0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n012.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % DateTime : Thu Jul 15 06:06:31 EDT 2021 0.13/0.34 % CPUTime : 4.15/4.24 ============================== Prover9 =============================== 4.15/4.24 Prover9 (32) version 2009-11A, November 2009. 4.15/4.24 Process 2798 was started by sandbox2 on n012.cluster.edu, 4.15/4.24 Thu Jul 15 06:06:35 2021 4.15/4.24 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_2490_n012.cluster.edu". 4.15/4.24 ============================== end of head =========================== 4.15/4.24 4.15/4.24 ============================== INPUT ================================= 4.15/4.24 4.15/4.24 % Reading from file /tmp/Prover9_2490_n012.cluster.edu 4.15/4.24 4.15/4.24 set(prolog_style_variables). 4.15/4.24 set(auto2). 4.15/4.24 % set(auto2) -> set(auto). 4.15/4.24 % set(auto) -> set(auto_inference). 4.15/4.24 % set(auto) -> set(auto_setup). 4.15/4.24 % set(auto_setup) -> set(predicate_elim). 4.15/4.24 % set(auto_setup) -> assign(eq_defs, unfold). 4.15/4.24 % set(auto) -> set(auto_limits). 4.15/4.24 % set(auto_limits) -> assign(max_weight, "100.000"). 4.15/4.24 % set(auto_limits) -> assign(sos_limit, 20000). 4.15/4.24 % set(auto) -> set(auto_denials). 4.15/4.24 % set(auto) -> set(auto_process). 4.15/4.24 % set(auto2) -> assign(new_constants, 1). 4.15/4.24 % set(auto2) -> assign(fold_denial_max, 3). 4.15/4.24 % set(auto2) -> assign(max_weight, "200.000"). 4.15/4.24 % set(auto2) -> assign(max_hours, 1). 4.15/4.24 % assign(max_hours, 1) -> assign(max_seconds, 3600). 4.15/4.24 % set(auto2) -> assign(max_seconds, 0). 4.15/4.24 % set(auto2) -> assign(max_minutes, 5). 4.15/4.24 % assign(max_minutes, 5) -> assign(max_seconds, 300). 4.15/4.24 % set(auto2) -> set(sort_initial_sos). 4.15/4.24 % set(auto2) -> assign(sos_limit, -1). 4.15/4.24 % set(auto2) -> assign(lrs_ticks, 3000). 4.15/4.24 % set(auto2) -> assign(max_megs, 400). 4.15/4.24 % set(auto2) -> assign(stats, some). 4.15/4.24 % set(auto2) -> clear(echo_input). 4.15/4.24 % set(auto2) -> set(quiet). 4.15/4.24 % set(auto2) -> clear(print_initial_clauses). 4.15/4.24 % set(auto2) -> clear(print_given). 4.15/4.24 assign(lrs_ticks,-1). 4.15/4.24 assign(sos_limit,10000). 4.15/4.24 assign(order,kbo). 4.15/4.24 set(lex_order_vars). 4.15/4.24 clear(print_given). 4.15/4.24 4.15/4.24 % formulas(sos). % not echoed (4552 formulas) 4.15/4.24 4.15/4.24 ============================== end of input ========================== 4.15/4.24 4.15/4.24 % From the command line: assign(max_seconds, 1200). 4.15/4.24 4.15/4.24 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 4.15/4.24 4.15/4.24 % Formulas that are not ordinary clauses: 4.15/4.24 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 3 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 4 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 5 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 6 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 8 (all A all B -((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,C) & r2_hidden(D,B))))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 9 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(C,D) & r2_hidden(D,A))))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 10 (all A exists B ((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 11 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (D = F <-> E = G))) & (all D -((all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 13 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 14 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 15 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 16 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 17 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 19 (all A all B all C ((all D (r2_hidden(D,C) <-> D = B | D = A)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 21 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 23 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 24 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 25 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 26 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 27 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 29 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (r2_hidden(A,f1_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 30 (all A all B all C -(r1_xboole_0(A,B) & r2_hidden(C,k2_xboole_0(A,B)) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 31 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 32 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 33 (all A all B (r1_xboole_0(A,B) <-> k1_xboole_0 = k3_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 34 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 35 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 36 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 37 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 38 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 39 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 41 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 42 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 43 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 44 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 45 (all A all B (r2_xboole_0(A,B) <-> r1_tarski(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 46 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 47 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 48 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 49 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 50 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 51 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 52 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> -r2_hidden(D,B) & r2_hidden(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 53 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 54 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 55 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 56 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))) <-> k2_xboole_0(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 57 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 58 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 59 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 60 (all A all B all C (-(r2_hidden(A,C) <-> r2_hidden(A,B)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 61 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 65 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 66 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 67 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 68 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 69 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 70 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 71 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 72 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 73 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 74 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 75 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> k1_xboole_0 = A)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 76 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 77 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 78 (all A all B all C all D (r1_xboole_0(C,D) & r1_xboole_0(B,D) & r1_xboole_0(A,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 79 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 80 (all A all B k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 81 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 82 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 83 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 84 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k4_xboole_0(B,A))) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 85 (all A all B all C all D (r1_xboole_0(B,D) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 86 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) & r1_tarski(A,C) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 87 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 88 (all A all B k3_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B))) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 89 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 90 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 91 (all A all B k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B)) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 92 (all A (-(-r1_xboole_0(A,A) & A = k1_xboole_0) & -(A != k1_xboole_0 & r1_xboole_0(A,A)))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 93 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 94 (all A all B all C k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),C)) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 95 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 96 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 97 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 98 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 99 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 100 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 101 (all A all B k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 102 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> A = B)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 103 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 104 (all A all B all C (-(-(r1_xboole_0(A,C) & r1_xboole_0(A,B)) & r1_xboole_0(A,k2_xboole_0(B,C))) & -(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,B) & r1_xboole_0(A,C)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 105 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 106 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 107 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 108 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 109 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 110 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 111 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 112 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 113 (all A all B -(r2_xboole_0(A,B) & k4_xboole_0(B,A) = k1_xboole_0)) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 114 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 115 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 116 (all A all B all C k3_xboole_0(k5_xboole_0(A,C),B) = k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 117 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 118 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k2_xboole_0(A,B))) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 119 (all A all B k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 120 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 121 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 122 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 123 (all A all B all C (k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 124 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 125 (all A all B all C all D (r1_xboole_0(C,A) & r1_xboole_0(D,B) & k2_xboole_0(C,D) = k2_xboole_0(A,B) -> C = B)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 126 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 127 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 128 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 129 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 130 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 131 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 132 (all A all B all C (r2_xboole_0(B,C) & r1_tarski(A,B) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 133 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 134 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 135 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 136 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 137 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 138 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 139 (all A all B k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 140 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 141 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 142 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 143 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 144 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 145 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 146 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 147 (all A all B (-v1_xboole_0(B) -> -(r1_tarski(B,A) & r1_xboole_0(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 148 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,A) & r1_xboole_0(A,B) & r1_tarski(C,B)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 149 (all A all B -(-r1_xboole_0(A,B) & r1_xboole_0(k3_xboole_0(A,B),B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 150 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 151 (all A all B all C (r2_xboole_0(A,B) & r1_tarski(B,C) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 152 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 153 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 154 (all A all B A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 155 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 156 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 157 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 158 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 159 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 160 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 161 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 162 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 163 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 164 (all A all B A = k3_xboole_0(A,k2_xboole_0(A,B))) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 165 (all A all B (-(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 166 (all A all B k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 167 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 168 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 169 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 170 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 171 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 172 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 173 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k4_xboole_0(A,C),B)) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 174 (all A all B all C k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 175 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 176 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 177 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C))) = k4_xboole_0(k5_xboole_0(A,B),C)) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 178 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 179 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 180 (all A all B all C ((all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 181 (all A all B all C k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A)) = k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 182 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 183 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> A = k1_xboole_0 | k1_xboole_0 = B | B = D & C = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 184 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 185 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 | k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 186 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 187 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 188 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 189 (all A all B all C all D k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) = k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 190 (all A all B -((all C -(B != C & r2_hidden(C,A))) & k1_xboole_0 != A & A != k1_tarski(B))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 191 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 192 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 193 (all A all B (A = k1_tarski(B) | k1_xboole_0 = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 194 (all A all B (A = k1_xboole_0 | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 195 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 196 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 197 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) -> r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)))) # label(t107_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 198 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 199 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 200 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 201 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 202 (all A all B (k2_zfmisc_1(B,B) = k2_zfmisc_1(A,A) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 203 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.24 204 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 205 (all A all B all C -(k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 206 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 207 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 208 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 209 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 210 (all A all B all C -(-r2_hidden(A,B) & -r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 211 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 212 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 213 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 214 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 215 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 216 (all A all B all C all D k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 217 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> D = C | r1_xboole_0(C,D))) -> k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_xboole_0(A,B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 218 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 219 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 220 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 221 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 222 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 223 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_xboole_0 & A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 224 (all A all B k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 225 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 226 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 227 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 228 (all A all B all C -(B != C & B != k1_xboole_0 & k1_xboole_0 != C & k1_tarski(A) = k2_xboole_0(B,C))) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 229 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t95_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 230 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(B,C)) & r2_hidden(A,k2_zfmisc_1(D,E)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 231 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 232 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 233 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 234 (all A all B (A != B -> k2_tarski(A,B) = k5_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 235 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 236 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 237 (all A all B all C -(-r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 238 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 239 (all A all B r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t84_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 240 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <-> r2_hidden(A,C) & B = D)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 241 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(A,C) & r1_tarski(B,D) | k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 242 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(C,B))) -> r1_tarski(k3_tarski(A),B))) # label(t94_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 243 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 244 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 245 (all A all B all C all D all E -((all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))) & r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 246 (all A all B all C all D -(C != A & A != D & k2_tarski(C,D) = k2_tarski(A,B))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 247 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 248 (all A all B (r1_tarski(k2_xboole_0(k1_tarski(A),B),B) -> r2_hidden(A,B))) # label(t45_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 249 (all A all B all C -(-(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_tarski(A) = B & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 250 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 251 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 252 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 253 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E C != k4_tarski(D,E)))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 254 (all A all B all C (k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) & k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 255 (all A all B all C k1_xboole_0 != k2_xboole_0(k2_tarski(A,B),C)) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 256 (all A all B (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(B,k1_tarski(A)))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 257 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 258 (all A all B r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B))))) # label(t105_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 259 (all A all B (-r2_hidden(A,B) -> r1_xboole_0(k1_tarski(A),B))) # label(t56_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 260 (all A all B all C (k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k4_xboole_0(A,B),C))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 261 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 262 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 263 (all A all B ((all C (r2_hidden(C,A) -> r1_xboole_0(C,B))) -> r1_xboole_0(k3_tarski(A),B))) # label(t98_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 264 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 265 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 266 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k2_tarski(B,C) != A & A != k1_tarski(C) & A != k1_tarski(B) & k1_xboole_0 != A))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 267 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 268 (all A all B all C (r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) -> r2_hidden(A,C))) # label(t47_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 269 (all A all B r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t97_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 270 (all A all B (k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) -> k1_xboole_0 = B | A = B | k1_xboole_0 = A)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 271 (all A all B all C all D (D = B & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 272 (all A all B all C (k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) & k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) = k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 273 (all A all B all C all D (r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F (r2_hidden(k4_tarski(E,F),A) -> r2_hidden(k4_tarski(E,F),D))) -> r1_tarski(A,D))) # label(t109_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 274 (all A all B (r1_tarski(A,k2_zfmisc_1(B,A)) | r1_tarski(A,k2_zfmisc_1(A,B)) -> k1_xboole_0 = A)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 275 (all A all B all C (-r2_hidden(B,C) & -r2_hidden(A,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 276 (all A all B all C -(r2_hidden(A,C) & r1_xboole_0(k2_tarski(A,B),C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 277 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 278 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 279 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 280 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 281 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 282 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 283 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 284 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 285 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 286 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0 <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 287 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 288 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 289 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 290 (all A all B all C -(r2_hidden(B,C) & B != A & k1_tarski(A) = k3_xboole_0(k2_tarski(A,B),C))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 291 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 292 (all A all B all C all D k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 293 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 294 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 295 (all A all B -(k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)) & A != k1_xboole_0 & A != k1_tarski(B))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 296 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 297 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> B = k2_xboole_0(k2_tarski(A,C),B))) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 298 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B)))) # label(t81_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 299 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 300 (all A all B all C (r1_tarski(A,B) -> r2_hidden(C,A) | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 301 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 302 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 303 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 304 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 305 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k1_tarski(C) = k2_tarski(A,B))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 306 (all A all B (B != A -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 307 (all A all B (-r2_hidden(A,B) -> k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 308 (all A exists B ((all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 309 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 310 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 311 (all A all B all C ((B = A | r2_hidden(B,C)) & -r2_hidden(A,C) <-> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 312 (all A all B all C (k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 313 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 314 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B)))) # label(t86_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 315 (all A all B k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 316 (all A all B -(r2_hidden(A,B) & r1_xboole_0(k1_tarski(A),B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 317 (all A k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 318 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A) & k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 319 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> A = C & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 320 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 321 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 322 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 323 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 324 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 325 (all A all B all C (k2_zfmisc_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 326 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 327 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 328 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 329 (all A all B (k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 330 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 331 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 332 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 333 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 334 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 335 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 336 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 337 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 338 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 339 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 340 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 341 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 342 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 343 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 344 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 345 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 346 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)))))) # label(t41_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 347 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 348 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) | r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 349 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,k3_subset_1(A,C)) <-> r1_tarski(B,C)))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 350 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 351 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 352 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 353 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 354 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 355 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 356 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 357 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 358 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 359 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 360 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 361 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))))))) # label(t42_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 362 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & -r2_hidden(E,D) <-> r2_hidden(E,B)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 363 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 364 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> r1_xboole_0(B,k3_subset_1(A,B)))) # label(t26_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 365 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 366 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 367 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B))))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 368 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> A = B))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 369 (all A all B (r2_hidden(A,B) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)))) # label(t63_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 370 (all A all B ((v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))) & (-v1_xboole_0(A) -> (m1_subset_1(B,A) <-> r2_hidden(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 371 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 372 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 373 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 374 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k5_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 375 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 376 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,D) <-> r2_hidden(E,C))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 377 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 378 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 379 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> -r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 380 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 381 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 382 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 383 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 385 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 386 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 387 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 388 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 389 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 390 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 391 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 392 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 393 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (A != k1_xboole_0 -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 394 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 395 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,C) & r2_hidden(B,k3_subset_1(A,C))))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 396 (exists A ((all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))) & m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 397 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 398 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 399 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k2_subset_1(A)))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 400 (all A (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 401 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 402 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) -> r2_subset_1(B,A)))) # label(symmetry_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 403 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 404 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 405 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 406 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 407 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 408 (exists A ((all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 409 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 410 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 411 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 412 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 413 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 414 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 415 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (k1_xboole_0 != A -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 416 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 417 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 418 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 419 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 420 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 421 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 422 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 423 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 424 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 425 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 426 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 427 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 428 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 429 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 430 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 431 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 432 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.25 433 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 434 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 435 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> k3_subset_1(A,C) = B))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 436 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 437 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 438 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 439 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 440 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),C) -> r1_tarski(k3_subset_1(A,C),B)))))) # label(t36_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 441 (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]. 