all K (m2_relset_1(K,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),J),k1_funct_1(k8_pboole(B,A,F,C),J)) & v1_funct_2(K,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),J),k1_funct_1(k8_pboole(B,A,F,C),J)) & v1_funct_1(K) -> (all L (v1_funct_1(L) & m2_relset_1(L,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),J),k1_funct_1(k8_pboole(B,A,F,D),J)) & v1_funct_2(L,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),J),k1_funct_1(k8_pboole(B,A,F,D),J)) -> (k1_funct_1(G,J) = K & L = k1_funct_1(H,J) -> k4_pralg_2(A,B,C,D,E,F,J,K,L) = k1_funct_1(I,J))))))))))))))))))))))))) # label(d11_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4399 $T # label(t6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4400 (all A (v1_pralg_2(A) & v1_fraenkel(A) -> (all B ((A = k1_xboole_0 -> (B = k1_xboole_0 <-> k1_pralg_2(A) = B)) & (k1_xboole_0 != A -> (k1_pralg_2(A) = B <-> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,A) -> B = k1_relat_1(C)))))))))) # label(d2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4401 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) & -v2_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> k15_pralg_2(A,B,C) = g3_msualg_1(B,k11_pralg_2(A,B,C),k14_pralg_2(A,B,C)))))) # label(d21_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4402 (all A all B all C all D (l1_msualg_1(B) & m1_subset_1(C,u1_struct_0(B)) & m2_pralg_2(D,A,B) & -v3_struct_0(B) -> m1_pboole(k10_pralg_2(A,B,C,D),A))) # label(dt_k10_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4403 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> r6_pboole(B,k7_pboole(B,A,E,k11_pboole(A,C,D)),k11_pboole(B,k7_pboole(B,A,E,C),k7_pboole(B,A,E,D))))))))))) # label(t9_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4404 $T # label(t4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4405 (all A all B all C all D (-v3_struct_0(C) & m2_pralg_2(D,B,C) & l1_msualg_1(C) & -v1_xboole_0(B) -> ((exists E (m1_subset_1(E,B) & A = k7_pralg_2(C,k6_pralg_2(B,C,D,E)))) <-> r2_hidden(A,a_3_0_pralg_2(B,C,D))))) # label(fraenkel_a_3_0_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4406 (all A all B all C (-v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) -> v1_funcop_1(k12_pralg_2(A,B,C)) & m1_pboole(k12_pralg_2(A,B,C),A))) # label(dt_k12_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4407 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & v2_relat_1(D) & v1_funct_1(E) & v1_funct_1(I) & v1_funct_2(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) & m1_relset_1(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) & m1_relset_1(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & v1_funct_2(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & v1_funct_1(H) & m1_relset_1(F,B,A) & v1_funct_2(F,B,A) & v1_funct_1(F) & m1_relset_1(E,B,k3_finseq_2(A)) & v1_funct_2(E,B,k3_finseq_2(A)) & m1_pboole(D,A) & m1_pboole(C,A) & v2_relat_1(C) -> v1_funct_2(k4_pralg_2(A,B,C,D,E,F,G,H,I),k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & m2_relset_1(k4_pralg_2(A,B,C,D,E,F,G,H,I),k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & v1_funct_1(k4_pralg_2(A,B,C,D,E,F,G,H,I)))) # label(dt_k4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4408 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> (all B (m1_pboole(B,k4_card_3(k2_funct_6(A))) & v1_funcop_1(B) -> (k3_pralg_2(A) = B <-> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k4_card_3(k2_funct_6(A))) -> k15_pralg_1(A,C) = k1_funct_1(B,C))))))))) # label(d8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4409 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & -v2_msualg_1(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(E,k2_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D)))) -> A = k1_relat_1(E) & (all F (m1_subset_1(F,A) -> r2_hidden(k1_funct_1(E,F),k4_msualg_1(B,D,k6_pralg_2(A,B,C,F)))))))))))))))) # label(t16_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4410 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (-v3_struct_0(C) & -v2_msualg_1(C) & l1_msualg_1(C) -> (all D (m2_pralg_2(D,A,C) -> (all E (m1_subset_1(E,u1_msualg_1(C)) -> k5_msualg_1(C,E,k6_pralg_2(A,C,D,B)) = k1_funct_1(k13_pralg_2(A,C,D,E),B))))))))))) # label(t14_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4411 (all A all B all C (-v3_struct_0(B) & m2_pralg_2(C,A,B) & l1_msualg_1(B) & -v2_msualg_1(B) -> l3_msualg_1(k15_pralg_2(A,B,C),B))) # label(dt_k15_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4412 (all A all B all C (m2_pralg_2(C,A,B) & l1_msualg_1(B) & -v3_struct_0(B) -> v2_relat_1(k11_pralg_2(A,B,C)) & -v3_relat_1(k11_pralg_2(A,B,C)) & v1_funct_1(k11_pralg_2(A,B,C)) & v1_relat_1(k11_pralg_2(A,B,C)))) # label(fc7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4413 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_pboole(D,u1_struct_0(B)) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> k4_card_3(k10_pralg_2(A,B,E,C)) = k1_funct_1(D,E))) <-> k11_pralg_2(A,B,C) = D))))))) # label(d17_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4414 $T # label(d5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4415 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m2_pralg_2(D,A,B) -> (all E (m1_pboole(E,A) -> (A != k1_xboole_0 -> ((all F -((all G (l3_msualg_1(G,B) -> -(k1_funct_1(E,F) = k1_funct_1(u4_msualg_1(B,G),C) & k1_funct_1(D,F) = G))) & r2_hidden(F,A))) <-> k10_pralg_2(A,B,C,D) = E)) & (A = k1_xboole_0 -> (E = k1_xboole_0 <-> k10_pralg_2(A,B,C,D) = E)))))))))) # label(d16_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4416 $T # label(d3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4417 (all A all B all C all D (m2_pralg_2(C,A,B) & m1_subset_1(D,A) & l1_msualg_1(B) & -v3_struct_0(B) & -v1_xboole_0(A) -> k6_pralg_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4418 (all A (v1_pralg_2(A) & v1_fraenkel(A) & -v1_xboole_0(A) -> (all B (m1_pralg_2(B,A) -> m1_pboole(B,k1_pralg_2(A)))))) # label(dt_m1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4419 $T # label(t5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4420 (all A all B (l1_msualg_1(B) & -v2_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m3_pboole(D,u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C))) -> (A != k1_xboole_0 -> ((all E (m1_subset_1(E,u1_msualg_1(B)) -> k1_funct_1(D,E) = k1_cqc_lang(k1_msualg_1(B,E),k1_xboole_0,k10_funct_6(k13_pralg_2(A,B,C,E)),k2_pralg_2(k3_pralg_2(k13_pralg_2(A,B,C,E)))))) <-> D = k14_pralg_2(A,B,C))) & (A = k1_xboole_0 -> D = k14_pralg_2(A,B,C)))))))) # label(d20_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4421 (all A all B all C (l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & v5_msualg_1(B,A) & -v3_struct_0(A) -> l3_msualg_1(k9_pralg_2(A,B,C),A))) # label(dt_k9_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4422 $T # label(t3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4423 (all A (-v3_struct_0(A) & -v2_msualg_1(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> k3_msualg_1(A,C,B) = k4_card_3(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))) & k1_funct_1(u4_msualg_1(A,B),k2_msualg_1(A,C)) = k4_msualg_1(A,C,B) & k1_relat_1(k1_msualg_1(A,C)) = k1_relat_1(k5_relat_1(k1_msualg_1(A,C),u4_msualg_1(A,B))))))))) # label(t10_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4424 (all A (v1_pralg_2(A) & v1_fraenkel(A) & -v1_xboole_0(A) -> (all B (m1_pralg_2(B,A) <-> m1_subset_1(B,A))))) # label(redefinition_m1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4425 (all A (-v1_xboole_0(A) -> (all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> k8_pralg_2(A,B,C) = k3_tarski(a_3_0_pralg_2(A,B,C)))))))) # label(d14_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4426 (all A (-v3_struct_0(A) & l1_msualg_1(A) & -v2_msualg_1(A) -> (all B (l3_msualg_1(B,A) -> (all C (m1_subset_1(C,u1_msualg_1(A)) -> (k1_xboole_0 = k1_msualg_1(A,C) -> k1_tarski(k1_xboole_0) = k3_msualg_1(A,C,B)))))))) # label(t11_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4427 (all A all B all C (l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & -v3_struct_0(A) -> v4_msualg_1(k9_pralg_2(A,B,C),A))) # label(fc5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4428 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) -> (exists C m2_pralg_2(C,A,B)))) # label(existence_m2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4429 (all A (v1_pralg_2(A) & v1_fraenkel(A) -> (k1_tarski(k1_xboole_0) = A -> k1_xboole_0 = k1_pralg_2(A)))) # label(t2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4430 (all A all B all C all D (m1_subset_1(D,A) & m2_pralg_2(C,A,B) & l1_msualg_1(B) & -v3_struct_0(B) & -v1_xboole_0(A) -> l3_msualg_1(k6_pralg_2(A,B,C,D),B) & v5_msualg_1(k6_pralg_2(A,B,C,D),B))) # label(dt_k6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4431 (all A all B all C all D (-v3_struct_0(B) & l1_msualg_1(B) & m1_subset_1(D,u1_msualg_1(B)) & m2_pralg_2(C,A,B) & -v2_msualg_1(B) -> m1_pboole(k13_pralg_2(A,B,C,D),A) & v1_funcop_1(k13_pralg_2(A,B,C,D)))) # label(dt_k13_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4432 (all A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funcop_1(k3_pralg_2(A)) & m1_pboole(k3_pralg_2(A),k4_card_3(k2_funct_6(A))))) # label(dt_k3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4433 (all A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k3_pralg_2(A) = k7_funct_6(A))) # label(redefinition_k3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4434 (all A (l1_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) -> k7_pralg_2(A,B) = k3_tarski(k2_relat_1(u4_msualg_1(A,B))))))) # label(d13_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4435 $T # label(dt_k7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4436 (all A all B (l1_msualg_1(B) & -v2_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> k1_funct_1(k10_funct_6(k12_pralg_2(A,B,C)),D) = k13_pralg_2(A,B,C,D))))))) # label(d19_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.84 4437 (all A (-v1_xboole_0(A) -> (all B (-v2_msualg_1(B) & l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> r2_hidden(k10_funct_6(k12_pralg_2(A,B,C)),k1_funct_2(u1_msualg_1(B),k1_funct_2(A,k2_relat_1(k4_funct_5(k12_pralg_2(A,B,C)))))))))))))) # label(t13_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4438 (all A all B all C (m1_pboole(C,A) & v2_relat_1(C) & m1_pboole(B,A) & v2_relat_1(B) -> v2_relat_1(k11_pboole(A,B,C)) & v1_funct_1(k11_pboole(A,B,C)) & v1_relat_1(k11_pboole(A,B,C)))) # label(fc2_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4439 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & -v2_msualg_1(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(E,k1_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D)))) -> A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),k1_fraenkel(k1_relat_1(k1_msualg_1(B,D)),k8_pralg_2(A,B,C))) & (all F (m1_subset_1(F,A) -> r2_hidden(k1_funct_1(E,F),k3_msualg_1(B,D,k6_pralg_2(A,B,C,F)))))))))))))))) # label(t17_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4440 (all A all B all C (-v2_msualg_1(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) & -v3_struct_0(B) -> m3_pboole(k14_pralg_2(A,B,C),u1_msualg_1(B),k8_pboole(u1_msualg_1(B),k3_finseq_2(u1_struct_0(B)),u2_msualg_1(B),k6_pboole(u1_struct_0(B),k11_pralg_2(A,B,C))),k8_pboole(u1_msualg_1(B),u1_struct_0(B),u3_msualg_1(B),k11_pralg_2(A,B,C))))) # label(dt_k14_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4441 (all A (v1_relat_1(A) & v1_funct_1(A) -> (k1_relat_1(A) = k1_tarski(k1_xboole_0) -> A = k2_pralg_2(A)))) # label(t8_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4442 $T # label(d9_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4443 (exists A (v1_pralg_2(A) & v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4444 (all A all B (-v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) -> -v1_xboole_0(k7_pralg_2(A,B)))) # label(fc3_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4445 (all A all B all C (-v3_struct_0(B) & m2_pralg_2(C,A,B) & l1_msualg_1(B) -> m1_pboole(k11_pralg_2(A,B,C),u1_struct_0(B)))) # label(dt_k11_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4446 (all A all B all C all D all E all F all G all H (v2_relat_1(D) & m1_pboole(D,A) & v1_funct_1(E) & v1_funct_2(E,B,k3_finseq_2(A)) & v1_funct_1(F) & m1_relset_1(F,B,A) & m3_pboole(H,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),k8_pboole(B,A,F,D)) & m3_pboole(G,B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),k8_pboole(B,A,F,C)) & v1_funct_2(F,B,A) & m1_relset_1(E,B,k3_finseq_2(A)) & m1_pboole(C,A) & v2_relat_1(C) & -v1_xboole_0(A) -> m3_pboole(k5_pralg_2(A,B,C,D,E,F,G,H),B,k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),k8_pboole(B,A,F,k11_pboole(A,C,D))))) # label(dt_k5_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4447 (all A (-v1_xboole_0(A) -> (all B (-v2_msualg_1(B) & l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_subset_1(D,u1_msualg_1(B)) -> (all E (r2_hidden(E,k2_relat_1(k3_pralg_2(k13_pralg_2(A,B,C,D)))) -> v1_funct_1(E) & v1_relat_1(E))))))))))) # label(t15_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4448 (all A ((all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,A) & r2_hidden(B,A) -> k1_relat_1(C) = k1_relat_1(B)))))) <-> v1_pralg_2(A))) # label(d1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4449 (all A all B (-v3_struct_0(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> (all D (m1_pboole(D,A) & v1_funcop_1(D) -> (k1_xboole_0 = A -> (k1_xboole_0 = D <-> k12_pralg_2(A,B,C) = D)) & (A != k1_xboole_0 -> (k12_pralg_2(A,B,C) = D <-> (all E -((all F (l3_msualg_1(F,B) -> -(u5_msualg_1(B,F) = k1_funct_1(D,E) & k1_funct_1(C,E) = F))) & r2_hidden(E,A))))))))))) # label(d18_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4450 (all A (-v3_struct_0(A) & l1_msualg_1(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) -> (all C (v5_msualg_1(C,A) & l3_msualg_1(C,A) -> k9_pralg_2(A,B,C) = g3_msualg_1(A,k11_pboole(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)),k5_pralg_2(u1_struct_0(A),u1_msualg_1(A),u4_msualg_1(A,B),u4_msualg_1(A,C),u2_msualg_1(A),u3_msualg_1(A),u5_msualg_1(A,B),u5_msualg_1(A,C))))))))) # label(d15_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4451 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & m2_pralg_2(D,A,B) & l1_msualg_1(B) -> v2_relat_1(k10_pralg_2(A,B,C,D)) & v1_funct_1(k10_pralg_2(A,B,C,D)) & v1_relat_1(k10_pralg_2(A,B,C,D)))) # label(fc6_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4452 (all A all B (l1_msualg_1(B) & -v3_struct_0(B) -> (all C (m1_pboole(C,A) -> (m2_pralg_2(C,A,B) <-> (all D (r2_hidden(D,A) -> l3_msualg_1(k1_funct_1(C,D),B) & v5_msualg_1(k1_funct_1(C,D),B)))))))) # label(d12_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4453 (all A all B all C (-v1_xboole_0(A) & -v3_struct_0(B) & l1_msualg_1(B) & m2_pralg_2(C,A,B) -> -v1_xboole_0(k8_pralg_2(A,B,C)))) # label(fc4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4454 (all A all B (-v3_struct_0(B) & -v2_msualg_1(B) & l1_msualg_1(B) -> (all C (m2_pralg_2(C,A,B) -> r6_pboole(u1_struct_0(B),u4_msualg_1(B,k15_pralg_2(A,B,C)),k11_pralg_2(A,B,C)) & r6_pboole(u1_msualg_1(B),u5_msualg_1(B,k15_pralg_2(A,B,C)),k14_pralg_2(A,B,C)))))) # label(t20_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4455 $T # label(d7_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4456 (all A (v1_fraenkel(A) & v1_pralg_2(A) & -v1_xboole_0(A) -> (exists B m1_pralg_2(B,A)))) # label(existence_m1_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4457 (all A (-v1_xboole_0(A) -> (all B all C (v2_relat_1(C) & m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> (all E (v1_funct_2(E,B,k3_finseq_2(A)) & m2_relset_1(E,B,k3_finseq_2(A)) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,A) & v1_funct_2(F,B,A) & v1_funct_1(F) -> (all G all H (v1_funct_2(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & m2_relset_1(H,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,C)),G),k1_funct_1(k8_pboole(B,A,F,C),G)) & v1_funct_1(H) -> (all I (v1_funct_1(I) & v1_funct_2(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) & m2_relset_1(I,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,D)),G),k1_funct_1(k8_pboole(B,A,F,D),G)) -> (r2_hidden(G,B) -> (all J (v1_funct_1(J) & v1_funct_2(J,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) & m2_relset_1(J,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G),k1_funct_1(k8_pboole(B,A,F,k11_pboole(A,C,D)),G)) -> ((all K (v1_funct_1(K) & v1_relat_1(K) -> (r2_hidden(K,k1_funct_1(k8_pboole(B,k3_finseq_2(A),E,k6_pboole(A,k11_pboole(A,C,D))),G)) -> k4_tarski(k1_funct_1(H,k15_mcart_1(K)),k1_funct_1(I,k16_mcart_1(K))) = k1_funct_1(J,K)))) <-> J = k4_pralg_2(A,B,C,D,E,F,G,H,I))))))))))))))))))) # label(d10_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4458 $T # label(d4_pralg_2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4459 (all A all B (m1_pboole(B,A) -> v1_funct_2(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v10_closure2(k6_partfun1(k6_closure2(A,B)),A,B) & m2_relset_1(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(k6_partfun1(k6_closure2(A,B))))) # label(t30_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4460 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) -> (v9_closure2(C,A,B) & k8_closure2(A,B,D,C) = k8_closure2(A,B,C,D) & v9_closure2(D,A,B) -> v9_closure2(k8_closure2(A,B,D,C),A,B)))))))) # label(t37_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4461 (all A all B (m1_pboole(B,A) -> (exists C (v1_pralg_2(C) & v1_closure2(C,A,B) & v2_closure2(C,A,B) & v5_closure2(C,A,B) & v6_closure2(C,A,B) & v4_closure2(C,A,B) & v3_closure2(C,A,B) & v1_fraenkel(C) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))))))) # label(rc4_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4462 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v15_closure2(B,A) -> v14_closure2(B,A)))))) # label(cc10_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4463 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> v1_relat_1(k4_closure2(A,B,C)) & v1_funct_1(k4_closure2(A,B,C)) & v2_relat_1(k4_closure2(A,B,C)))) # label(fc5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4464 (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)) = k1_funct_1(k3_closure2(k1_tarski(B)),A)))) # label(t18_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4465 (all A (l1_struct_0(A) -> (exists B (v11_closure2(B,A) & l1_closure2(B,A))))) # label(rc6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4466 (all A all B all C (l1_struct_0(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) -> v11_closure2(g1_closure2(A,B,C),A) & v5_msualg_1(g1_closure2(A,B,C),A))) # label(fc14_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4467 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v13_closure2(B,A) <-> v2_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))))))) # label(d17_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4468 (all A all B (l1_closure2(B,A) & v14_closure2(B,A) & l1_struct_0(A) -> v3_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v1_fraenkel(u1_closure2(A,B)))) # label(fc10_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4469 (all A (v1_xboole_0(A) -> v1_fraenkel(A))) # label(cc1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4470 (all A (l1_struct_0(A) -> (all B (m1_pboole(B,u1_struct_0(A)) -> (all C (v1_funct_1(C) & v8_closure2(C,u1_struct_0(A),B) & v9_closure2(C,u1_struct_0(A),B) & m2_relset_1(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & v7_closure2(C,u1_struct_0(A),B) & v1_funct_2(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) -> (all D (v15_closure2(D,A) & l1_closure2(D,A) & v11_closure2(D,A) -> (D = k10_closure2(A,B,C) <-> r6_pboole(u1_struct_0(A),u4_msualg_1(A,D),B) & u1_closure2(A,D) = a_3_1_closure2(A,B,C)))))))))) # label(d23_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4471 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) -> (v7_closure2(C,A,B) & (all D (m1_closure2(D,A,B,k6_closure2(A,B)) -> r2_pboole(A,k7_closure2(A,B,C,D),D))) -> v9_closure2(C,A,B)))))) # label(t32_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4472 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m4_pboole(D,A,B) -> ((all E (m1_pboole(E,A) -> (r2_hidden(E,C) -> r2_pboole(A,D,E)))) -> r2_pboole(A,D,k6_mssubfam(A,B,k5_closure2(A,B,C)))))))))) # label(t25_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4473 (all A all B all C all D all E (m1_pboole(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) -> (r2_hidden(A,a_4_0_closure2(B,C,D,E)) <-> (exists F (m1_closure2(F,B,C,k2_closure2(B,C)) & r2_hidden(F,D) & k1_funct_1(F,E) = A))))) # label(fraenkel_a_4_0_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4474 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> m1_subset_1(k5_subset_1(k1_closure2(A,B),C,D),k1_zfmisc_1(k1_closure2(A,B))))))))) # label(t5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4475 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) -> (v9_closure2(C,A,B) <-> (all D (m1_closure2(D,A,B,k6_closure2(A,B)) -> r6_pboole(A,k7_closure2(A,B,C,D),k7_closure2(A,B,C,k7_closure2(A,B,C,D)))))))))) # label(d14_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4476 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v4_closure2(C,A,B) -> v3_closure2(C,A,B) & v1_fraenkel(C)))))) # label(cc3_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4477 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v17_closure2(B,A) <-> v6_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))))))) # label(d21_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4478 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k1_relat_1(k3_closure2(k1_tarski(A))))) # label(t16_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4479 (all A all B (l1_struct_0(A) & l2_msualg_1(B,A) -> v12_closure2(k9_closure2(A,B),A) & v13_closure2(k9_closure2(A,B),A) & v15_closure2(k9_closure2(A,B),A) & v16_closure2(k9_closure2(A,B),A) & v17_closure2(k9_closure2(A,B),A) & v14_closure2(k9_closure2(A,B),A) & v11_closure2(k9_closure2(A,B),A))) # label(fc6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4480 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v13_closure2(B,A) -> v17_closure2(B,A)))))) # label(cc12_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4481 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) -> ((all D (m1_closure2(D,A,B,k6_closure2(A,B)) -> (all E (m1_closure2(E,A,B,k6_closure2(A,B)) -> k2_pboole(A,k7_closure2(A,B,C,D),k7_closure2(A,B,C,E)) = k1_funct_1(C,k2_pboole(A,D,E)))))) <-> v10_closure2(C,A,B)))))) # label(d15_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4482 $T # label(dt_k1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4483 (all A all B (m1_pboole(B,A) -> (exists C (m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_partfun1(C,k6_closure2(A,B),k6_closure2(A,B)) & v9_closure2(C,A,B) & v10_closure2(C,A,B) & v8_closure2(C,A,B) & v7_closure2(C,A,B) & -v1_xboole_0(C))))) # label(rc5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4484 (all A all B (m1_pboole(B,A) -> (all C (m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) -> (v1_funct_1(C) & v10_closure2(C,A,B) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) -> v1_partfun1(C,k6_closure2(A,B),k6_closure2(A,B)) & v8_closure2(C,A,B) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) & -v1_xboole_0(C)))))) # label(cc8_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4485 (all A (l1_struct_0(A) -> (exists B l1_closure2(B,A)))) # label(existence_l1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4486 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v4_closure2(C,A,B) -> v5_closure2(C,A,B) & v1_fraenkel(C)))))) # label(cc4_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4487 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) -> (v8_closure2(C,A,B) <-> (all D (m1_closure2(D,A,B,k6_closure2(A,B)) -> (all E (m1_closure2(E,A,B,k6_closure2(A,B)) -> (r2_pboole(A,D,E) -> r2_pboole(A,k7_closure2(A,B,C,D),k7_closure2(A,B,C,E)))))))))))) # label(d13_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4488 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> m1_subset_1(k7_subset_1(k1_closure2(A,B),C,D),k1_zfmisc_1(k1_closure2(A,B))))))))) # label(t7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4489 $T # label(d2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4490 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v5_closure2(C,A,B) -> -v1_xboole_0(C) & v1_fraenkel(C)))))) # label(cc5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4491 (all A all B (v12_closure2(B,A) & l1_closure2(B,A) & l1_struct_0(A) -> v1_fraenkel(u1_closure2(A,B)) & v1_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)))) # label(fc8_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4492 (all A all B (m1_pboole(B,A) -> (exists C (v1_pralg_2(C) & v1_fraenkel(C) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))))))) # label(rc2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4493 (exists A (v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_fraenkel(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4494 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v2_closure2(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> (r1_tarski(D,C) -> r2_hidden(k2_mboolean(A,k5_closure2(A,B,D)),C))))))))) # label(d6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4495 (all A all B all C all D (v15_closure2(C,B) & l1_closure2(C,B) & m4_pboole(D,u1_struct_0(B),u4_msualg_1(B,C)) & l1_struct_0(B) -> ((exists E (A = E & r2_pboole(u1_struct_0(B),D,E) & r2_hidden(E,u1_closure2(B,C)) & m1_closure2(E,u1_struct_0(B),u4_msualg_1(B,C),k6_closure2(u1_struct_0(B),u4_msualg_1(B,C))))) <-> r2_hidden(A,a_3_2_closure2(B,C,D))))) # label(fraenkel_a_3_2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4496 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v1_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) <-> v12_closure2(B,A)))))) # label(d16_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4497 (all A all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k2_closure2(A,B)) -> (all D (m1_closure2(D,A,B,k2_closure2(A,B)) -> r2_hidden(k5_pboole(A,C,D),k2_closure2(A,B)))))))) # label(t13_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4498 (all A all B all C (v1_fraenkel(B) & -v1_xboole_0(B) -> ((exists D (k1_funct_1(D,C) = A & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_0_closure2(B,C))))) # label(fraenkel_a_2_0_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4499 (all A all B (m1_pboole(B,A) -> (all C (m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(D) -> (v10_closure2(C,A,B) & v10_closure2(D,A,B) -> v10_closure2(k8_closure2(A,B,D,C),A,B)))))))) # label(t38_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4500 (all A all B all C all D (l1_struct_0(B) & m1_pboole(C,u1_struct_0(B)) & v1_funct_2(D,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v7_closure2(D,u1_struct_0(B),C) & v8_closure2(D,u1_struct_0(B),C) & v9_closure2(D,u1_struct_0(B),C) & m2_relset_1(D,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v1_funct_1(D) -> ((exists E (A = E & r6_pboole(u1_struct_0(B),k7_closure2(u1_struct_0(B),C,D,E),E) & m1_closure2(E,u1_struct_0(B),C,k6_closure2(u1_struct_0(B),C)))) <-> r2_hidden(A,a_3_1_closure2(B,C,D))))) # label(fraenkel_a_3_1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4501 $T # label(d11_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4502 (all A (v1_xboole_0(A) & v1_fraenkel(A) -> v1_xboole_0(k3_closure2(A)) & v1_relat_1(k3_closure2(A)) & v1_funct_1(k3_closure2(A)) & v2_funct_1(k3_closure2(A)) & v1_finset_1(k3_closure2(A)) & v1_fraenkel(k3_closure2(A)))) # label(fc3_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4503 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v15_closure2(B,A) -> v16_closure2(B,A)))))) # label(cc11_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4504 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_closure2(D,A,B,k2_closure2(A,B)) -> (all E (m1_closure2(E,A,B,k2_closure2(A,B)) -> (C = k2_tarski(D,E) -> r6_pboole(A,k6_mssubfam(A,B,k5_closure2(A,B,C)),k3_pboole(A,D,E))))))))))) # label(t24_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4505 (all A all B all C (l1_struct_0(A) & l2_msualg_1(B,A) & v6_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) -> v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v17_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A))) # label(fc20_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4506 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> ((all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k3_pboole(A,D,E),C)))))) <-> v3_closure2(C,A,B)))))) # label(d7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4507 (all A all B all C (l1_struct_0(A) & m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) & l1_closure2(B,A) & v15_closure2(B,A) -> m1_closure2(k11_closure2(A,B,C),u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))))) # label(dt_k11_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4508 (all A all B all C (v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> v3_relat_1(k4_closure2(A,B,C)) & v1_pre_circ(k4_closure2(A,B,C),A) & v1_funct_1(k4_closure2(A,B,C)) & v1_relat_1(k4_closure2(A,B,C)))) # label(fc4_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4509 (all A all B (l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) -> v5_msualg_1(k9_closure2(A,B),A) & v12_closure2(k9_closure2(A,B),A) & v13_closure2(k9_closure2(A,B),A) & v14_closure2(k9_closure2(A,B),A) & v15_closure2(k9_closure2(A,B),A) & v17_closure2(k9_closure2(A,B),A) & v16_closure2(k9_closure2(A,B),A) & v11_closure2(k9_closure2(A,B),A))) # label(fc7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4510 