4.15/4.26 442 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> (r2_hidden(B,k8_setfam_1(A,C)) <-> (all D (r2_hidden(D,C) -> r2_hidden(B,D))))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 443 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 444 (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]. 4.15/4.26 445 (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]. 4.15/4.26 446 (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))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 447 (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]. 4.15/4.26 448 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 449 (all A all B all C (C = k2_setfam_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k2_xboole_0(E,F))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 450 (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]. 4.15/4.26 451 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 452 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 453 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 454 (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]. 4.15/4.26 455 (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]. 4.15/4.26 456 (all A all B all C ((all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) & r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 457 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_xboole_0 != B & k7_setfam_1(A,B) = k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 458 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k3_xboole_0(E,F) & r2_hidden(E,A))))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 459 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_xboole_0 -> A = k8_setfam_1(A,B)) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 460 (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]. 4.15/4.26 461 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 462 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 463 (all A all B -(B != k1_xboole_0 & -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]. 4.15/4.26 464 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 465 (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(C,B) <-> r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B))))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 466 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 467 (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]. 4.15/4.26 468 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 469 (all A all B -(k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 470 (all A all B (r2_setfam_1(B,A) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 471 (all A all B ((A = k1_xboole_0 -> (B = k1_xboole_0 <-> k1_setfam_1(A) = B)) & (A != k1_xboole_0 -> ((all C ((all D (r2_hidden(D,A) -> r2_hidden(C,D))) <-> r2_hidden(C,B))) <-> B = k1_setfam_1(A))))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 472 (all A all B (B != k1_xboole_0 -> k2_xboole_0(A,k1_setfam_1(B)) = k1_setfam_1(k2_setfam_1(k1_tarski(A),B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 473 (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,B) = C <-> (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]. 4.15/4.26 474 (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]. 4.15/4.26 475 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 476 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 477 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 478 (all A all B (B != k1_xboole_0 -> 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]. 4.15/4.26 479 (all A all B (v1_setfam_1(B) & v1_setfam_1(A) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 480 (all A (-v2_setfam_1(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,A))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 481 (all A all B all 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))))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 482 (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]. 4.15/4.26 483 (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]. 4.15/4.26 484 (all A all B all C (r2_hidden(C,A) & r1_tarski(k3_tarski(A),B) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 485 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 486 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 487 (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]. 4.15/4.26 488 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 489 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 490 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 491 (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]. 4.15/4.26 492 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 493 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 494 (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]. 4.15/4.26 495 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 496 (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]. 4.15/4.26 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B)) = k6_setfam_1(A,k7_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 498 (all A all B k3_setfam_1(A,B) = k3_setfam_1(B,A)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 499 (all A all B ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,B) & r1_tarski(C,D))))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 500 (all A ((all B (-v1_xboole_0(B) -> -r2_hidden(B,A))) <-> v2_setfam_1(A))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 501 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 502 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 503 (all A all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 504 (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]. 4.15/4.26 505 (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]. 4.15/4.26 506 (all A (r1_setfam_1(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 507 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 508 (all A all B k3_tarski(k3_setfam_1(k1_tarski(A),B)) = k3_xboole_0(A,k3_tarski(B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 509 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 510 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 511 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k5_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 512 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 513 (all A all B k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_setfam_1(A,B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 514 (all A all B k1_setfam_1(k2_tarski(A,B)) = k3_xboole_0(A,B)) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 515 (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]. 4.15/4.26 516 (all A all B ((all C -((all D -(r2_hidden(D,A) & r1_tarski(D,C))) & r2_hidden(C,B))) <-> r2_setfam_1(A,B))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 517 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 518 (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]. 4.15/4.26 519 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 520 (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]. 4.15/4.26 521 (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]. 4.15/4.26 522 (all A all B all C (r1_xboole_0(A,C) & r2_hidden(A,B) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 523 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 524 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 525 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 526 (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]. 4.15/4.26 527 (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]. 4.15/4.26 528 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 529 (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]. 4.15/4.26 530 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | A = k1_xboole_0)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 531 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 532 (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]. 4.15/4.26 533 (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]. 4.15/4.26 534 (all A all B (r1_tarski(A,B) <-> m1_subset_1(A,k1_zfmisc_1(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 535 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 536 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 537 (all A all B all C -(m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 538 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 539 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 540 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 541 (all A all B (v1_relat_1(B) -> r1_tarski(k7_relat_1(B,A),B))) # label(t88_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 542 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 543 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 544 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 545 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 546 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 547 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) = k7_relat_1(B,A))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 548 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k1_xboole_0 = k10_relat_1(B,A)))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 549 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 550 (all A all B (v1_relat_1(B) -> r1_tarski(k8_relat_1(A,B),B))) # label(t117_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 551 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 552 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 553 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 554 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 555 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B))))) # label(t104_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 556 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 557 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 558 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))))) # label(t155_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 559 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))))))) # label(t15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 560 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t178_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 561 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k2_relat_1(B)) -> k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A)))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 562 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) <-> (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 563 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)))))) # label(t92_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 564 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 565 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(A,C) & r2_hidden(k4_tarski(A,B),D)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 566 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)))))) # label(t44_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 567 (all A all B (v1_relat_1(B) -> (r1_tarski(A,B) -> v1_relat_1(A)))) # label(t3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 568 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 569 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 570 (all A all B (v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 571 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 572 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 573 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 574 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 575 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 576 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 577 (all A (k2_relat_1(k6_relat_1(A)) = A & k1_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 578 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 579 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 580 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C))))) # label(t131_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 581 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 582 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))) = k7_relat_1(A,k1_relat_1(B)))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 583 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 584 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 585 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))))) # label(t147_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 586 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 587 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B)))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 588 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 589 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 590 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 591 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A))))))) # label(t179_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 592 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 593 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 594 (all A (v1_relat_1(A) -> (v2_relat_1(A) <-> -r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(d9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 595 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 596 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))))))) # label(t34_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 597 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 598 (all A (v1_relat_1(A) -> k2_relat_1(A) = k9_relat_1(A,k1_relat_1(A)))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 599 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C))))))) # label(t132_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 600 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t89_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 601 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 602 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 603 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 604 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 605 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 606 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 607 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 608 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 609 (all A all B all C (v1_relat_1(C) -> k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 610 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t118_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 611 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 612 (all A all B (v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k4_tarski(C,C),B))) -> r1_tarski(k6_relat_1(A),B)))) # label(t73_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 613 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 614 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A))) # label(t87_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 615 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 616 (all A all B (v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)))) # label(t10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 617 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 618 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 619 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (C = k5_relat_1(A,B) <-> (all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 620 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 621 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 622 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 623 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 624 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 625 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)))) # label(t161_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 626 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 627 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 628 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 629 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t157_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 630 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 631 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 632 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 633 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 634 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 635 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(k5_relat_1(A,B),C))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 636 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 637 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 638 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 639 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,C) = k7_relat_1(A,C) & k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 640 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 641 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k2_relat_1(B))) & r2_hidden(A,k1_relat_1(B))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 642 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)))))) # label(t45_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 643 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))))) # label(t163_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 644 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 645 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (k8_relat_1(A,B) = C <-> (all D all E (r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 646 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 647 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 648 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 649 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 650 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 651 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 652 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 653 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k1_relat_1(k4_relat_1(A)) = k2_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 654 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k5_relat_1(B,D) = k6_relat_1(A) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 655 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 656 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))))))) # label(t28_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 657 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k7_relat_1(B,A)))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 658 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 659 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k1_xboole_0 = k9_relat_1(B,A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 660 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 661 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 662 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 663 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 664 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> k2_relat_1(E) = k2_tarski(B,D) & k1_relat_1(E) = k2_tarski(A,C)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 665 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 666 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 667 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 668 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 669 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 670 (all A all B all C (v1_relat_1(C) -> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t176_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 671 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 672 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_relat_1(A)) = A)) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 673 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k1_relat_1(B))) & r2_hidden(A,k2_relat_1(B))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 674 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A))))))) # label(t105_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 675 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 676 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t48_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 677 (all A (v1_relat_1(A) <-> (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 678 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))))))))) # label(t52_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 679 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 680 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 681 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 682 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 683 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 684 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k7_relat_1(C,B)) = k7_relat_1(k8_relat_1(A,C),B))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 685 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 686 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 687 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 688 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 689 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(C,A) & C = D <-> r2_hidden(k4_tarski(C,D),B))) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 690 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 691 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 692 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 693 (all A all B (v1_relat_1(B) -> k5_relat_1(k6_relat_1(A),B) = k7_relat_1(B,A))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 694 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> B = k2_relat_1(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 695 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C))) <-> r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C)))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 696 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))))) # label(t183_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 697 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 698 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 699 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 700 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 701 (exists A (v1_relat_1(A) & (all B all C (p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1) & r2_hidden(B,f1_s1_relat_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 702 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 703 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 704 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(A),k3_relat_1(A)) & r1_tarski(k2_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.26 705 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 706 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 707 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)))))) # label(t93_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 708 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 709 (all A (v1_relat_1(A) -> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 710 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 711 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 712 (all A (v1_relat_1(A) -> A = k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 713 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 714 (all A all B all C all D v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 715 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)))) # label(t144_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 716 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 717 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 718 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 719 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 720 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 721 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 722 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 723 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 724 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k1_xboole_0 = k5_relat_1(A,B)))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 725 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))))))))) # label(t53_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 726 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 727 (all A (v1_relat_1(A) -> k3_relat_1(k4_relat_1(A)) = k3_relat_1(A))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 728 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 729 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 730 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 731 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 732 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 733 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))))) # label(t177_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 734 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(E,D),A))) <-> r2_hidden(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 735 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 736 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A)))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 737 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))))))))) # label(t49_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 738 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k7_relat_1(B,A) = k1_xboole_0))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 739 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t99_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 740 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t27_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 741 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 742 (all A (v1_xboole_0(A) -> v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 743 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 744 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 745 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 746 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)))))) # label(t121_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 747 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 748 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k8_relat_1(A,B)))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 749 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 750 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 751 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A))) # label(t116_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 752 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t154_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 753 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 754 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 755 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 756 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 757 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 758 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 759 (all A all B (v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(t9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 760 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 761 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 762 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 != A))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 763 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))))) # label(t170_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 764 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 765 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 766 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 767 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 768 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 769 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 770 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> k5_relat_1(A,B) = C))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 771 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 772 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 773 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 774 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(C,A) = k5_relat_1(B,A) & k1_relat_1(C) = k1_relat_1(B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> B = C)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 775 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & k1_funct_1(A,E) = D)))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 776 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 777 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 778 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 779 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 780 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (D = k1_funct_1(A,C) <-> k1_funct_1(B,D) = C))) & k1_relat_1(B) = k2_relat_1(A) & k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 781 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 782 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 783 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> k1_funct_1(A,B) = C)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 784 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 785 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 786 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 787 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 788 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_1(A)) & v1_relat_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 789 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 790 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k9_relat_1(k8_relat_1(A,C),B) = k3_xboole_0(A,k9_relat_1(C,B)))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 791 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 792 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 793 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 794 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 795 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 796 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 797 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 798 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 799 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 800 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 801 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 802 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 803 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 804 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 805 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 806 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 807 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))) = k3_xboole_0(k9_relat_1(C,A),B))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 808 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 809 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & k2_relat_1(A) = k1_relat_1(B) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 810 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 811 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 812 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 813 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 814 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -((all B -p1_s2_funct_1(A,B)) & r2_hidden(A,f1_s2_funct_1))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 815 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 816 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 817 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,A) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 818 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 819 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 820 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 821 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) & k1_relat_1(C) = A -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 822 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 823 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 824 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 825 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 826 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 827 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 828 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 829 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 830 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 831 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 832 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 833 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k1_relat_1(A) = k2_relat_1(B) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 834 (all A all B -(-(A = k1_xboole_0 & B != k1_xboole_0) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -(k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 835 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A))))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 836 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) & r2_hidden(C,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 837 (all A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A) -> v1_funct_1(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 838 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 839 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 840 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 841 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 842 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 843 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 844 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 845 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 846 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) & k1_relat_1(B) = k1_relat_1(C) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 847 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 848 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k10_relat_1(B,k1_tarski(A)) != k1_xboole_0))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 849 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A & k1_relat_1(C) = A -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 850 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 851 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D ((r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k2_relat_1(A) = k1_relat_1(B) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 852 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 853 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 854 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 855 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 856 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 857 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 858 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(D) = A & k1_relat_1(C) = A & k2_relat_1(B) = A -> C = D))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 859 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k10_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 860 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 861 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 862 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 863 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 864 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 865 (all A (A != k1_xboole_0 -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = A & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 866 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 867 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.15/4.27 868 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 869 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 870 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 871 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 872 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 873 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 874 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) <-> (all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 875 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 876 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 877 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) <-> k8_relat_1(A,C) = B))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 878 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 879 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 880 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 881 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 882 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 883 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 884 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k2_relat_1(A) & A = k5_relat_1(A,B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 885 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 886 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 887 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 888 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 889 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 890 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 891 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 892 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 893 (all A all B (r2_hidden(B,A) -> B = k1_funct_1(k6_relat_1(A),B))) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 894 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 895 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 896 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 897 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 898 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 899 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 900 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 901 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 902 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 903 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 904 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 905 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 906 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 907 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 908 (all A all B all C (v1_relat_1(C) -> k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 909 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 910 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 911 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> f2_s3_funct_1(B) = k1_funct_1(A,B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 912 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(C)) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(k5_relat_1(B,C),k9_relat_1(C,A)))))))) # label(t160_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 913 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 914 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 915 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 916 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 917 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 918 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 919 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 920 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 921 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 922 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 923 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 924 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 925 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 926 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 927 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 928 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 929 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 930 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 931 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & r1_tarski(A,k1_relat_1(C)) & v2_funct_1(C) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 932 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C ((exists D (r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D))) <-> r2_hidden(C,B))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 933 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 934 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 935 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 936 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 937 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 938 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 939 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 940 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 941 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A)))))) # label(t146_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 942 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 943 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 944 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 945 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 946 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 947 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 948 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 949 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 950 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 951 (all A all B (v1_relat_1(B) -> ((all C -(k10_relat_1(B,k1_tarski(C)) = k1_xboole_0 & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 952 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 953 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(C = k1_funct_1(B,D) & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 954 (all A all B all C (v1_relat_1(C) -> r1_tarski(k3_xboole_0(A,k10_relat_1(C,B)),k10_relat_1(C,k3_xboole_0(k9_relat_1(C,A),B))))) # label(t151_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 955 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 956 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 957 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 958 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 959 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 960 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 961 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 962 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 963 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 964 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r1_tarski(k5_relat_1(A,A),A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 965 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 966 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v5_relat_2(k4_relat_1(A))))) # label(t36_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 967 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 968 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k2_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 969 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(A) -> v2_relat_2(k4_xboole_0(A,B))))))) # label(t33_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 970 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 971 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.27 972 (all A (v1_relat_1(A) -> (v4_relat_2(A) -> v4_relat_2(k4_relat_1(A))))) # label(t40_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 973 (all A (v1_relat_1(A) -> (r2_relat_2(A,k3_relat_1(A)) <-> v2_relat_2(A)))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 974 (all A (v1_relat_1(A) -> (r1_relat_2(A,k3_relat_1(A)) <-> v1_relat_2(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 975 (all A (v1_relat_1(A) -> (r4_relat_2(A,k3_relat_1(A)) <-> v4_relat_2(A)))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 976 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k1_relat_1(k4_relat_1(A)) = k1_relat_1(A)))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 977 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r8_relat_2(A,k3_relat_1(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 978 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v6_relat_2(A) & v1_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 979 (all A (v1_relat_1(A) -> (r1_xboole_0(k6_relat_1(k3_relat_1(A)),A) <-> v2_relat_2(A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 980 (all A (v1_relat_1(A) -> (v8_relat_2(A) -> v8_relat_2(k4_relat_1(A))))) # label(t42_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 981 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) <-> (all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 982 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 983 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 984 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 985 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 986 (all A (v1_relat_1(A) -> (v5_relat_2(A) <-> r5_relat_2(A,k3_relat_1(A))))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 987 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 988 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> v1_relat_2(k4_relat_1(A))))) # label(t27_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 989 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 990 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 991 (all A (v1_relat_1(A) -> (v3_relat_2(A) -> v3_relat_2(k4_relat_1(A))))) # label(t34_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 992 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 993 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 994 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) -> v5_relat_2(k4_xboole_0(A,B))))))) # label(t38_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 995 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 996 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 997 (all A (v1_relat_1(A) -> (A = k4_relat_1(A) <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 998 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,C),A) & r2_hidden(C,B))) <-> r2_relat_2(A,B))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 999 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1000 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1001 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1002 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(B) & v2_relat_2(A) -> v2_relat_2(k2_xboole_0(A,B)) & v2_relat_2(k3_xboole_0(A,B))))))) # label(t32_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1003 (all A (v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1004 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1005 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k3_xboole_0(A,B)) & v4_relat_2(k4_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1006 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1007 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1008 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r6_relat_2(A,k3_relat_1(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1009 (all A all B (v1_relat_1(B) -> (r4_relat_2(B,A) <-> r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1010 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1011 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1012 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1013 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1014 (all A (v1_relat_1(A) -> (v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1015 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1016 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A)))))) # label(t45_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1017 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v4_relat_2(A) & v2_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1018 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1019 (all A (v1_relat_1(A) -> (all B (r7_relat_2(A,B) <-> (all C all D -(-r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1020 (all A (v1_relat_1(A) -> (r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A))) <-> v4_relat_2(A)))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1021 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1022 (all A (v1_relat_1(A) -> (r1_tarski(k6_relat_1(k3_relat_1(A)),A) <-> v1_relat_2(A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1023 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> r7_relat_2(A,k3_relat_1(A))))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1024 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1025 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) & v5_relat_2(B) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1026 (all A all B (v1_relat_1(B) -> (r5_relat_2(B,A) -> r4_relat_2(k2_xboole_0(B,k6_relat_1(A)),A)))) # label(t20_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1027 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_ordinal1(A,B) <-> r1_tarski(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1028 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1029 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1030 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1031 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1032 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1033 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) <-> v5_ordinal1(A)))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1034 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1035 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1036 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> A = B | r2_hidden(A,B))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1037 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1038 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1039 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D))))))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1040 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1041 (all A exists B ((all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))) & -r2_hidden(B,A) & v3_ordinal1(B))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1042 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B) & r1_tarski(B,A))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1043 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r1_ordinal1(k1_ordinal1(A),B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1044 (all A all B all C all D -(r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1045 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1046 (all A all B (m1_ordinal1(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1047 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1048 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1049 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1050 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A (v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1051 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1052 (all A all B (m1_ordinal1(B,A) -> (all C (v3_ordinal1(C) -> m1_ordinal1(k2_ordinal1(B,C),A))))) # label(t48_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1053 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1054 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1055 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1056 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1057 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1058 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1059 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v1_relat_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1060 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1061 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k3_tarski(A)))) # label(t35_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1062 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1063 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1064 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1065 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1066 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1067 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1068 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1069 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1070 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1071 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A)))) <-> v4_ordinal1(A)))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1072 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_xboole_0(A,B) -> r2_hidden(A,B)))))) # label(t21_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1073 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1074 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1075 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1076 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1077 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1078 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1079 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1080 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1081 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1082 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1083 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1084 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1085 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,B) | r2_hidden(B,A))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1086 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(C,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1087 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1088 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1089 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1090 (all A all B all C -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1091 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1092 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(C,D))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1093 (all A (v3_ordinal1(A) -> -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)) & -((exists B (v3_ordinal1(B) & k1_ordinal1(B) = A)) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1094 (all A all B (r1_tarski(A,B) -> (all C (m1_ordinal1(C,A) -> m1_ordinal1(C,B))))) # label(t47_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1095 (all A -((all B (v3_ordinal1(B) -> -r1_tarski(A,B))) & (all B (r2_hidden(B,A) -> v3_ordinal1(B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1096 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1097 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,f1_s4_ordinal1) & C = k2_ordinal1(A,B) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1098 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1099 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1100 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1101 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1102 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1103 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1104 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s2_ordinal1(B)))) -> p1_s2_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> p1_s2_ordinal1(A))) # label(s2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1105 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & B = k2_ordinal1(f3_s3_ordinal1,A) -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1106 (all A (A = k3_tarski(A) <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1107 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1108 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & B = f3_s5_ordinal1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f2_s5_ordinal1(A) = k1_funct_1(f1_s5_ordinal1,A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1109 (all A all B all C (m1_relset_1(C,A,B) -> m2_relset_1(k6_relset_1(A,B,C),B,A))) # label(dt_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1110 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k11_relset_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1111 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1112 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1113 (all A all B all C all D (m2_relset_1(D,B,C) -> (r1_tarski(A,D) -> m2_relset_1(A,B,C)))) # label(t4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1114 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1115 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1116 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1117 (all A all B all C (m2_relset_1(C,A,B) -> (k5_relset_1(A,B,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C))))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1118 (all A all B all C (m1_relset_1(C,A,B) <-> m2_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1119 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(A,B) -> m2_relset_1(D,B,C)))) # label(t15_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1120 (all A all B all C all D (m2_relset_1(D,A,C) -> m2_relset_1(k8_relset_1(A,C,D,B),B,C))) # label(t33_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1121 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A)))) # label(t10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1122 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1123 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1124 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k4_xboole_0(C,D) = k3_relset_1(A,B,C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1125 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(k2_relat_1(D),B) -> m2_relset_1(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1126 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(k1_relat_1(D),B) -> m2_relset_1(D,B,C)))) # label(t13_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1127 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1128 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1129 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> C = k1_xboole_0))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1130 (all A all B all C (m1_relset_1(C,A,B) -> C = k6_relset_1(A,B,k6_relset_1(A,B,C)))) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1131 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1132 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1133 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1134 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1135 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(A,B) -> m2_relset_1(D,C,B)))) # label(t16_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1136 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1137 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(E,D),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1138 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1139 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1140 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1141 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1142 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)))) # label(t19_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1143 (all A all B all C (m1_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k1_relat_1(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1144 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1145 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k5_relset_1(B,A,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C))))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1146 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1147 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> k8_relset_1(B,A,D,C) = D))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1148 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1149 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1150 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_xboole_0(C,D) = k2_relset_1(A,B,C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1151 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1152 (all A all B all C (m1_relset_1(C,A,B) <-> r1_tarski(C,k2_zfmisc_1(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1153 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & B = k5_relat_1(B,k6_relat_1(A)))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1154 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1155 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1156 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C)))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1157 (all A all B all C all D (m1_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(dt_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1158 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1159 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1160 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1161 (all A all B all C all D (m2_relset_1(D,C,A) -> m2_relset_1(k9_relset_1(C,A,B,D),C,B))) # label(t35_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1162 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1163 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1164 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1165 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1166 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1167 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k5_relset_1(A,B,D)) & r1_tarski(C,k4_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1168 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1169 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k11_relset_1(A,B,C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1170 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1171 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1172 (all A all B all C all D (m1_relset_1(C,A,B) -> m2_relset_1(k8_relset_1(A,B,C,D),A,B))) # label(dt_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1173 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1174 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> m2_relset_1(B,A,k2_relat_1(B))))) # label(t9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1175 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1176 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1177 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1178 (all A all B all C all D (m1_relset_1(D,A,B) -> k8_relat_1(C,D) = k9_relset_1(A,B,C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1179 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1180 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1181 (exists A (m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1) & (all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (p1_s2_relset_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))))))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1182 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1183 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> r1_tarski(B,k5_relset_1(B,A,C)) & B = k4_relset_1(B,A,C)))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1184 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1185 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1186 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k2_relset_1(A,B,C,D),A,B))) # label(dt_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1187 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1188 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1189 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1190 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1191 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1192 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1193 (all A all B all C all D (m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k8_relset_1(A,B,C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1194 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1195 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1196 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1197 (all A all B all C (m2_relset_1(C,B,A) -> k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) & k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1198 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1199 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1200 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1201 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1202 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1203 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1204 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1205 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1206 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(B,C) & r1_tarski(A,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1207 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1208 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(C,A),k4_partfun1(C,B)))) # label(t127_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1209 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1210 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1211 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1212 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1213 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1214 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1215 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1216 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1217 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1218 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1219 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1220 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1221 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1222 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1223 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1224 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1225 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1226 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1227 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1228 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1229 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1230 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1231 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1232 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1233 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1234 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1235 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1236 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1237 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1238 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1239 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1240 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1241 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1242 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1243 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1244 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1245 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1246 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A)))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1247 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1248 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1249 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_partfun1 & (all B (r2_hidden(B,f1_s1_partfun1) -> (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)) & (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1250 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1251 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1252 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1253 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1254 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1255 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1256 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1257 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1258 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1259 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1260 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1261 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1262 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1263 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1264 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1265 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.28 1266 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1267 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))) & (all B (p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1268 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1269 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1270 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1271 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1272 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1273 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1274 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1275 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1276 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1277 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1278 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1279 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1280 (all A exists B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B) & v1_relat_2(B) & v1_relat_1(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1281 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1282 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1283 (all A (v8_relat_2(A) & v3_relat_2(A) & v1_relat_1(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1284 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1285 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1286 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_funct_1(C) & C = k2_xboole_0(A,B) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1287 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1288 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1289 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1290 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1291 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1292 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1293 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1294 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)) & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1295 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1296 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1297 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1298 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1299 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1300 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1301 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1302 