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v13_closure2(B,A) -> v12_closure2(B,A)))))) # label(cc9_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4511 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v15_closure2(B,A) <-> v4_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))))))) # label(d19_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4512 (all A all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k2_closure2(A,B)) -> (all D (m1_closure2(D,A,B,k2_closure2(A,B)) -> r2_hidden(k2_pboole(A,C,D),k2_closure2(A,B)))))))) # label(t11_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4513 (all A all B all C (l1_struct_0(A) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) -> v11_closure2(g1_closure2(A,B,C),A) & l1_closure2(g1_closure2(A,B,C),A))) # label(dt_g1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4514 (all A (l1_struct_0(A) -> (all B (m1_pboole(B,u1_struct_0(A)) -> (all C (v1_funct_1(C) & v1_funct_2(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & v7_closure2(C,u1_struct_0(A),B) & m2_relset_1(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & v9_closure2(C,u1_struct_0(A),B) & v8_closure2(C,u1_struct_0(A),B) -> k12_closure2(A,k10_closure2(A,B,C)) = C)))))) # label(t43_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4515 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_closure2(D,A,C,k2_closure2(A,C)) -> r2_hidden(k4_pboole(A,D,B),k2_closure2(A,C)))))))) # label(t12_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4516 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k3_closure2(k2_tarski(A,B))))))) # label(t17_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4517 (all A all B (m1_pboole(B,A) -> m2_relset_1(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v7_closure2(k6_partfun1(k6_closure2(A,B)),A,B) & v1_funct_2(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(k6_partfun1(k6_closure2(A,B))))) # label(t27_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4518 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(k1_closure2(A,C)))))))) # label(t8_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4519 (all A all B all C (l1_struct_0(A) & v2_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) & l2_msualg_1(B,A) -> v12_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v13_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A))) # label(fc16_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4520 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> -v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) & v1_fraenkel(k2_tarski(A,B)))) # label(fc1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4521 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> (r2_hidden(C,D) -> r1_pboole(A,C,k5_closure2(A,B,D))))))))) # label(t22_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4522 (all A all B all C all D (m1_pboole(B,A) & v1_funct_1(C) & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & m1_subset_1(D,k6_closure2(A,B)) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) -> m1_closure2(k7_closure2(A,B,C,D),A,B,k6_closure2(A,B)))) # label(dt_k7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4523 $T # label(t2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4524 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) & m1_pboole(B,A) -> (all D (m1_subset_1(D,C) <-> m1_closure2(D,A,B,C))))) # label(redefinition_m1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4525 (all A (l1_struct_0(A) -> (all B (v15_closure2(B,A) & l1_closure2(B,A) -> (all C (v1_funct_2(C,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & v8_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & v9_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & m2_relset_1(C,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & v7_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & v1_funct_1(C) -> ((all D (m1_closure2(D,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> r6_pboole(u1_struct_0(A),k7_closure2(u1_struct_0(A),u4_msualg_1(A,B),C,D),k11_closure2(A,B,D)))) <-> k12_closure2(A,B) = C))))))) # label(d25_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4526 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v16_closure2(B,A) <-> v5_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))))))) # label(d20_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4527 (all A all B all C (m1_pboole(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,C))) -> m1_subset_1(k4_xboole_0(D,B),k1_zfmisc_1(k1_closure2(A,C))))))) # label(t6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4528 (all A (v1_fraenkel(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (A != k1_xboole_0 -> (k3_closure2(A) = B <-> (exists C (v1_fraenkel(C) & k1_setfam_1(a_1_0_closure2(C)) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> a_2_0_closure2(C,D) = k1_funct_1(B,D))) & C = A & -v1_xboole_0(C))))) & (A = k1_xboole_0 -> (B = k3_closure2(A) <-> B = k1_xboole_0)))))) # label(d3_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4529 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (r2_hidden(k1_pboole(A),C) <-> v6_closure2(C,A,B)))))) # label(d10_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4530 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (C != k1_xboole_0 -> k3_closure2(C) = k4_closure2(A,B,C)) & (k1_xboole_0 = C -> k1_pboole(A) = k4_closure2(A,B,C)))))) # label(d4_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4531 (all A all B (m1_pboole(B,A) -> (all C (m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) -> (all D (v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(D) -> (v7_closure2(D,A,B) & v7_closure2(C,A,B) -> v7_closure2(k8_closure2(A,B,D,C),A,B)))))))) # label(t35_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4532 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) & v15_closure2(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & v1_funct_2(C,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> ((all D (m1_closure2(D,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> r6_pboole(u1_struct_0(A),k7_closure2(u1_struct_0(A),u4_msualg_1(A,B),C,D),k11_closure2(A,B,D)))) -> v7_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & v8_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & v9_closure2(C,u1_struct_0(A),u4_msualg_1(A,B))))))))) # label(t42_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4533 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v1_closure2(C,A,B) <-> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k2_pboole(A,D,E),C))))))))))) # label(d5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4534 (all A all B all C all D (m1_subset_1(D,k6_closure2(A,B)) & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) & m1_pboole(B,A) -> k7_closure2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4535 (all A all B (m1_pboole(B,A) -> v1_funct_1(k6_partfun1(k6_closure2(A,B))) & v8_closure2(k6_partfun1(k6_closure2(A,B)),A,B) & m2_relset_1(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)))) # label(t28_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4536 (all A all B (m1_pboole(B,A) -> v1_closure2(k6_closure2(A,B),A,B) & v5_closure2(k6_closure2(A,B),A,B) & m1_subset_1(k6_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))) & v6_closure2(k6_closure2(A,B),A,B) & v4_closure2(k6_closure2(A,B),A,B) & v3_closure2(k6_closure2(A,B),A,B) & v2_closure2(k6_closure2(A,B),A,B))) # label(dt_k6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4537 