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1303 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1304 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1305 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1306 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1307 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> A = k1_xboole_0)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1308 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1309 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1310 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1311 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1312 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1313 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1314 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1315 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1316 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1317 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1318 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1319 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1320 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1321 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1322 (all A (m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1323 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k2_partfun1(A,B,C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1324 (all A all B all C (C = k4_partfun1(A,B) <-> (all D ((exists E (v1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1325 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1326 (all A all B all C all D all E all F (r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1327 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1328 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1329 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1330 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1331 (all A (v1_relat_1(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1332 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1333 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1334 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1335 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1336 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1337 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1338 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (v1_relat_1(C) & v1_funct_1(C) -> C != k2_xboole_0(A,B))) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1339 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k9_relat_1(D,A))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1340 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1341 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1342 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1343 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1344 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1345 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1346 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1347 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1348 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1349 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1350 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1351 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1352 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1353 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1354 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1355 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1356 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> C = D)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & (all B all C (r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1357 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1358 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1359 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) <-> k1_tarski(C) = k5_partfun1(A,B,C)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1360 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1361 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1362 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1363 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_relat_1(D) = k1_tarski(A) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1364 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1365 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1366 (all A all B r1_tarski(k4_partfun1(k1_xboole_0,A),k4_partfun1(B,A))) # label(t126_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1367 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1368 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1369 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) <-> r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1370 (all A all B all C (m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1371 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1372 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1373 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1374 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1375 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1376 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1377 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1378 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1379 (all A all B exists C (v1_funct_1(C) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1380 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1381 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1382 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1383 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1384 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1385 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1386 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1387 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1388 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1389 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1390 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1391 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(C,k6_relat_1(B)) = C)) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1392 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> B = C)) & (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1393 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1394 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1395 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & E = F)) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1396 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1397 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1398 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1399 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1400 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1401 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1402 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1403 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1404 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1405 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1406 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)))) # label(t125_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1407 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1408 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1409 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1410 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1411 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1412 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k10_mcart_1(A,B,C,D,E),C))) # label(dt_k10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1413 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k4_tarski(k4_tarski(A,B),C),D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1414 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1415 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1416 (all A all B all C all D k3_mcart_1(k4_tarski(A,B),C,D) = k4_mcart_1(A,B,C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1417 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & C != k2_mcart_1(C))))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1418 (all A all B all C -(B != k1_xboole_0 & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (D = k3_mcart_1(E,F,G) & -(k5_mcart_1(A,B,C,D) = E & k6_mcart_1(A,B,C,D) = F & G = k7_mcart_1(A,B,C,D)))))) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1419 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1420 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_tarski(C,D) = B)))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1421 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1422 (all A all B all C all D all E all F all G all H (r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) & r1_tarski(A,B) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1423 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E)) = k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1424 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1425 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1426 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(B,F) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1427 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1428 (all A all B all C all D all E all F all G all H -(A != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != D & F != k1_xboole_0 & k1_xboole_0 != G & H != k1_xboole_0 & (exists I ((exists J (J = I & -(k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I) & k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I)) & m1_subset_1(J,k4_zfmisc_1(E,F,G,H)))) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != E & k1_xboole_0 != C)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1429 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B (B = k2_mcart_1(A) <-> (all C all D (k4_tarski(C,D) = A -> B = D)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1430 (all A all B all C -(B != k1_xboole_0 & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1431 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> (C = k1_mcart_1(A) | k1_mcart_1(A) = B) & k2_mcart_1(A) = D)) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1432 (all A all B all C all D -(k1_xboole_0 != A & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k9_mcart_1(A,B,C,D,E) != E & k11_mcart_1(A,B,C,D,E) != E & k10_mcart_1(A,B,C,D,E) != E & k8_mcart_1(A,B,C,D,E) != E)) & k1_xboole_0 != D & C != k1_xboole_0 & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1433 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> k13_mcart_1(A,B,C,D,E,F) = k3_zfmisc_1(D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1434 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & D != k1_xboole_0 & B != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1435 (all A all B all C (r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E k4_tarski(D,E) != A))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1436 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1437 (all A all B all C -(A != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k6_mcart_1(A,B,C,D) & D != k7_mcart_1(A,B,C,D) & D != k5_mcart_1(A,B,C,D))) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1438 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k5_mcart_1(A,B,C,D),A))) # label(dt_k5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1439 (all A all B all C all D all E all F all G all H (r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) <-> r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F) & r2_hidden(A,E))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1440 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(E,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1441 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1442 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> (all G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) -> (r2_hidden(G,k3_zfmisc_1(D,E,F)) -> r2_hidden(k5_mcart_1(A,B,C,G),D) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k7_mcart_1(A,B,C,G),F)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1443 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1444 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> C = F & B = E & A = D)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1445 (all A all B all C all D all E all F -(A != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != F & (exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (H = G & -(k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H) & k6_mcart_1(D,E,F,H) = k6_mcart_1(A,B,C,G) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H)) & m1_subset_1(H,k3_zfmisc_1(D,E,F)))))) & E != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1446 (all A all B all C all D k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1447 (all A all B all C all D k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1448 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1449 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (E = k7_mcart_1(A,B,C,D) <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1450 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> C = k1_xboole_0 | D = k1_xboole_0 | G = C & H = D & B = F & E = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1451 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = F))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k5_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1452 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1453 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1454 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> C = k2_mcart_1(A) & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1455 (all A all B all C all D all E all F all G all H (m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(A)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1456 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & r1_xboole_0(B,A))))) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1457 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> D = H & G = C & B = F & E = A | k1_xboole_0 = k4_zfmisc_1(A,B,C,D))) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1458 (all A all B all C all D all E all F (A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1459 (all A all B all C all D all E all F (r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)) <-> r2_hidden(A,D) & r2_hidden(B,E) & r2_hidden(C,F))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1460 (all A all B -(-(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1461 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & k1_xboole_0 != C & (exists E exists F exists G (-(k5_mcart_1(A,B,C,D) = E & G = k7_mcart_1(A,B,C,D) & F = k6_mcart_1(A,B,C,D)) & D = k3_mcart_1(E,F,G))) & B != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1462 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k8_mcart_1(A,B,C,D,E),A))) # label(dt_k8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1463 (all A ((exists B exists C k4_tarski(B,C) = A) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1464 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1465 (all A all B all C all D all E all F (r1_tarski(A,B) & r1_tarski(E,F) & r1_tarski(C,D) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1466 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1467 (all A -(A != k1_xboole_0 & (all B -((all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k4_mcart_1(C,D,E,F))) & r2_hidden(B,A))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1468 (all A all B all C all D all E all F all G all H (m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1469 (all A all B all C all D k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) = k4_zfmisc_1(A,B,C,D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1470 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1471 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> G = E))))))))) -> k1_xboole_0 = B | D = k1_xboole_0 | E = k8_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1472 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> H = D))))))) -> C = k1_xboole_0 | D = k7_mcart_1(A,B,C,E) | B = k1_xboole_0 | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1473 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | D = A & E = B & C = F)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1474 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = G))))))) -> A = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1475 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k1_mcart_1(A) = B & k2_mcart_1(A) = C)) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.29 1476 (all A all B all C all D all E all F k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1477 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1478 (all A all B all C all D k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1479 (all A -((all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & k1_xboole_0 != A)) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1480 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != C & (exists F exists G exists H exists I (-(k10_mcart_1(A,B,C,D,E) = H & I = k11_mcart_1(A,B,C,D,E) & G = k9_mcart_1(A,B,C,D,E) & F = k8_mcart_1(A,B,C,D,E)) & E = k4_mcart_1(F,G,H,I))) & k1_xboole_0 != D & B != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1481 (all A all B all C all D -(C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = H)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != D & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1482 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1483 (all A all B -(B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & C != k1_mcart_1(C))) & k1_xboole_0 != A)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1484 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(I,D) & k4_mcart_1(G,H,I,J) = F & r2_hidden(J,E) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1485 (all A -(k1_xboole_0 != A & (all B -((all C all D all E -((r2_hidden(D,A) | r2_hidden(C,A)) & B = k3_mcart_1(C,D,E))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1486 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k6_mcart_1(A,B,C,D),B))) # label(dt_k6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1487 (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,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_mcart_1(k1_funct_1(A,C)))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1488 (all A all B all C k4_tarski(k4_tarski(A,B),C) = k3_mcart_1(A,B,C)) # label(d3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1489 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = H))))))))) -> D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | B = k1_xboole_0 | A = k1_xboole_0))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1490 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(C,F) & -r1_xboole_0(B,E) & -r1_xboole_0(A,D))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1491 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k11_mcart_1(A,B,C,D,E),D))) # label(dt_k11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1492 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1493 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (k10_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = I))))))) & k1_xboole_0 != D & k1_xboole_0 != C & B != k1_xboole_0 & A != k1_xboole_0)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1494 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1495 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1496 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1497 (all A ((exists B exists C k4_tarski(B,C) = A) -> k2_mcart_1(A) != A & k1_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1498 (all A all B all C all D ((all E ((exists F exists G exists H (r2_hidden(F,B) & r2_hidden(H,D) & k3_mcart_1(F,G,H) = E & r2_hidden(G,C))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1499 (all A all B (k2_mcart_1(k4_tarski(A,B)) = B & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1500 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1501 (all A all B all C all D k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1502 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> r2_hidden(k2_mcart_1(A),C) & k1_mcart_1(A) = B)) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1503 (all A all B all C all D -(C != k1_xboole_0 & k1_xboole_0 != D & (exists E ((exists F exists G exists H exists I (E = k4_mcart_1(F,G,H,I) & -(G = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & k10_mcart_1(A,B,C,D,E) = H & F = k8_mcart_1(A,B,C,D,E)))) & m1_subset_1(E,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1504 (all A all B all C all D -(k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = J)) <-> k11_mcart_1(A,B,C,D,E) = F))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1505 (all A all B all C all D all E all F (m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(A)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1506 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k9_mcart_1(A,B,C,D,E),B))) # label(dt_k9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1507 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1508 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1509 (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,k1_relat_1(A)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) <-> B = k16_mcart_1(A)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1510 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k1_xboole_0 = A | C = k1_xboole_0 | D = A & E = B & F = C | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1511 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> (k5_mcart_1(A,B,C,D) = E <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> F = E))))))) & k1_xboole_0 != C & k1_xboole_0 != A)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1512 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k7_mcart_1(A,B,C,D),C))) # label(dt_k7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1513 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(G,C) & r2_hidden(F,B))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1514 (all A all B all C -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k2_mcart_1(D) = k7_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D)))))) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1515 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1516 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> I = E))))))))) -> B = k1_xboole_0 | C = k1_xboole_0 | k10_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | k1_xboole_0 = A))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1517 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> A = B)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1518 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1519 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> (D = k2_mcart_1(A) | C = k2_mcart_1(A)) & k1_mcart_1(A) = B)) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1520 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(A,B,C)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(C,A,B))) -> A = k1_xboole_0)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1521 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1522 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1523 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (k1_mcart_1(A) = C | B = k1_mcart_1(A)) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1524 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (k4_tarski(C,D) = A -> B = C)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1525 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> (E = k6_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = G))))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1526 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E))) & k1_xboole_0 != C)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1527 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(F,G) & r2_hidden(G,B) & r2_hidden(E,F) & r2_hidden(D,E) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.23/4.30 1528 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = J))))))))) -> k1_xboole_0 = A | k11_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | k1_xboole_0 = C | k1_xboole_0 = B))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1529 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1530 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> r2_hidden(k1_mcart_1(A),B) & (k2_mcart_1(A) = C | k2_mcart_1(A) = D))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1531 (all A k1_mcart_1(k1_mcart_1(A)) = k17_mcart_1(A)) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1532 (all A all B all C all D -(r2_hidden(A,k3_zfmisc_1(B,C,D)) & (all E all F all G -(r2_hidden(F,C) & k3_mcart_1(E,F,G) = A & r2_hidden(G,D) & r2_hidden(E,B))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1533 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> E = A & H = D & G = C & F = B)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1534 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1535 (all A all B all C all D -(k1_xboole_0 != A & C != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> (F = k8_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> G = F))))))) & k1_xboole_0 != B)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1536 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (k2_mcart_1(A) = E | k2_mcart_1(A) = D) & (k1_mcart_1(A) = C | B = k1_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1537 (all A all B all C all D (k4_zfmisc_1(A,B,C,D) != k1_xboole_0 <-> B != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & A != k1_xboole_0)) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1538 (all A -((all B -((all C all D all E all F (r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1539 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k10_mcart_1(A,B,C,D,I),G)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1540 (all A all B all C k1_tarski(k3_mcart_1(A,B,C)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1541 (all A all B all C (v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1542 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(C) & k2_relat_1(B) = A -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1543 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1544 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1545 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1546 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1547 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1548 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1549 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_2(C,A,A) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1550 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1551 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1552 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1553 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1554 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1555 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(A != k1_xboole_0 & B != k1_xboole_0 & -((all D all E (v1_funct_1(E) & m2_relset_1(E,D,A) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> E = F))))) <-> v2_funct_1(C))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1556 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1557 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1558 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1559 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1560 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1561 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1562 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1563 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1564 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_1(B) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1565 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1566 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1567 (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1568 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1569 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1570 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (f3_s10_funct_2 != B -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1571 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1572 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1573 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> B = k1_xboole_0 | v2_funct_1(C) & k2_relat_1(D) = A))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1574 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1575 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)))) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1576 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1577 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1578 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1579 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1580 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1581 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1582 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1583 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)) & k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1584 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1585 (all A all B all C (m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1586 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1587 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1588 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (all E k1_tarski(E) != B) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1589 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1590 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1591 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1592 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_1(A))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1593 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1594 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1595 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1596 (all A -((all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_1(A))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1597 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1598 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1599 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1600 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1601 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1602 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1603 (all A all B all C ((all D ((exists E (E = D & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k1_funct_2(A,B))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1604 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1605 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1606 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1607 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> k1_xboole_0 != A & B = k1_xboole_0 | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1608 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1609 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1610 (all A all B all C (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1611 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | B = k1_xboole_0 & k1_xboole_0 != A | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1612 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1613 (all A all B (-v1_xboole_0(B) -> -v1_xboole_0(k1_funct_2(A,B)))) # label(fc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1614 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1615 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1616 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,B,C) & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1617 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1618 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1619 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> B = C))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1620 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1621 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1622 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1623 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1624 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1625 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1626 (all A all B all C (m1_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1627 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1628 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1629 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1630 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> A != k1_xboole_0 & k1_xboole_0 = B | v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1631 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1632 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1633 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1634 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1635 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1636 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1637 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1638 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1639 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1640 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1641 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1642 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1643 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) & B = k2_relat_1(C) -> k1_xboole_0 = B | D = k2_funct_1(C) | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1644 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1645 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1646 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1647 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> ((all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1648 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f4_s11_funct_2 != B & f3_s11_funct_2 != B))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2)) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1649 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 != A & B = k1_xboole_0 | D = C))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1650 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1651 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1652 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1653 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1654 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1655 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1656 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1657 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1658 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1659 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1660 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1661 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v2_funct_1(C) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1662 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D))))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1663 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1664 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1665 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -((all F -(k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1666 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k1_xboole_0 = B | k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C)))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1667 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1668 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))) & (B = k1_xboole_0 -> A = k1_xboole_0 | (v1_funct_2(C,A,B) <-> C = k1_xboole_0)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1669 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C)) & B = k2_relat_1(D) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1670 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1671 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1672 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1673 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> D = E)) <-> v2_funct_1(C))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1674 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1675 (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1676 (all A all B all C all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> B = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.30 1677 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1678 (all A all B all C all D (-v1_xboole_0(A) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1679 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) & k2_relat_1(D) = B -> k1_xboole_0 != B & C = k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1680 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1681 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1682 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1683 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1684 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1685 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1686 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A ((all B all C (r2_hidden(C,f2_s5_funct_2) & r2_hidden(B,f1_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_1(A))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1687 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1688 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1689 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1690 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1691 (all A all B all C all D all E all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(D,A) & r2_hidden(E,B) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1692 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1693 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1694 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (-(A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1695 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1696 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B != k1_xboole_0 -> (B = k2_relat_1(C) <-> (all D (k1_xboole_0 != D -> (all E (v1_funct_1(E) & m2_relset_1(E,B,D) & v1_funct_2(E,B,D) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1697 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1698 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,C,B) & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1699 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1700 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1701 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1702 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) & v2_funct_1(D) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | B = k1_xboole_0))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1703 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1704 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1705 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1706 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k5_funct_2(A,B,C) = C -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1707 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1708 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1709 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & k5_partfun1(A,B,D) = k5_partfun1(A,B,C) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1710 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -(D = k1_funct_1(C,E) & r2_hidden(E,A))))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1711 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1712 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1713 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1714 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1715 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1716 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1717 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v1_partfun1(C,A,B) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1718 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1719 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-v2_funct_1(C) & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & B != k1_xboole_0))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1720 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1721 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1722 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1723 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1724 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1725 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1726 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1727 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1728 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1729 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1730 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | B = k1_xboole_0 & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1731 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1732 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1733 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1734 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1735 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1736 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1737 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1738 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | k1_xboole_0 = B))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1739 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1740 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1741 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1742 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_1(k4_funct_2(A,B,C)) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_2(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1743 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1744 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1745 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1746 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1747 (all A all B r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B))) # label(t141_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1748 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1749 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1750 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (m1_subset_1(B,f2_s14_funct_2) & p1_s14_funct_2(A,B))))) -> (exists A (v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1751 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1752 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> B = k1_funct_1(D,C)))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1753 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & (all E all F ((E = k1_funct_1(C,F) & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1754 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1755 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1756 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1757 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = a_2_1_domain_1(A,B))))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1758 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(E,A) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1759 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,A) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(G,C) & -v1_xboole_0(D) -> k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1760 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists D (r2_hidden(D,C) & D = A & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_1_domain_1(B,C))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1761 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k14_domain_1(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1762 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1763 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <-> (exists F ((exists G ((exists H (m1_subset_1(H,D) & (exists I (m1_subset_1(I,E) & k4_mcart_1(F,G,H,I) = A)))) & m1_subset_1(G,C))) & m1_subset_1(F,B)))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1764 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> (r2_hidden(A,a_4_2_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(I,E) & p1_s4_domain_1(F,G,H,I) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D)))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1765 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_3_domain_1(A,B,C) = k6_subset_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1766 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & C = A)) <-> r2_hidden(A,a_1_0_domain_1(B))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1767 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1768 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1769 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k1_mcart_1(C) = k1_mcart_1(D) & k2_mcart_1(C) = k2_mcart_1(D) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1770 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(G,D) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(F,C) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1771 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1772 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> F = A))))))) <-> k5_mcart_1(B,C,D,E) = A))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1773 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,B) & -(r2_hidden(E,C) <-> r2_hidden(E,D)) & E = A)) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1774 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F ((exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (F = k4_mcart_1(G,H,I,J) & m1_subset_1(J,E))) & m1_subset_1(I,D))))) & m1_subset_1(G,B))) <-> r2_hidden(F,A))) <-> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1775 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & p2_s5_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1776 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_5_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1777 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1778 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,C,B) = k7_domain_1(A,B,C))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1779 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1780 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> k10_domain_1(A,B,C,D,E,F) = k3_enumset1(B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1781 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1782 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$T & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_domain_1(B))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1783 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F ((exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))) & m1_subset_1(F,B))) <-> r2_hidden(E,A))) -> k3_zfmisc_1(B,C,D) = A))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1784 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> A != k4_tarski(D,E)))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1785 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) = k3_domain_1(A,B,C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1786 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> J = A)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1787 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1788 (all A ((exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & B = A)) <-> r2_hidden(A,a_0_4_domain_1))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1789 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p1_s6_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_5_domain_1(B))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1790 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1791 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E ((-r2_hidden(E,D) <-> r2_hidden(E,C)) & E = A & m1_subset_1(E,B)))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1792 (all A (r2_hidden(A,a_0_3_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & p2_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1793 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1794 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(E) -> (r2_hidden(A,a_4_0_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(I,E) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1795 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (m1_subset_1(J,E) & k4_mcart_1(G,H,I,J) = F)) & m1_subset_1(I,D))))) & m1_subset_1(G,B))))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1796 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> k4_zfmisc_1(A,B,C,D) = a_4_0_domain_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1797 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1798 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1799 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1800 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_6_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1801 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D) & k4_domain_1(B,C,D,E,F,G) = A & p1_s3_domain_1(E,F,G))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1802 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> G = A))))))) <-> k6_mcart_1(B,C,D,E) = A))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1803 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1804 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k8_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> G = A)))))))))))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1805 (all A all B all C all D all E (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_1_domain_1(B,C,D,E)) <-> (exists F exists G (m1_subset_1(F,B) & m1_subset_1(G,C) & r2_hidden(G,E) & r2_hidden(F,D) & k1_domain_1(B,C,F,G) = A))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1806 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1807 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1808 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1809 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (E = A & (r2_hidden(E,C) & -r2_hidden(E,D) | r2_hidden(E,D) & -r2_hidden(E,C)) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_4_domain_1(B,C,D))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1810 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1811 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1812 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C & p1_s1_domain_1(C)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1813 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1814 (all A ((exists B exists C (m1_subset_1(C,f2_s9_domain_1) & p1_s9_domain_1(B,C) & A = f4_s9_domain_1(B,C) & m1_subset_1(B,f1_s9_domain_1))) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1815 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1816 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (m1_subset_1(B,f1_s8_domain_1) & p1_s8_domain_1(B) & f3_s8_domain_1(B) = A)))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1817 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(C) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(F,k1_zfmisc_1(B)) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists J exists K exists L exists M (m1_subset_1(K,C) & m1_subset_1(M,E) & A = k5_domain_1(B,C,D,E,J,K,L,M) & r2_hidden(J,F) & r2_hidden(M,I) & r2_hidden(L,H) & r2_hidden(K,G) & m1_subset_1(L,D) & m1_subset_1(J,B))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1818 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists D exists E (k1_domain_1(B,C,D,E) = A & p1_s2_domain_1(D,E) & m1_subset_1(E,C) & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_3_domain_1(B,C))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1819 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (A = E & -r2_hidden(E,D) & r2_hidden(E,C) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1820 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1821 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1822 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = a_2_2_domain_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1823 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1824 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1825 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_6_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C & p2_s6_domain_1(C)))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1826 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1827 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1828 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1829 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1830 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1831 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1832 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E (m1_subset_1(E,B) & (exists F ((exists G (m1_subset_1(G,D) & A = k3_mcart_1(E,F,G))) & m1_subset_1(F,C))))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1833 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & p1_s7_domain_1(B) & B = A)))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1834 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> a_3_0_domain_1(A,B,C) = k3_zfmisc_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1835 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,B) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_tarski(C,D) = k1_domain_1(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1836 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> H = A))))))))) <-> k9_mcart_1(B,C,D,E,F) = A))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1837 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) & -v1_xboole_0(C) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1838 (all A all B all C all D all E all F all G (m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G)) <-> (exists H exists I exists J (m1_subset_1(H,B) & m1_subset_1(I,C) & r2_hidden(H,E) & r2_hidden(I,F) & r2_hidden(J,G) & k4_domain_1(B,C,D,H,I,J) = A & m1_subset_1(J,D)))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1839 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_5_domain_1(B,C,D)) <-> (exists E (A = E & (-r2_hidden(E,C) <-> r2_hidden(E,D)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1840 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k7_domain_1(A,B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1841 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1842 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1843 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1844 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1845 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(B,A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1846 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> k12_domain_1(A,B,C,D,E,F,G,H) = k5_enumset1(B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1847 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1848 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1849 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1850 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1851 (all A (-v1_xboole_0(A) -> a_1_1_domain_1(A) = k1_subset_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1852 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1853 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> k2_enumset1(B,C,D,E) = k9_domain_1(A,B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1854 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1855 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1856 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & -v1_xboole_0(A) -> k11_domain_1(A,B,C,D,E,F,G) = k4_enumset1(B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1857 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1858 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> k12_mcart_1(A,B,C,D) = a_4_1_domain_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1859 (all A all B all C all D all E all F all G all H all I (m1_subset_1(E,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k6_enumset1(B,C,D,E,F,G,H,I) = k13_domain_1(A,B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1860 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_4_domain_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1861 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1862 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1863 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (A = k7_mcart_1(B,C,D,E) <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> H = A)))))))))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1864 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_6_domain_1(A) = a_1_5_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1865 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1866 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1867 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1868 (all A all B all C all D all E all F all G (m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1869 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (A = C & p1_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1870 (all A all B all C all D all E all F all G all H (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.31 1871 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1872 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_domain_1(B,C)) <-> (exists D exists E (k1_domain_1(B,C,D,E) = A & m1_subset_1(E,C) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1873 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E (r2_hidden(E,A) <-> (exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))))))))) <-> A = k3_zfmisc_1(B,C,D)))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1874 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k8_mcart_1(A,B,C,D,E) = k8_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,F) = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1875 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_2_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & -r2_hidden(D,C) & A = D))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1876 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) & k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1877 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k8_domain_1(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1878 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1879 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1880 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> k18_mcart_1(D) = k15_domain_1(A,B,C,D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1881 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1882 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) -> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1883 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1884 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1885 (all A (-v1_xboole_0(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,B,C) = a_3_2_domain_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1886 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (A = k10_mcart_1(B,C,D,E,F) <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A)))))))))))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1887 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_1_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & r2_hidden(E,C) & r2_hidden(E,D)))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1888 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & A = B)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1889 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1890 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E ((r2_hidden(E,C) | r2_hidden(E,D)) & E = A & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_2_domain_1(B,C,D))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1891 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1892 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1893 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> k7_funcop_1(A,B,C,E,F) = D))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1894 (all A (k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1895 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1896 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1897 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> k3_funcop_1(C,D,E) = k6_funcop_1(A,B,C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1898 (all A all B k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1899 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1900 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1901 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1902 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1903 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> ((all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> k3_funcop_1(C,A,B) = D))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1904 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1905 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1906 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1907 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1908 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> -((all D all E k4_tarski(D,E) != k1_funct_1(A,C)) & k1_funct_1(A,C) != k1_funct_1(B,C)) & (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))))) <-> k1_funcop_1(A) = B))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1909 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1910 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1911 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1912 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1913 (all A k13_funct_3(k6_partfun1(A),k6_partfun1(A)) = k12_funct_3(A)) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1914 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1915 (all A all B (v1_xboole_0(B) -> v2_funct_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1916 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1917 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1918 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C)))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1919 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1920 (all A all B all C (-r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0)) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1921 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1922 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1923 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1924 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) = k4_funcop_1(A,B,C)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1925 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1926 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1927 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1928 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1929 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1930 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1931 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1932 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1933 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1934 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1935 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1936 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1937 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1938 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1939 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1940 (all A all B (v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1941 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1942 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1943 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1944 (all A all B (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1945 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1946 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1947 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> B = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C | C = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1948 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1949 (all A all B all C (r2_hidden(B,A) -> k1_funct_1(k2_funcop_1(A,C),B) = C)) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1950 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(A) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1951 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1952 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1953 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,B) & m2_relset_1(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1954 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) = k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F)))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1955 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & m1_subset_1(D,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1956 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1957 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) & k1_relat_1(A) = k1_xboole_0 -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1959 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1960 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1961 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1962 (all A all B (-v1_xboole_0(B) -> v1_funct_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1963 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1964 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1965 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1966 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(C) & -v1_xboole_0(B) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1967 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1968 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1969 (all A (v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1970 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1971 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funcop_1(B,A,C,D,E) = k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1972 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.26/4.32 1973 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1974 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1975 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1976 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1977 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1978 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1979 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1980 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1981 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1982 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1983 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1984 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1985 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1986 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1987 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1988 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & v1_funct_1(k5_funcop_1(C,E,D)))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1989 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1990 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> v1_funct_1(k3_funcop_1(C,D,E)) & m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1991 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1992 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1993 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1994 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1995 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1996 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1997 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1998 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 1999 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.32 2000 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2001 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != k1_xboole_0 & r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2002 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2003 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2004 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2005 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2006 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2007 (all A all B all C k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2008 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2009 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> A = k1_xboole_0 | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2010 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2011 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2012 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f4_s8_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2013 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0))) <-> f2_s6_ordinal2(A) = B)))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,A) = f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_xboole_0) = f4_s6_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2014 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2015 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2016 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k9_ordinal2(C) = B & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2017 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r2_hidden(C,A)))) -> r1_ordinal1(k7_ordinal2(B),A))))) # label(t28_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2018 (exists A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2019 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2020 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2021 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2022 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s3_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2023 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2024 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2025 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2026 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.40 2027 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_ordinal2(A) <-> (exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2028 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(B),A))))) # label(t22_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2029 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2030 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2031 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2032 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2033 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2034 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2035 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k7_ordinal2(A),k7_ordinal2(B)))) # label(t30_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2036 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2037 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2038 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2039 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2040 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C))) <-> B = f3_s10_ordinal2(A))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2041 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f3_s16_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s16_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_ordinal1(A) = k1_relat_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> k1_funct_1(f1_s16_ordinal2,A) = f3_s16_ordinal2(A)))) & v4_ordinal1(f2_s16_ordinal2) -> f3_s16_ordinal2(f2_s16_ordinal2) = f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2042 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(k6_ordinal2(B),B))))) # label(t25_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2043 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k15_ordinal2(A,k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D))) <-> C = k16_ordinal2(A,B)))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2044 (exists A (v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s2_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2045 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2046 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k16_ordinal2(k4_ordinal2,A) = k4_ordinal2)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2047 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> r1_ordinal1(A,k6_ordinal2(B)) | k2_ordinal2(B) = k1_xboole_0)))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2048 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2049 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2050 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2051 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v4_ordinal1(B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2052 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2053 (all A (A = k5_ordinal2 <-> r2_hidden(k1_xboole_0,A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2054 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,C))))))))) # label(t58_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2055 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2056 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(A,k7_ordinal2(B)))))) # label(t27_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2057 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2058 (all A all B (v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2059 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2060 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k8_ordinal2(C) = B & v1_funct_1(C) & v1_relat_1(C))) <-> B = k11_ordinal2(A)))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2061 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2062 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2063 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2064 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t49_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2065 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2066 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2067 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> A = k1_xboole_0 | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2068 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2069 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2070 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2071 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2072 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,C))))))))) # label(t51_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2073 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2074 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2075 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2076 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2077 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2078 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f4_s15_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s15_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_funct_1(C)))))))) -> (all A (v3_ordinal1(A) -> f2_s15_ordinal2(A,f4_s15_ordinal2(A)) = f4_s15_ordinal2(k1_ordinal1(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.41 2079 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k1_setfam_1(A)))) # label(t17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2080 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & k14_ordinal2(B,C) = A)) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2081 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> k1_xboole_0 = B | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2082 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2083 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f2_s12_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f6_s12_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & B = k1_ordinal2(C)))))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> A = k1_xboole_0 | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2084 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2085 (all A (v3_ordinal1(A) -> A = k15_ordinal2(k4_ordinal2,A) & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2086 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_ordinal2(A),k3_ordinal2(B)))) # label(t14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2087 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2088 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t50_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2089 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & k1_ordinal1(B) = k1_relat_1(D))) <-> C = k14_ordinal2(A,B)))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2090 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B) <-> k7_ordinal2(A) = B))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.46/4.56 2091 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2092 (exists A (v2_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2093 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2094 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2095 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2096 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2097 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_ordinal2(A),k2_ordinal2(B)))) # label(t11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2098 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_relat_1(C))) & B != A & (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_ordinal2(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2099 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v5_ordinal1(B) & A = k1_ordinal2(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & v1_ordinal2(B) & v1_funct_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2100 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2101 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2102 (all A k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A))) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2103 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2104 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.54/4.57 2105 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s9_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2106 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k14_ordinal2(k1_funct_1(D,E),B) = k1_funct_1(D,k1_ordinal1(E))))) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2107 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2108 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2109 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2110 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2111 f1_s4_ordinal2 = k1_relat_1(f5_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2112 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2113 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2114 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2115 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(C) & v1_relat_1(C))) & A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & B = k1_ordinal2(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2116 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & k1_funct_1(B,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(B) & k1_ordinal2(B) = A & v5_ordinal1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2117 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_funct_1(A,B) = C & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2118 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (D = C & v4_ordinal1(D) & v3_ordinal1(D))))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2119 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2120 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F))))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (A = k1_xboole_0 -> ((exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_xboole_0))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2121 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2122 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(C,A),k15_ordinal2(C,B))))))))) # label(t59_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2123 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2124 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2125 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (k12_ordinal2(A) = B <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2126 (exists A (v1_relat_1(A) & v5_ordinal1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2127 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2128 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2129 (all A all B ((all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))) <-> B = k2_ordinal2(A))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2130 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2131 (all A all B all C (v1_finset_1(A) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2132 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2133 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2134 (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]. 4.57/4.61 2135 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2136 (all A -(v1_finset_1(A) & k1_xboole_0 != A & (all B -((all C (r2_hidden(C,A) -> r1_tarski(B,C))) & r2_hidden(B,A))) & v6_ordinal1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2137 (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]. 4.57/4.61 2138 (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]. 4.57/4.61 2139 (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]. 4.57/4.61 2140 (all A all B all C (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2141 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(k1_relat_1(A)) <-> v1_finset_1(A)))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2142 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2143 (all A -(v1_finset_1(A) & v6_ordinal1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2144 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2145 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2146 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2147 (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]. 4.57/4.61 2148 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2149 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))) <-> v1_finset_1(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2150 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2151 (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]. 4.57/4.61 2152 (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]. 4.57/4.61 2153 (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]. 4.57/4.61 2154 (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]. 4.57/4.61 2155 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2156 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2157 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2158 (all A exists B (v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2159 (all A all B (-v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2160 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2161 (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]. 4.57/4.61 2162 (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]. 4.57/4.61 2163 (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]. 4.57/4.61 2164 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2165 (all A all B (v1_funct_1(A) & v1_finset_1(B) & v1_relat_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2166 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2167 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2168 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2169 (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]. 4.57/4.61 2170 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2171 (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]. 4.57/4.61 2172 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2173 (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]. 4.57/4.61 2174 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_finset_1 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B)) & (-p1_s1_finset_1(B) -> k1_funct_1(A,B) = f3_s1_finset_1(B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2175 p1_s2_finset_1(k1_xboole_0) & (all A all B (p1_s2_finset_1(B) & r1_tarski(B,f1_s2_finset_1) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2176 (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]. 4.57/4.61 2177 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2178 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2179 (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]. 4.57/4.61 2180 (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 -(r2_hidden(C,B) & (all D (r1_tarski(C,D) & r2_hidden(D,B) -> D = C))))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2181 (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(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2182 (all A (v1_finset_1(k3_tarski(A)) <-> v1_finset_1(A) & (all B (r2_hidden(B,A) -> v1_finset_1(B))))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2183 (all A (v1_relat_1(A) & v1_funct_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]. 4.57/4.61 2184 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2185 (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]. 4.57/4.61 2186 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2187 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2188 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (A = B & np__0 = k1_funct_1(B,k13_arytm_3) & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2189 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2190 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2191 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2192 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2193 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2194 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2195 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2196 (exists A (v1_xboole_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2197 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2198 (all A (v1_xreal_0(A) -> (v3_xreal_0(A) <-> -r1_xreal_0(np__0,A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2199 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2200 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2201 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2202 (all A (v1_xreal_0(A) & v2_xreal_0(A) -> -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2203 (exists A (v1_xcmplx_0(A) & -v3_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2204 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2205 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2206 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2207 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2208 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2209 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2210 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2211 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2212 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2213 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2214 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2215 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & v1_xcmplx_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2216 (all A (v1_xreal_0(A) -> (v2_xreal_0(A) <-> -r1_xreal_0(A,np__0)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2217 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2218 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2219 (all A all B (v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2220 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2221 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2222 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2223 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(A) -> v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2224 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2225 (all A (v1_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2226 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) -> -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2227 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) & -v2_xreal_0(A) & -v1_xboole_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2228 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2229 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,A))) # label(reflexivity_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2230 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2231 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2232 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2233 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2234 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2235 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C ((exists D (k4_tarski(np__0,D) = B & r1_arytm_2(D,C) & A = k4_tarski(np__0,C) & m1_subset_1(D,k2_arytm_2))) & m1_subset_1(C,k2_arytm_2))))) & -(-(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) <-> r1_xreal_0(A,B))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & C = A & r1_arytm_2(C,D) & D = B)))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2236 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v3_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2237 (all A all B (-v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2238 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2239 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,B) | r1_xreal_0(B,A))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2240 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2241 (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]. 4.57/4.61 2242 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.61 2243 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_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]. 4.57/4.62 2244 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2245 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_int_1(A),np__0) & v1_int_1(A)) & -(r1_xreal_0(k4_int_1(A),np__0) & -v1_int_1(A)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2246 (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]. 4.57/4.62 2247 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2248 (all A (v1_xreal_0(A) -> k4_int_1(A) = k3_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2249 (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(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2250 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k2_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2251 (all A (v1_xreal_0(A) -> k3_int_1(A) = k6_xcmplx_0(A,k1_int_1(A)))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2252 (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]. 4.57/4.62 2253 (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]. 4.57/4.62 2254 (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]. 4.57/4.62 2255 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__1 & np__1 = A | k1_real_1(np__1) = A & B = k1_real_1(np__1) <-> np__1 = k3_xcmplx_0(A,B)))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2256 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2257 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2258 (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]. 4.57/4.62 2259 (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]. 4.57/4.62 2260 (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]. 4.57/4.62 2261 (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]. 4.57/4.62 2262 (all A (v1_int_1(A) -> k5_int_1(A,np__0) = np__0)) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2263 (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]. 4.57/4.62 2264 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]. 4.57/4.62 2265 (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]. 4.57/4.62 2266 (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]. 4.57/4.62 2267 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2268 (all A (v1_xreal_0(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)) & v1_int_1(A)))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2269 (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]. 4.57/4.62 2270 (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]. 4.57/4.62 2271 (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))))) & p1_s4_int_1(f1_s4_int_1) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2272 (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) -> C = B | r1_xreal_0(C,k6_xcmplx_0(A,np__1)) | r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2273 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2274 (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]. 4.57/4.62 2275 (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]. 4.57/4.62 2276 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2277 (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]. 4.57/4.62 2278 (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]. 4.57/4.62 2279 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> 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(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2280 (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]. 4.57/4.62 2281 (all A (v1_xreal_0(A) -> (k2_int_1(A) = k1_int_1(A) <-> k2_int_1(A) != k2_xcmplx_0(k1_int_1(A),np__1)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2282 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2283 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2284 (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]. 4.57/4.62 2285 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2286 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2287 (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]. 4.57/4.62 2288 (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]. 4.57/4.62 2289 (all A (v1_int_1(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2290 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)) & -(-r1_xreal_0(k2_int_1(A),A) & v1_int_1(A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2291 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k1_int_1(A),B) = k1_int_1(k2_xcmplx_0(A,B)))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2292 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A) & -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2293 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2294 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__1 = B & A = k1_real_1(np__1) | A = np__1 & k1_real_1(np__1) = B <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2295 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2296 (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) & k3_xcmplx_0(A,B) = C -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2297 (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]. 4.57/4.62 2298 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2299 (all A (v1_xreal_0(A) -> k1_int_1(A) = k2_int_1(k1_int_1(A)))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2300 (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]. 4.57/4.62 2301 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2302 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2303 (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) -> -(r1_xreal_0(np__1,C) & C = k6_xcmplx_0(B,A)))) & -r1_xreal_0(B,A)))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2304 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2305 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2306 (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]. 4.57/4.62 2307 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_int_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_int_1(A),B))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2308 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2309 (all A (v1_xreal_0(A) -> -r1_xreal_0(np__1,k4_int_1(A)) & r1_xreal_0(np__0,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2310 (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]. 4.57/4.62 2311 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2312 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2313 (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]. 4.57/4.62 2314 (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]. 4.57/4.62 2315 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2316 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2317 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2318 (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]. 4.57/4.62 2319 (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]. 4.57/4.62 2320 (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]. 4.57/4.62 2321 (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]. 4.57/4.62 2322 (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]. 4.57/4.62 2323 (all A (v1_xreal_0(A) -> k1_int_1(k4_int_1(A)) = np__0)) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2324 (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]. 4.57/4.62 2325 (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) & p1_s6_int_1(A))) -> (exists A (v1_int_1(A) & p1_s6_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2326 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)) & -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2327 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2328 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2329 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2330 (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]. 4.57/4.62 2331 (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]. 4.57/4.62 2332 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2333 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2334 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (v1_int_1(D) & k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2335 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__0 -> np__0 = k6_int_1(A,B)) & (B != np__0 -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2336 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2337 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2338 (all A (v1_int_1(A) -> (A != np__0 -> k5_int_1(A,A) = np__1))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2339 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2340 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> 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]. 4.57/4.62 2341 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (k2_xcmplx_0(B,A) = C -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2342 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2343 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(k2_xcmplx_0(A,np__1),B) & r1_xreal_0(A,B) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2344 (exists A (v1_int_1(A) & p1_s5_int_1(A))) & (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) -> (exists A (p1_s5_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))) & v1_int_1(A))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2345 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2346 (all A all B (v1_int_1(A) & v1_int_1(B) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2347 (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]. 4.57/4.62 2348 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2349 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> 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]. 4.57/4.62 2350 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2351 (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]. 4.57/4.62 2352 (all A (k4_numbers = A <-> (all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != C & k1_real_1(C) != B)) <-> r2_hidden(B,A))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2353 (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]. 4.57/4.62 2354 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k2_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2355 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2356 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2357 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2358 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v2_ordinal1(A) & -v3_xreal_0(A) & v1_int_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2359 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2360 (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]. 4.57/4.62 2361 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_int_1(A)) & r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers)))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2362 (all A all B (v1_funct_1(B) & v1_relat_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]. 4.57/4.62 2363 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2364 (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]. 4.57/4.62 2365 (all A all B all C (r1_tarski(A,B) & r2_wellord2(A,C) & r1_tarski(B,C) -> r2_wellord2(B,C) & r2_wellord2(A,B))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2366 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2367 (all A (v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2368 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2369 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2370 (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]. 4.57/4.62 2371 (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]. 4.57/4.62 2372 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2373 (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]. 4.57/4.62 2374 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2375 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,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]. 4.57/4.62 2376 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2377 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2378 (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]. 4.57/4.62 2379 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2380 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2381 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2382 (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]. 4.57/4.62 2383 (all A all B all C all D (r2_wellord2(A,B) & r2_hidden(C,A) & r2_hidden(D,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]. 4.57/4.62 2384 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2385 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2386 (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]. 4.57/4.62 2387 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2388 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B = A <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2389 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2390 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2391 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2392 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2393 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2394 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2395 (all A ((exists B (v3_ordinal1(B) & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))) & A = B)) <-> v1_card_1(A))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2396 (all A all B (v1_card_1(B) -> ((all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) & r2_hidden(k1_card_1(A),B) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2397 (all A all B ((exists C (v1_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2398 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2399 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2400 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2401 (all A all B (r2_wellord2(A,B) <-> k1_card_1(B) = k1_card_1(A))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2402 (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]. 4.57/4.62 2403 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2404 (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]. 4.57/4.62 2405 (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]. 4.57/4.62 2406 (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]. 4.57/4.62 2407 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) <-> -r1_xreal_0(B,A)))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2408 (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) <-> r1_ordinal1(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2409 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2410 (all A (v1_finset_1(A) -> k1_card_1(A) = k4_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2411 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D)))))) & (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) & v1_funct_1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2412 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2413 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2414 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2415 (exists A (v1_ordinal1(A) & v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2416 (all A all B (v1_card_1(B) -> (k1_card_1(A) = B <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2417 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2418 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2419 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2420 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> r1_tarski(A,B) & B != A))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2421 (all A (v1_card_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2422 (all A (v3_ordinal1(A) -> v1_card_1(k3_card_1(A)) & v3_ordinal1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2423 (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]. 4.57/4.62 2424 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2425 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2426 (all A (v3_ordinal1(A) -> k2_card_1(k3_card_1(A)) = k3_card_1(k1_ordinal1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2427 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2428 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2429 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2430 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2431 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(A) = k1_card_1(B) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2432 (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]. 4.57/4.62 2433 (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]. 4.57/4.62 2434 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2435 (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]. 4.57/4.62 2436 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2437 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> B = k4_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2438 (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]. 