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> m1_pboole(k4_closure2(A,B,C),A))) # label(dt_k4_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4538 (all A all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k2_closure2(A,B)) -> (all D (m1_closure2(D,A,B,k2_closure2(A,B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(E,k6_closure2(A,B),k6_closure2(A,B)) -> (all F (m1_closure2(F,A,B,k6_closure2(A,B)) -> (v10_closure2(E,A,B) & r6_pboole(A,F,k4_pboole(A,C,D)) -> r2_pboole(A,k4_pboole(A,k7_closure2(A,B,E,C),k7_closure2(A,B,E,D)),k7_closure2(A,B,E,F))))))))))))) # label(t34_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4539 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) -> k1_relat_1(k3_closure2(C)) = A)))) # label(t14_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4540 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> (all D (m1_closure2(D,A,B,C) -> m4_pboole(D,A,B))))) # label(dt_m1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4541 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) -> (v7_closure2(C,A,B) <-> (all D (m1_closure2(D,A,B,k6_closure2(A,B)) -> r2_pboole(A,D,k7_closure2(A,B,C,D))))))))) # label(d12_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4542 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) & m1_pboole(B,u1_struct_0(A)) & l1_struct_0(A) -> (all D all E all F (g1_closure2(A,B,C) = g1_closure2(D,E,F) -> A = D & C = F & E = B)))) # label(free_g1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4543 (all A all B (m1_pboole(B,A) -> k1_closure2(A,B) = k2_closure2(A,B))) # label(redefinition_k2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4544 (all A (l1_struct_0(A) -> (all B (l2_msualg_1(B,A) -> g1_closure2(A,u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) = k9_closure2(A,B))))) # label(d22_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4545 (all A all B (l1_closure2(B,A) & l1_struct_0(A) -> (v11_closure2(B,A) -> g1_closure2(A,u4_msualg_1(A,B),u1_closure2(A,B)) = B))) # label(abstractness_v11_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4546 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) & m1_pboole(B,A) -> (exists D m1_closure2(D,A,B,C)))) # label(existence_m1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4547 (all A all B (v15_closure2(B,A) & l1_closure2(B,A) & l1_struct_0(A) -> v1_funct_2(k12_closure2(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & v7_closure2(k12_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v9_closure2(k12_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & m2_relset_1(k12_closure2(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & v8_closure2(k12_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v1_funct_1(k12_closure2(A,B)))) # label(dt_k12_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4548 (all A all B (l2_msualg_1(B,A) & l1_struct_0(A) -> l1_closure2(k9_closure2(A,B),A))) # label(dt_k9_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4549 (all A all B (l1_closure2(B,A) & v15_closure2(B,A) & l1_struct_0(A) -> -v1_xboole_0(u1_closure2(A,B)) & v3_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v5_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v4_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v1_fraenkel(u1_closure2(A,B)))) # label(fc11_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4550 (all A all B (l1_struct_0(A) & l1_closure2(B,A) & v16_closure2(B,A) -> v5_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v1_fraenkel(u1_closure2(A,B)) & -v1_xboole_0(u1_closure2(A,B)))) # label(fc12_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4551 (all A all B all C (l2_msualg_1(B,A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) & v5_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & l1_struct_0(A) -> v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v16_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A))) # label(fc19_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4552 (all A all B (l1_closure2(B,A) & v13_closure2(B,A) & l1_struct_0(A) -> -v1_xboole_0(u1_closure2(A,B)) & v1_fraenkel(u1_closure2(A,B)) & v6_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v2_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v1_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)))) # label(fc9_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4553 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> k5_closure2(A,B,C) = k4_closure2(A,B,C))) # label(redefinition_k5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4554 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (r1_tarski(B,C) -> r1_tarski(k8_funct_2(A,A,k6_partfun1(A),B),k8_funct_2(A,A,k6_partfun1(A),C))))))))) # label(t1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4555 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> m4_pboole(k5_closure2(A,B,C),A,k1_mboolean(A,B)))) # label(dt_k5_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4556 (all A all B all C (l1_struct_0(A) & l2_msualg_1(B,A) & v4_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) -> v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v14_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v15_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A))) # label(fc18_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4557 (all A (l1_struct_0(A) -> (exists B (l1_closure2(B,A) & v5_msualg_1(B,A) & v11_closure2(B,A) & v14_closure2(B,A) & v15_closure2(B,A) & v17_closure2(B,A) & v16_closure2(B,A) & v13_closure2(B,A) & v12_closure2(B,A))))) # label(rc7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4558 (all A all B (-v1_xboole_0(B) & v1_fraenkel(B) -> ((exists C (k1_relat_1(C) = A & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_0_closure2(B))))) # label(fraenkel_a_1_0_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4559 (all A all B (m1_pboole(B,A) -> k1_closure2(A,B) = k6_closure2(A,B))) # label(redefinition_k6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4560 (all A all B (m1_pboole(B,A) -> v1_funct_2(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v9_closure2(k6_partfun1(k6_closure2(A,B)),A,B) & m2_relset_1(k6_partfun1(k6_closure2(A,B)),k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(k6_partfun1(k6_closure2(A,B))))) # label(t29_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4561 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) -> (v8_closure2(D,A,B) & v8_closure2(C,A,B) -> v8_closure2(k8_closure2(A,B,D,C),A,B)))))))) # label(t36_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4562 (all A all B (l1_struct_0(A) & l1_closure2(B,A) -> m1_subset_1(u1_closure2(A,B),k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))))) # label(dt_u1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4563 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) & v15_closure2(B,A) -> (all C (m1_closure2(C,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> (all D (v1_funct_1(D) & v1_funct_2(D,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & m2_relset_1(D,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> (r2_hidden(C,u1_closure2(A,B)) & (all E (m1_closure2(E,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> r6_pboole(u1_struct_0(A),k7_closure2(u1_struct_0(A),u4_msualg_1(A,B),D,E),k11_closure2(A,B,E)))) -> r6_pboole(u1_struct_0(A),k7_closure2(u1_struct_0(A),u4_msualg_1(A,B),D,C),C)))))))))) # label(t40_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4564 (all A all B all C (l1_struct_0(A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) & v3_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & l2_msualg_1(B,A) -> v14_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A))) # label(fc17_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4565 (all A all B all C (m1_pboole(C,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (m1_subset_1(F,k1_zfmisc_1(k1_closure2(B,C))) -> (k2_tarski(D,E) = F & r2_hidden(A,B) -> k1_funct_1(k4_closure2(B,C,F),A) = k2_tarski(k1_funct_1(D,A),k1_funct_1(E,A))))))))))) # label(t21_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4566 (all A all B all C (l1_struct_0(A) & v1_closure2(C,u1_struct_0(A),u4_msualg_1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) & l2_msualg_1(B,A) -> v12_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A) & v11_closure2(g1_closure2(A,u4_msualg_1(A,B),C),A))) # label(fc15_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4567 (all A all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k2_closure2(A,B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) -> (r6_pboole(A,C,B) & v7_closure2(D,A,B) -> r6_pboole(A,C,k7_closure2(A,B,D,C))))))))) # label(t31_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4568 (all A all B (m1_pboole(B,A) -> -v1_xboole_0(k1_closure2(A,B)) & v1_fraenkel(k1_closure2(A,B)) & v1_pralg_2(k1_closure2(A,B)))) # label(fc2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4569 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_closure2(A,B,k2_closure2(A,B)),k7_mssubfam(A,B)))) # label(t26_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4570 (all A (l1_struct_0(A) -> (all B (m1_pboole(B,u1_struct_0(A)) -> (all C (v7_closure2(C,u1_struct_0(A),B) & v8_closure2(C,u1_struct_0(A),B) & m2_relset_1(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & v1_funct_2(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(A),B))) -> (a_3_0_closure2(A,B,C) = D -> l1_closure2(g1_closure2(A,B,D),A) & v15_closure2(g1_closure2(A,B,D),A)))))))))) # label(t39_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4571 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> (r1_tarski(D,C) -> r2_hidden(k6_mssubfam(A,B,k5_closure2(A,B,D)),C)))) <-> v4_closure2(C,A,B)))))) # label(d8_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4572 (all A all B (m1_pboole(B,A) -> (exists C (v1_xboole_0(C) & v2_funct_1(C) & v1_fraenkel(C) & v1_finset_1(C) & v1_funct_1(C) & v1_relat_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))))))) # label(rc3_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4573 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,B))) -> (E = k2_tarski(C,D) -> r6_pboole(A,k2_mboolean(A,k5_closure2(A,B,E)),k2_pboole(A,C,D))))))))))) # label(t23_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4574 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) & v15_closure2(B,A) -> (all C (m1_closure2(C,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> (all D (v1_funct_1(D) & m2_relset_1(D,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) & v1_funct_2(D,k6_closure2(u1_struct_0(A),u4_msualg_1(A,B)),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> ((all E (m1_closure2(E,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> r6_pboole(u1_struct_0(A),k7_closure2(u1_struct_0(A),u4_msualg_1(A,B),D,E),k11_closure2(A,B,E)))) & r6_pboole(u1_struct_0(A),k7_closure2(u1_struct_0(A),u4_msualg_1(A,B),D,C),C) -> r2_hidden(C,u1_closure2(A,B))))))))))) # label(t41_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4575 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) & v15_closure2(B,A) -> (all C (m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) -> (all D (m1_closure2(D,u1_struct_0(A),u4_msualg_1(A,B),k6_closure2(u1_struct_0(A),u4_msualg_1(A,B))) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) & r6_pboole(u1_struct_0(A),D,k6_mssubfam(u1_struct_0(A),u4_msualg_1(A,B),k5_closure2(u1_struct_0(A),u4_msualg_1(A,B),E))) & E = a_3_2_closure2(A,B,C))) <-> k11_closure2(A,B,C) = D))))))))) # label(d24_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4576 (all A (v1_fraenkel(A) -> v1_funct_1(k3_closure2(A)) & v1_relat_1(k3_closure2(A)))) # label(dt_k3_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4577 (all A all B all C all D (v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & m1_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(D) & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(C) & m1_pboole(B,A) -> k5_relat_1(C,D) = k8_closure2(A,B,C,D))) # label(redefinition_k8_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.85 4578 (all A all B all C (m1_pboole(C,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_closure2(B,C))) -> (E = k1_tarski(D) & r2_hidden(A,B) -> k1_funct_1(k4_closure2(B,C,E),A) = k1_tarski(k1_funct_1(D,A))))))))) # label(t19_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4579 (all A all B all C all D (l1_struct_0(B) & m1_pboole(C,u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & m2_relset_1(D,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v8_closure2(D,u1_struct_0(B),C) & v7_closure2(D,u1_struct_0(B),C) -> ((exists E (r6_pboole(u1_struct_0(B),k7_closure2(u1_struct_0(B),C,D,E),E) & E = A & m1_closure2(E,u1_struct_0(B),C,k6_closure2(u1_struct_0(B),C)))) <-> r2_hidden(A,a_3_0_closure2(B,C,D))))) # label(fraenkel_a_3_0_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4580 (all A all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k2_closure2(A,B)) -> (all D (m1_closure2(D,A,B,k2_closure2(A,B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(E,k6_closure2(A,B),k6_closure2(A,B)) -> (all F (m1_closure2(F,A,B,k6_closure2(A,B)) -> (v8_closure2(E,A,B) & r6_pboole(A,F,k3_pboole(A,C,D)) -> r2_pboole(A,k7_closure2(A,B,E,F),k3_pboole(A,k7_closure2(A,B,E,C),k7_closure2(A,B,E,D)))))))))))))) # label(t33_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4581 (all A all B (m1_pboole(B,A) -> (all C ((all D (r2_hidden(D,C) <-> m4_pboole(D,A,B))) <-> k1_closure2(A,B) = C)))) # label(d1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4582 (all A (l1_struct_0(A) -> (all B (v15_closure2(B,A) & l1_closure2(B,A) -> g1_closure2(A,u4_msualg_1(A,B),u1_closure2(A,B)) = k10_closure2(A,u4_msualg_1(A,B),k12_closure2(A,B)))))) # label(t44_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4583 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v2_closure2(C,A,B) -> v1_closure2(C,A,B) & v1_fraenkel(C)))))) # label(cc2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4584 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v5_closure2(C,A,B) <-> r2_hidden(B,C)))))) # label(d9_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4585 (all A all B all C (v1_funct_1(C) & v7_closure2(C,u1_struct_0(A),B) & v9_closure2(C,u1_struct_0(A),B) & m1_relset_1(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & v8_closure2(C,u1_struct_0(A),B) & v1_funct_2(C,k6_closure2(u1_struct_0(A),B),k6_closure2(u1_struct_0(A),B)) & m1_pboole(B,u1_struct_0(A)) & l1_struct_0(A) -> v15_closure2(k10_closure2(A,B,C),A) & l1_closure2(k10_closure2(A,B,C),A) & v11_closure2(k10_closure2(A,B,C),A))) # label(dt_k10_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4586 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> (v14_closure2(B,A) <-> v3_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B))))))) # label(d18_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4587 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v6_closure2(C,A,B) -> -v1_xboole_0(C) & v1_fraenkel(C)))))) # label(cc7_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4588 (all A all B (m1_pboole(B,A) -> m1_subset_1(k2_closure2(A,B),k1_zfmisc_1(k1_closure2(A,B))))) # label(dt_k2_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4589 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (-v1_xboole_0(C) -> (all D (r2_hidden(D,A) -> a_4_0_closure2(A,B,C,D) = k1_funct_1(k4_closure2(A,B,C),D)))))))) # label(t15_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4590 (all A all B all C all D (m1_pboole(B,A) & v1_funct_1(C) & m1_relset_1(C,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_2(D,k6_closure2(A,B),k6_closure2(A,B)) & m1_relset_1(D,k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(D) & v1_funct_2(C,k6_closure2(A,B),k6_closure2(A,B)) -> v1_funct_2(k8_closure2(A,B,C,D),k6_closure2(A,B),k6_closure2(A,B)) & m2_relset_1(k8_closure2(A,B,C,D),k6_closure2(A,B),k6_closure2(A,B)) & v1_funct_1(k8_closure2(A,B,C,D)))) # label(dt_k8_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4591 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> m1_subset_1(k4_subset_1(k1_closure2(A,B),C,D),k1_zfmisc_1(k1_closure2(A,B))))))))) # label(t4_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4592 (all A all B (l1_struct_0(A) & v17_closure2(B,A) & l1_closure2(B,A) -> -v1_xboole_0(u1_closure2(A,B)) & v6_closure2(u1_closure2(A,B),u1_struct_0(A),u4_msualg_1(A,B)) & v1_fraenkel(u1_closure2(A,B)))) # label(fc13_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4593 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> m1_subset_1(k2_tarski(B,D),k1_zfmisc_1(k1_closure2(A,C)))))))))) # label(t9_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4594 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (v2_closure2(C,A,B) -> v6_closure2(C,A,B) & v1_fraenkel(C)))))) # label(cc6_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4595 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> r1_tarski(k2_relat_1(C),k3_tarski(k2_relat_1(k7_mssubfam(A,B)))))))))) # label(t3_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4596 (all A all B (m1_pboole(B,A) -> (all C (m1_closure2(C,A,B,k2_closure2(A,B)) -> (all D (m1_closure2(D,A,B,k2_closure2(A,B)) -> r2_hidden(k3_pboole(A,C,D),k2_closure2(A,B)))))))) # label(t10_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4597 (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(k3_closure2(k2_tarski(B,C)))) -> k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k1_funct_1(k3_closure2(k2_tarski(B,C)),A)))))) # label(t20_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4598 (all A (l1_struct_0(A) -> (all B (l1_closure2(B,A) -> l2_msualg_1(B,A))))) # label(dt_l1_closure2) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4599 $T # label(dt_k1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4600 (all A all B all C (m1_pboole(C,B) & -v1_xboole_0(B) -> ((exists D (k1_xboole_0 != k1_funct_1(C,D) & D = A & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_0_closure3(B,C))))) # label(fraenkel_a_2_0_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4601 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> m1_subset_1(k4_closure3(A,B,C,D),k1_zfmisc_1(k1_closure2(A,B))))) # label(dt_k4_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4602 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> r2_closure3(A,B,C,C))) # label(reflexivity_r2_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4603 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) & m1_pboole(B,A) -> (all D (m1_closure3(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4604 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,B))) -> (r2_closure3(A,B,D,E) & r2_closure3(A,B,C,D) -> r2_closure3(A,B,C,E)))))))))) # label(t5_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4605 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & -v1_xboole_0(C) -> (exists D m1_closure3(D,A,B,C)))) # label(existence_m1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4606 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> m4_pboole(k2_closure3(A,B,C),A,B))) # label(dt_k2_closure3) # label(axiom) # label(non_clause). [assumption]. 174.42/174.86 4607 (all A all B all C all D (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> k4_closure3(A,B,C,C) = C)) # label(idempotence_k4_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4608 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> (r1_closure3(A,B,C,D) <-> (all E -((all F -(r1_tarski(E,F) & r2_hidden(F,C))) & r2_hidden(E,D)))))))))) # label(d1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4609 (all A all B all C all D (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> k4_closure3(A,B,D,C) = k4_closure3(A,B,C,D))) # label(commutativity_k4_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4610 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> r1_closure3(A,B,D,D))) # label(reflexivity_r1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4611 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> (all D (m1_closure3(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4612 (all A all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,B))) -> (r1_closure3(A,B,D,C) & r1_closure3(A,B,E,D) -> r1_closure3(A,B,E,C)))))))))) # label(t4_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4613 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> k3_closure3(A,B,C,C) = C)) # label(idempotence_k3_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4614 (all A all B (-v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v5_msualg_1(B,A) & -v3_struct_0(A) -> v11_closure2(k5_closure3(A,B),g1_struct_0(u1_struct_0(A))) & l1_closure2(k5_closure3(A,B),g1_struct_0(u1_struct_0(A))))) # label(dt_k5_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4615 (all A all B all C (-v1_xboole_0(B) & m1_pboole(C,B) & v2_relat_1(C) -> (r2_hidden(A,a_2_1_closure3(B,C)) <-> (exists D (m1_subset_1(D,B) & k1_funct_1(C,D) != k1_xboole_0 & A = D))))) # label(fraenkel_a_2_1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4616 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> k3_closure3(A,B,D,C) = k3_closure3(A,B,C,D))) # label(commutativity_k3_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4617 (all A (l1_msualg_1(A) & -v2_msualg_1(A) & -v3_struct_0(A) -> (all B (l3_msualg_1(B,A) & v5_msualg_1(B,A) & v4_msualg_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_closure2(u1_struct_0(A),u4_msualg_1(A,B)))) -> (r1_tarski(C,k6_msualg_2(A,B)) -> (all D (m4_pboole(D,u1_struct_0(A),u4_msualg_1(A,B)) -> (r6_pboole(u1_struct_0(A),D,k6_mssubfam(u1_struct_0(A),u4_msualg_1(A,B),k5_closure2(u1_struct_0(A),u4_msualg_1(A,B),C))) -> v3_msualg_2(D,A,B))))))))))) # label(t3_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4618 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> C = k1_funct_4(B,C))))))) # label(t1_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4619 (all A all B all C all D (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> k3_closure3(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k3_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4620 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_pboole(B,A) -> m1_subset_1(k3_closure3(A,B,C,D),k1_zfmisc_1(k1_closure2(A,B))))) # label(dt_k3_closure3) # label(axiom) # label(non_clause). [assumption]. 174.48/174.86 4621 (all A all B all C all D (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) -> k4_closure3(A,B,C,D) = k3_xboole_0(C,D)Alarm clock 179.64/180.02 Prover9 interrupted 179.64/180.02 EOF