4.57/4.62 2439 (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]. 4.57/4.62 2440 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2441 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2442 (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (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) -> A = k1_xboole_0 | p1_s1_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]. 4.57/4.62 2443 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2444 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (v1_funct_1(C) & r1_tarski(A,k2_relat_1(C)) & k1_relat_1(C) = B & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2445 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2446 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2447 (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) -> k3_card_1(C) = k1_funct_1(B,C)))) & A = k1_relat_1(B) -> k1_card_1(k8_ordinal2(B)) = k3_card_1(A))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2448 (all A all B (k1_card_1(B) = k1_card_1(A) -> k2_card_1(A) = k2_card_1(B))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2449 (all A all B all C all D (r1_xboole_0(C,D) & r2_wellord2(B,D) & r2_wellord2(A,C) & r1_xboole_0(A,B) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2450 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2451 (all A (v1_card_1(A) -> (v2_card_1(A) <-> (all B (v1_card_1(B) -> A != k2_card_1(B)))))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.57/4.62 2452 (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]. 4.60/4.62 2453 (all A all B (r2_wellord2(A,B) -> k2_card_1(B) = k2_card_1(A))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2454 (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]. 4.60/4.62 2455 (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]. 4.60/4.62 2456 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2457 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(A) = A)) # label(t66_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2458 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2459 (all A all B ((exists C k1_tarski(C) = A) <-> k1_card_1(k1_tarski(B)) = k1_card_1(A))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2460 (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]. 4.60/4.62 2461 (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]. 4.60/4.62 2462 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2463 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2464 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2465 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(B) = k3_card_1(A) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2466 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(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)))) & k3_finseq_1(A) = f1_s2_finseq_1)) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2467 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2468 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2469 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2470 (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) -> (k3_finseq_1(B) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2471 (all A all B (m1_finseq_1(B,A) -> v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2472 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) = k2_finseq_1(A)))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2473 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2474 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & A = k2_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2475 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (np__2 = k3_finseq_1(C) & k1_funct_1(C,np__2) = B & k1_funct_1(C,np__1) = A <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2476 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> A = B))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2477 (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]. 4.60/4.62 2478 (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) -> (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]. 4.60/4.62 2479 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2480 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2481 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2482 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2483 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2484 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2485 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k3_finseq_1(A) = np__0 <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2486 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)))) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2487 (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) & v1_finseq_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = D & 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]. 4.60/4.62 2488 (all A all B (v1_funct_1(B) & v1_finseq_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]. 4.60/4.62 2489 (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) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & -r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(C = k1_nat_1(k3_finseq_1(A),D) & r2_hidden(D,k4_finseq_1(B)))))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2490 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(k1_card_1(A)) & k4_card_1(A) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2491 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2492 (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) -> (k2_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & v2_funct_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2493 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2494 (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]. 4.60/4.62 2495 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2496 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2497 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k3_finseq_1(A) = np__0 <-> A = k6_finseq_1(B))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2498 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k4_tarski(C,k1_funct_1(B,C)) & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2499 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2500 (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 (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> -(r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> C != k7_finseq_1(A,E))) & k7_finseq_1(A,B) = k7_finseq_1(C,D)))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2501 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2502 (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]. 4.60/4.62 2503 (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]. 4.60/4.62 2504 (all A (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2505 (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]. 4.60/4.62 2506 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2507 p1_s3_finseq_1(k1_xboole_0) & (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))))))) -> (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2508 (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]. 4.60/4.62 2509 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,B) & p1_s1_finseq_1(A,C) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B -p1_s1_finseq_1(A,B)) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))))) -> (exists A (v1_relat_1(A) & v1_funct_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))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2510 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> k1_funct_1(B,np__1) = A & k1_relat_1(B) = k2_finseq_1(np__1)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2511 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2512 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2513 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2514 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2515 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> A = k7_finseq_1(k1_xboole_0,A) & A = k7_finseq_1(A,k1_xboole_0))) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2516 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 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(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2518 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_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]. 4.60/4.62 2519 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2520 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2521 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(A,k2_finseq_1(B)) <-> r1_xreal_0(np__1,A) & r1_xreal_0(A,B)))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2522 (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_relat_1(C) & v1_funct_1(C) & v1_finseq_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]. 4.60/4.62 2523 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2524 (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]. 4.60/4.62 2525 (all A all B (m1_finseq_1(B,A) -> v1_xboole_0(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2526 (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) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(B)) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2527 (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 (k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1) & (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]. 4.60/4.62 2528 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2529 (all A (v4_ordinal2(A) -> A = np__0 | r2_hidden(A,k2_finseq_1(A)))) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2530 (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) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2531 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.62 2532 (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)) -> A = B))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2533 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (A = k3_finseq_1(C) & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2534 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2535 (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 (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (C = k7_finseq_1(A,B) <-> k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) = k4_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D))))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2536 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (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) & r1_xreal_0(F,E) & F = k1_funct_1(B,D) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,C)))))))))) <-> B = k14_finseq_1(A)))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2537 (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]. 4.60/4.63 2538 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2539 (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]. 4.60/4.63 2540 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2541 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2542 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2543 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2544 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,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)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2545 (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]. 4.60/4.63 2546 (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]. 4.60/4.63 2547 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2548 (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) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2549 (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) -> k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2550 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_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(B,C) & m2_finseq_1(A,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2551 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2552 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2553 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> k15_finseq_1(A) = k5_relat_1(k14_finseq_1(k1_relat_1(A)),A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2554 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (A = k1_funct_1(B,np__1) & np__1 = k3_finseq_1(B) <-> k9_finseq_1(A) = B))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2555 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (A = k1_xboole_0 <-> k1_xboole_0 = k14_finseq_1(A)))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2556 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2557 (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 (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(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2558 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2559 (all A all B (v1_funct_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2560 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2561 (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & C = B & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2562 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2563 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2564 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(C,k3_relat_1(A)) & (exists E (v1_relat_1(E) & C = k1_funct_1(E,np__1) & (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)))) & k1_funct_1(E,k3_finseq_1(E)) = D & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_finseq_1(E) & v1_funct_1(E))) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2565 (all A all B all C k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)) = k11_finseq_1(A,B,C)) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2566 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2567 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2568 (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_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2569 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2570 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k14_finseq_1(k1_relat_1(A))))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2571 (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]. 4.60/4.63 2572 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2573 (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]. 4.60/4.63 2574 (all A all B all C all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & A = k1_funct_1(D,np__1) & np__3 = k3_finseq_1(D) <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2575 (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]. 4.60/4.63 2576 (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]. 4.60/4.63 2577 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2578 (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]. 4.60/4.63 2579 (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]. 4.60/4.63 2580 (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]. 4.60/4.63 2581 (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) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2582 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2583 (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]. 4.60/4.63 2584 (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]. 4.60/4.63 2585 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2586 (all A (v4_ordinal2(A) -> k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(k2_xcmplx_0(A,np__1)))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2587 (all A all B (v4_ordinal2(B) -> ((exists C (r1_xreal_0(np__1,C) & r1_xreal_0(C,B) & A = C & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2588 (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]. 4.60/4.63 2589 (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) -> 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]. 4.60/4.63 2590 (all A (-v1_xboole_0(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_relat_1(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2591 (exists A (v1_finseq_1(A) & v1_finset_1(A) & v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2592 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2593 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k2_relat_1(B) & k4_finseq_1(B) = k2_finseq_1(np__1) <-> B = k9_finseq_1(A)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2594 (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 (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(C,B) = k7_finseq_1(A,B) | k7_finseq_1(B,C) = k7_finseq_1(B,A) -> A = C))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2595 (all A all B (v1_funct_1(A) & -v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2596 (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) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2597 (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]. 4.60/4.63 2598 (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]. 4.60/4.63 2599 (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]. 4.60/4.63 2600 (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 (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]. 4.60/4.63 2601 (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]. 4.60/4.63 2602 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = a_1_0_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2603 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2604 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -(k1_xboole_0 != 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)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2605 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2606 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2607 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2608 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2609 (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) -> 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]. 4.60/4.63 2610 (all A all B (B = k13_finseq_1(A) <-> (all C (m2_finseq_1(C,A) <-> r2_hidden(C,B))))) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2611 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2612 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2613 (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]. 4.60/4.63 2614 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k7_relat_1(B,k2_finseq_1(A)) -> k2_finseq_1(A) = k4_finseq_1(C) & k3_finseq_1(C) = A))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2615 (all A (v1_fraenkel(k13_finseq_1(A)) & -v1_xboole_0(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2616 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2617 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2618 (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(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]. 4.60/4.63 2619 (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_finseq_1(A,B) = k1_xboole_0 -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2620 (all A all B (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2621 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2622 (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 (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2623 (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]. 4.60/4.63 2624 (all A all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2625 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k1_tarski(A) = k2_relat_1(B) & np__1 = k3_finseq_1(B) <-> B = k9_finseq_1(A)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2626 (all A all B all C (v4_ordinal2(C) & m1_finseq_1(B,A) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2627 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) <-> r9_orders_1(k4_relat_1(A),B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2628 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2629 (all A (v1_relat_1(A) -> (all B all C (r1_orders_1(A,B) & r1_tarski(C,B) -> r1_orders_1(A,C))))) # label(t128_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2630 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) -> v4_relat_2(k2_wellord1(A,B)))))) # label(t184_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2631 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) -> r1_relat_2(k4_relat_1(A),B))))) # label(t189_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2632 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2633 (all A all B (v1_relat_1(B) -> (r7_relat_2(B,A) <-> r6_relat_2(B,A) & r1_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2634 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r7_orders_1(A,B) -> r9_orders_1(A,B))))) # label(t159_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2635 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2636 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r3_orders_1(A,B) & r2_orders_1(A,B) & r1_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2637 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2638 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v8_relat_2(A) & v4_relat_2(A) <-> v2_orders_1(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2639 (all A (v1_relat_1(A) -> (v1_orders_1(A) -> v1_orders_1(k4_relat_1(A))))) # label(t104_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2640 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) -> r1_orders_1(k4_relat_1(A),B))))) # label(t136_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2641 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2642 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2643 (all A (v1_relat_1(A) -> (v3_orders_1(A) <-> v1_relat_2(A) & v8_relat_2(A) & v6_relat_2(A) & v4_relat_2(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2644 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2645 (all A (-v1_xboole_0(A) -> -r2_hidden(k1_xboole_0,k1_orders_1(A)))) # label(t4_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2646 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2647 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) & v4_relat_2(A) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2648 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v1_orders_1(A) & v3_orders_1(A) & v2_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2649 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2650 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2651 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A) | B = C)) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2652 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2653 (all A (v1_relat_1(A) -> (v1_orders_1(A) -> r1_orders_1(A,k3_relat_1(A))))) # label(t127_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2654 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) <-> r7_orders_1(k4_relat_1(A),B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2655 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2656 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2657 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2658 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2659 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> r1_orders_1(A,B))))) # label(t126_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2660 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2661 (all A (v1_relat_1(A) -> (all B all C (r2_orders_1(A,B) & r1_tarski(C,B) -> r2_orders_1(A,C))))) # label(t131_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2662 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2663 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2664 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2665 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2666 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2667 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> r2_orders_1(k4_relat_1(A),B))))) # label(t137_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2668 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) -> r6_relat_2(k4_relat_1(A),B))))) # label(t192_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2669 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> r5_orders_1(k4_relat_1(A),B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2670 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) <-> r8_orders_1(k4_relat_1(A),B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2671 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2672 (all A all B all C (v1_relat_1(C) -> (r4_relat_2(C,A) & r1_tarski(B,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2673 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2674 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2675 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) <-> r1_relat_2(A,B) & r6_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2676 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2677 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) -> (m1_orders_1(B,A) <-> (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))))))))) # label(d1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2678 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2679 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r7_relat_2(C,A) -> r7_relat_2(C,B)))) # label(t96_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2680 (all A (v1_relat_1(A) -> (all B all C (r2_hidden(B,C) & r9_orders_1(A,B) & v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2681 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2682 (all A (v1_relat_1(A) -> (all B (v2_orders_1(A) -> v2_orders_1(k2_wellord1(A,B)))))) # label(t114_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2683 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t180_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2684 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2685 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2686 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2687 (all A (v1_relat_1(A) -> (all B (v3_orders_1(A) -> v3_orders_1(k2_wellord1(A,B)))))) # label(t115_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2688 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2689 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r6_orders_1(A,B) -> r8_orders_1(A,B))))) # label(t160_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2690 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2691 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2692 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2693 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v3_orders_1(k2_wellord1(A,B)))))) # label(t135_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2694 (all A -(k1_xboole_0 != A & (all B -((all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -((all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))) & r2_hidden(B,A))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2695 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2696 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> B = C | r2_hidden(k4_tarski(C,B),A))))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2697 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2698 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2699 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2700 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2701 (all A all B (v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2702 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2703 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> B = k1_xboole_0 | r2_hidden(k3_tarski(B),A))) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))))) & k1_xboole_0 != A)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2704 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -(v1_finset_1(B) & r1_tarski(B,k2_relat_1(A)) & (all C -(v1_finset_1(C) & B = k9_relat_1(A,C) & r1_tarski(C,k1_relat_1(A)))))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2705 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(C,k3_relat_1(A)) & r2_hidden(k4_tarski(B,C),A) & B != C)) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2706 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2707 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2708 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(C,k3_relat_1(A)) & B != C & r2_hidden(k4_tarski(C,B),A))) & r2_hidden(B,k3_relat_1(A)) <-> r7_orders_1(A,B))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2709 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> A = k5_relset_1(A,A,B) & A = k4_relset_1(A,A,B))) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2710 (all A (v1_relat_1(A) -> k2_wellord1(A,k1_xboole_0) = k1_xboole_0)) # label(t194_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2711 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2712 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2713 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v2_orders_1(k4_relat_1(A))))) # label(t105_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2714 (all A all B all C (v1_relat_1(C) -> (r8_relat_2(C,A) & r1_tarski(B,A) -> r8_relat_2(C,B)))) # label(t95_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2715 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2716 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2717 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.63 2718 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v2_orders_1(k2_wellord1(A,B)))))) # label(t132_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2719 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2720 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v2_orders_1(A) & v1_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2721 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2722 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2723 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2724 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2725 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> k3_relat_1(B) = A & A = k4_relset_1(A,A,B)))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2726 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v8_relat_2(A) <-> v1_orders_1(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2727 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v1_orders_1(B))) # label(t111_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2728 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2729 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (m1_subset_1(A,k1_zfmisc_1(B)) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2730 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2731 (all A k1_orders_1(A) = k4_xboole_0(k1_zfmisc_1(A),k1_tarski(k1_xboole_0))) # label(d2_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2732 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2733 (all A all B all C all D all E (v1_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_relat_2(E) & v4_relat_2(E) -> (r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(D,A) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2734 (all A -((all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(-p1_s2_orders_1(C,B) & -p1_s2_orders_1(B,C) & r2_hidden(C,A) & r2_hidden(B,A)))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (-p1_s2_orders_1(B,C) & r2_hidden(C,A) & m1_subset_1(C,f1_s2_orders_1))))) & r1_tarski(A,f1_s2_orders_1))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,C) -> p1_s2_orders_1(A,C)))))))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (p1_s2_orders_1(B,A) & p1_s2_orders_1(A,B) -> A = B))))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) -> (exists A ((all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & B != A))) & m1_subset_1(A,f1_s2_orders_1))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2735 (all A (v1_relat_1(A) -> (all B all C (v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r8_orders_1(A,B) & r2_hidden(B,C) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2736 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2737 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2738 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r6_relat_2(A,B) -> r6_relat_2(A,C))))) # label(t186_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2739 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2740 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.66 2741 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> m2_relset_1(B,A,k3_tarski(A)) & v1_funct_2(B,A,k3_tarski(A)) & v1_funct_1(B))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2742 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2743 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2744 (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,C) -> p1_s1_orders_1(A,C)))))))) & (all A -(r1_tarski(A,f1_s1_orders_1) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(B,A) & r2_hidden(C,A) & -p1_s1_orders_1(C,B) & -p1_s1_orders_1(B,C)))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (-p1_s1_orders_1(C,B) & r2_hidden(C,A) & m1_subset_1(C,f1_s1_orders_1))))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,A) -> B = A))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) -> (exists A (m1_subset_1(A,f1_s1_orders_1) & (all B (m1_subset_1(B,f1_s1_orders_1) -> -(p1_s1_orders_1(A,B) & A != B))))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2745 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2746 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r3_orders_1(k4_relat_1(A),B))))) # label(t138_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2747 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2748 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2749 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2750 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2751 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r3_orders_1(A,B) -> r3_orders_1(A,C))))) # label(t134_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2752 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B))))) # label(t125_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2753 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2754 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2755 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2756 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> (all C -(r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))))))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2757 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2758 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) -> v1_orders_1(k2_wellord1(A,B)))))) # label(t129_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2759 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2760 (all A (r1_orders_1(k6_partfun1(A),A) & r2_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2761 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & (all D -(r2_hidden(D,B) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))))))) <-> r5_orders_1(A,B))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2762 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2763 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2764 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2765 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2766 (all A (-((exists B (r2_hidden(B,A) & k1_xboole_0 != B)) & k1_xboole_0 = k3_tarski(A)) & -(k3_tarski(A) != k1_xboole_0 & (all B -(r2_hidden(B,A) & k1_xboole_0 != B))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2767 (all A (v1_relat_1(A) -> (v6_relat_2(A) -> v6_relat_2(k4_relat_1(A))))) # label(t188_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2768 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2769 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r2_wellord1(A,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2770 (all A (v1_relat_1(A) -> (all B k4_relat_1(k2_wellord1(A,B)) = k2_wellord1(k4_relat_1(A),B)))) # label(t193_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2771 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v4_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2772 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B) & r2_orders_1(A,B))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2773 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2774 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2775 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2776 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) -> v1_relat_2(k2_wellord1(A,B)))))) # label(t182_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2777 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2778 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2779 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) -> v6_relat_2(k2_wellord1(A,B)))))) # label(t185_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2780 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> r2_orders_1(A,k3_relat_1(A))))) # label(t130_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2781 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & (all C -r7_orders_1(A,C)) & r5_orders_1(A,B) & B = k3_relat_1(A))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2782 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2783 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r1_relat_2(C,A) -> r1_relat_2(C,B)))) # label(t93_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2784 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> r1_orders_1(B,A))) # label(t139_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2785 (all A -((all B -((all C -((all D (r2_hidden(D,B) -> r1_tarski(C,D))) & r2_hidden(C,A))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & C != B & r1_tarski(C,B))))) & k1_xboole_0 != A)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2786 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) <-> r6_orders_1(k4_relat_1(A),B))))) # label(t163_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2787 (all A (v1_relat_1(A) -> (all B -(r4_orders_1(A,B) & k1_xboole_0 = B)))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2788 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r1_tarski(A,B) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2789 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2790 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2791 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2792 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> r4_orders_1(k4_relat_1(A),B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2793 (all A all B all C (v4_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v1_relat_2(C) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t12_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2794 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2795 (all A (v1_relat_1(A) -> (all B (v1_orders_1(A) -> v1_orders_1(k2_wellord1(A,B)))))) # label(t113_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2796 (all A (v1_relat_1(A) -> (all B (r1_tarski(B,k3_relat_1(A)) & v1_relat_2(A) -> B = k3_relat_1(k2_wellord1(A,B)))))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2797 (all A -((all B -(r2_hidden(B,A) & (all C -(r1_tarski(C,B) & C != B & r2_hidden(C,A))))) & (all B (r1_tarski(B,A) & v6_ordinal1(B) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)) & A != k1_xboole_0)) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2798 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v3_orders_1(k4_relat_1(A))))) # label(t106_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2799 (all A all B (v4_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2800 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2801 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v4_relat_2(D) & v1_relat_2(D) -> (r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(B,A) -> B = C))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2802 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2803 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) -> v8_relat_2(k2_wellord1(A,B)))))) # label(t183_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2804 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2805 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2806 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2807 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2808 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2809 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2810 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2811 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2812 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2813 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2814 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2815 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2816 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2817 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> A = k3_relat_1(B))) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2818 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C (v1_relat_1(C) -> -(r1_tarski(A,C) & r3_orders_1(C,B) & k3_relat_1(C) = B))) & r2_orders_1(A,B))))) # label(t179_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2819 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2820 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B) <-> r2_orders_1(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2821 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2822 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2823 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2824 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2825 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2826 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2827 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.68 2828 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) <-> r8_relat_2(A,B) & r1_relat_2(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2829 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2830 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2831 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> r3_orders_1(A,k3_relat_1(A))))) # label(t133_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2832 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2833 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) & v4_relat_2(A) -> r7_orders_1(A,B))))) # label(t157_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2834 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) -> r8_relat_2(k4_relat_1(A),B))))) # label(t190_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2835 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2836 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2837 (all A (v1_relat_1(A) -> (all B -(B = k1_xboole_0 & r5_orders_1(A,B))))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2838 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) -> r4_relat_2(k4_relat_1(A),B))))) # label(t191_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2839 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2840 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2841 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2842 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k6_partfun1(A) = k4_eqrel_1(A,k6_partfun1(A),B))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2843 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> m2_relset_1(k3_eqrel_1(A,B,C),A,A))) # label(dt_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2844 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> ((exists C k6_eqrel_1(A,B,C) = A) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2845 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = A -> (B = k1_xboole_0 <-> m1_eqrel_1(B,A))) & (k1_xboole_0 != A -> (m1_eqrel_1(B,A) <-> k5_setfam_1(A,B) = A & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & -r1_xboole_0(C,D) & D != C)))))))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2846 (all A (v3_relat_2(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2847 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> -(B = k1_xboole_0 & (exists C r2_hidden(C,A))))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2848 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2849 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & -v1_xboole_0(A) -> v1_setfam_1(k7_eqrel_1(A,B)) & -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2850 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2851 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2852 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2853 (all A all B all C all D all E (v1_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v3_relat_2(E) -> (r2_hidden(B,k6_eqrel_1(A,E,C)) & r2_hidden(D,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2854 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2855 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2856 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_1(k1_eqrel_1(A)))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2857 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v3_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2858 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2859 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2860 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2861 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v3_relat_2(B) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2862 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,B,C) = k2_eqrel_1(A,C,B))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2863 (all A all B (m1_eqrel_1(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2864 (all A all B (m1_eqrel_1(B,A) -> (exists C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & B = k7_eqrel_1(A,C) & v8_relat_2(C) & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2865 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_eqrel_1(A,B,B) = B)) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2866 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2867 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) -> (k3_eqrel_1(A,B,C) = D -> (all E -(k6_eqrel_1(A,B,E) != k6_eqrel_1(A,D,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & r2_hidden(E,A)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2868 (all A all B (m2_relset_1(B,A,A) -> k2_eqrel_1(A,k1_eqrel_1(A),B) = B)) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2869 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2870 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2871 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2872 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2873 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) -> v3_relat_2(k4_eqrel_1(A,B,C)) & v8_relat_2(k4_eqrel_1(A,B,C)) & v1_partfun1(k4_eqrel_1(A,B,C),A,A) & m2_relset_1(k4_eqrel_1(A,B,C),A,A))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2874 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2875 (all A (v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v1_partfun1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2876 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2877 (all A all B (m2_relset_1(B,A,A) -> (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) <-> v1_relat_2(B) & A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2878 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2879 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v1_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) <-> r2_hidden(B,k6_eqrel_1(A,D,C))))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2880 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2881 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2882 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k8_eqrel_1(A,B) = k7_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2883 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B)))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2884 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> -(C != k1_eqrel_1(A) & k1_eqrel_1(A) != B & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2885 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2886 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2887 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2888 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,C,B) = k3_eqrel_1(A,B,C))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2889 (all A all B all C (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2890 (all A (r1_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2891 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2892 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A)))) -> ((all C (r2_hidden(C,B) -> v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A))) -> v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) | B = k1_xboole_0))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2893 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2894 (all A all B all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2895 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2896 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C -(r2_hidden(C,A) & (all D -r2_hidden(C,k6_eqrel_1(A,B,D))))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2897 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (k5_eqrel_1(A,B,C) = D <-> r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v3_relat_2(E) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E))))))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2898 (all A all B (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2899 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2900 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v3_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2901 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k4_eqrel_1(A,C,B) = k4_eqrel_1(A,B,C))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2902 (all A all B (r2_hidden(B,A) -> k1_tarski(B) = k6_eqrel_1(A,k6_partfun1(A),B))) # label(t33_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2903 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -(r2_hidden(A,k7_eqrel_1(B,C)) & (all D (m1_subset_1(D,B) -> k6_eqrel_1(B,C,D) != A))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2904 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D -(r2_hidden(C,A) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & r2_hidden(D,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2905 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_eqrel_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,A) & k6_eqrel_1(A,B,E) = D)))))))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2906 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)) = B)))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2907 (all A all B all C (v1_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2908 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2909 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B all C (p1_s1_eqrel_1(B,C) & p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(A,C))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) -> (exists A ((all B all C (r2_hidden(B,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) <-> r2_hidden(k4_tarski(B,C),A))) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A) & v3_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2910 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C k10_relset_1(A,A,B,k1_tarski(C)) = k6_eqrel_1(A,B,C)))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2911 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (A = k1_xboole_0 -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2912 (all A all B (r2_hidden(B,A) -> k6_eqrel_1(A,k1_eqrel_1(A),B) = A)) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2913 (all A all B (m2_relset_1(B,A,A) -> (exists C ((all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2914 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,B) = B)) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2915 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2916 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2917 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2918 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) & v8_relat_2(D) -> (all E (v8_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_relat_1(F) & v1_funct_1(F) & r1_xreal_0(np__1,k3_finseq_1(F)) & k1_funct_1(F,np__1) = A & k1_funct_1(F,k3_finseq_1(F)) = C & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))) & v1_finseq_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2919 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> m2_relset_1(k2_eqrel_1(A,B,C),A,A))) # label(dt_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2920 (all A all B all C all D all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2921 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k3_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k5_funct_5(A)))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2922 (all A all B all C (r1_xboole_0(A,B) -> r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2923 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2924 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_funct_5(C)) & r2_hidden(A,k1_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2925 (all A all B (r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))) & r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B))))) # label(t7_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2926 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(E = k1_funct_1(k3_funct_5(D),C) & k1_relat_1(E) = B & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,B) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F))))))) & r2_hidden(C,A) & k2_zfmisc_1(A,B) = k1_relat_1(D)))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2927 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_relat_1(k5_funct_5(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2928 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_funct_1(k3_funct_5(B),A) & r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B))))) = k1_relat_1(C) & r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(A,D),k1_relat_1(B)) & k1_funct_1(B,k4_tarski(A,D)) = k1_funct_1(C,D)))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2929 (all A all B (r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) & r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A))) # label(t12_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2930 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) & k3_funct_5(D) = k3_funct_5(C) & k1_relat_1(D) = k2_zfmisc_1(A,B) -> D = C))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2931 (all A all B all C (r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C))) & k1_card_1(k1_funct_2(A,k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)))) # label(t70_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2932 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_funct_5(A)) & v1_funct_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2933 (all A all B all C (B != A -> r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C)) & k1_card_1(k2_zfmisc_1(C,C)) = k1_card_1(k1_funct_2(k2_tarski(A,B),C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2934 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2935 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k3_funct_5(D) = k3_funct_5(C) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = D))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2936 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k4_funct_5(A) = B <-> (all C ((exists D exists E (v1_relat_1(E) & v1_funct_1(E) & (exists F (C = k4_tarski(D,F) & r2_hidden(F,k1_relat_1(E)) & k1_funct_1(A,D) = E & r2_hidden(D,k1_relat_1(A)))))) <-> r2_hidden(C,k1_relat_1(B)))) & (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(B)) & D = k1_funct_1(A,k1_mcart_1(C)) -> k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)))))))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2937 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2938 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A)))) -> k1_xboole_0 = k4_funct_5(A) & k1_xboole_0 = k6_funct_5(A)))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2939 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_5(A)) & v1_funct_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2940 (all A all B k1_tarski(k2_funcop_1(A,B)) = k1_funct_2(A,k1_tarski(B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2941 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k6_funct_5(A)) & v1_relat_1(k6_funct_5(A)))) # label(dt_k6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2942 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A) & k1_relat_1(k6_funct_5(C)) = k2_zfmisc_1(A,k1_relat_1(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2943 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_funct_5(A)) & v1_funct_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2944 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (D = k1_funct_1(k3_funct_5(C),A) & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B)) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2945 (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(k2_relat_1(C),k1_funct_2(A,B)) & k4_funct_5(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) -> A = k1_xboole_0 | C = D))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2946 (all A all B all C (k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) & r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2947 (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(k5_funct_5(C)) = B & k1_relat_1(k3_funct_5(C)) = A | k1_xboole_0 = k2_zfmisc_1(A,B)))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2948 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C))) & r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2949 (all A (v1_relat_1(A) -> k1_relat_1(A) = k1_funct_5(A) & k2_funct_5(A) = k2_relat_1(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2950 (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,k1_funct_5(k1_relat_1(A))) & (all D (v1_funct_1(D) & v1_relat_1(D) -> -(D = k1_funct_1(B,C) & k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(A,k4_tarski(C,E)) = k1_funct_1(D,E)))))))) & k1_relat_1(B) = k1_funct_5(k1_relat_1(A)) <-> k3_funct_5(A) = B))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2951 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_funct_1(k5_funct_5(B),A) = C & r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(D,A)) & r2_hidden(k4_tarski(D,A),k1_relat_1(B)))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & k1_relat_1(C) = k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A))))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2952 (all A all B all C all D (k1_card_1(C) = k1_card_1(D) & k1_card_1(B) = k1_card_1(A) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2953 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) -> r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C))) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) & k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) = k1_funct_1(D,B)))))) # label(t45_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2954 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funct_5(C) = k5_funct_5(D) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = D))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2955 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k2_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k1_funct_5(A))) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2956 (all A all B (k2_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) & k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) = k1_funct_5(k2_xboole_0(A,B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2957 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) -> C = D | r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2958 (all A k1_tarski(k1_xboole_0) = k1_funct_2(k1_xboole_0,A)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2959 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> A = k1_xboole_0 | k5_funct_5(k6_funct_5(C)) = C & k3_funct_5(k4_funct_5(C)) = C))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2960 (all A all B (r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2961 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_funct_1(k5_funct_5(C),B) = D & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(A,k1_relat_1(D)) & k1_funct_1(D,A) = k1_funct_1(C,k4_tarski(A,B))))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2962 (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s1_funct_5 & (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> k1_funct_1(A,B) = f2_s1_funct_5(B)))) & v1_funct_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2963 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> v1_relat_1(k1_funct_1(k3_funct_5(B),A)) & v1_funct_1(k1_funct_1(k3_funct_5(B),A))))) # label(t37_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2964 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & k1_relat_1(D) = k2_zfmisc_1(A,B) & r2_hidden(C,B) & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(A = k1_relat_1(E) & (all F (r2_hidden(F,A) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)))) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & k1_funct_1(k5_funct_5(D),C) = E)))))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2965 (all A (k1_xboole_0 = k2_funct_5(A) | k1_xboole_0 = k1_funct_5(A) -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2966 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) & D = k1_funct_1(C,A) -> r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C))) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2967 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(A,k1_relat_1(k3_funct_5(C))) & v1_relat_1(k1_funct_1(k3_funct_5(C),A)) & v1_funct_1(k1_funct_1(k3_funct_5(C),A))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2968 (all A all B (-(k1_xboole_0 = A & k2_zfmisc_1(B,A) = k1_xboole_0 & k2_zfmisc_1(A,B) = k1_xboole_0) -> B = k1_funct_5(k2_zfmisc_1(B,A)) & B = k2_funct_5(k2_zfmisc_1(A,B)))) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2969 (all A (k1_xboole_0 = k1_funct_5(A) <-> k1_xboole_0 = k2_funct_5(A))) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2970 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funct_5(C) = k5_funct_5(D) & k1_relat_1(D) = k2_zfmisc_1(A,B) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> D = C))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2971 (all A all B (k1_card_1(k1_funct_2(k1_tarski(B),A)) = k1_card_1(A) & r2_wellord2(A,k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2972 (all A all B all C (A != B -> r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)) & k1_card_1(k1_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2973 (all A all B (k1_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(A) & k1_tarski(B) = k2_funct_5(k1_tarski(k4_tarski(A,B))))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2974 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(C) = k6_funct_5(D) -> D = C | k1_xboole_0 = A))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2975 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k6_funct_5(k5_funct_5(C)) = C & k4_funct_5(k3_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2976 (all A all B (r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2977 (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(k3_funct_5(C)),A) & r1_tarski(k1_relat_1(k5_funct_5(C)),B)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2978 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k2_relat_1(k4_funct_5(C)),B) & r1_tarski(k2_relat_1(k6_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2979 (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)) -> k4_funct_5(k3_funct_5(C)) = C & k6_funct_5(k5_funct_5(C)) = C))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2980 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)))) # label(t63_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2981 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | C = k5_funct_5(k6_funct_5(C)) & C = k3_funct_5(k4_funct_5(C))))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2982 (all A (v1_relat_1(A) & v1_funct_1(A) -> k2_funct_4(k4_funct_5(A)) = k6_funct_5(A))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2983 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k1_funct_5(A),B) & r1_tarski(k2_funct_5(A),C))) # label(t13_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2984 (all A all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> k1_funct_5(A) = B)) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2985 (all A all B all C all D (r2_wellord2(A,B) & r2_wellord2(C,D) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)) & r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2986 (all A all B (k2_funct_5(A) = B <-> (all C ((exists D r2_hidden(k4_tarski(D,C),A)) <-> r2_hidden(C,B))))) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2987 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2988 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_funct_5(A) = k3_funct_5(k2_funct_4(A)))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2989 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2990 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C))) & r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2991 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_funct_5(A),k1_funct_5(B)) & r1_tarski(k2_funct_5(A),k2_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2992 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))) & r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A))))) # label(t43_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2993 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_relat_1(k1_funct_1(k5_funct_5(B),A)) & v1_funct_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2994 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2995 (all A all B all C all D (k2_tarski(B,D) = k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(A,C))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2996 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2997 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2998 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 2999 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))) & k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 3000 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(B,k1_relat_1(k5_funct_5(C))) & v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & v1_relat_1(k1_funct_1(k5_funct_5(C),B))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 3001 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 3002 (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(k2_relat_1(D),k4_partfun1(A,B)) & k4_funct_5(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | C = D | r2_hidden(k1_xboole_0,k2_relat_1(D))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 3003 (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]. 4.60/4.69 3004 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.69 3005 (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]. 4.60/4.69 3006 (all A (v4_ordinal2(A) -> v1_relat_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3007 (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)) -> k3_finseq_1(C) = A)))))) # label(t109_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3008 (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) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_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]. 4.60/4.70 3009 (all 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) -> (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]. 4.60/4.70 3010 (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]. 4.60/4.70 3011 (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]. 4.60/4.70 3012 (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]. 4.60/4.70 3013 (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) -> 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]. 4.60/4.70 3014 (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) & m1_subset_1(D,B) & A = k10_finseq_1(C,D)))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3015 (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(A,B)) = np__0))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3016 (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_finseq_1(C) & v1_funct_1(C) -> (k3_finseq_1(B) = k3_finseq_1(A) & r1_tarski(B,C) & r1_tarski(A,C) -> B = A))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3017 (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_finseq_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (all F (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]. 4.60/4.70 3018 (all A (v4_ordinal2(A) -> (all B k2_funcop_1(k2_finseq_1(A),B) = k2_finseq_2(A,B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3019 (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]. 4.60/4.70 3020 (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) -> (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]. 4.60/4.70 3021 (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) -> D = k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,np__1)))))))))) # label(t136_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3022 (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(D,B) & A = k11_finseq_1(C,D,E) & m1_subset_1(E,B) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3023 (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]. 4.60/4.70 3024 (all A (v4_ordinal2(A) -> (all B k2_finseq_1(A) = k4_finseq_1(k2_finseq_2(A,B))))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3025 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C) = k6_finseq_1(B))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3026 (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 (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (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]. 4.60/4.70 3027 (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 (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,A) -> (all J (m2_finseq_1(J,B) -> (J = k10_finseq_1(F,G) & I = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) = k3_funcop_1(H,I,J)))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3028 (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 (v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(E) -> (r1_xreal_0(B,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) | np__0 = B & A != np__0))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3029 (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]. 4.60/4.70 3030 (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 -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C))))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3031 (all A all B (v4_ordinal2(A) -> v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3032 (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]. 4.60/4.70 3033 (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) -> -(r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A))) & r2_hidden(A,k2_relat_1(B))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3034 (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_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_1(H) -> (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]. 4.60/4.70 3035 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3036 (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_relat_1(C) & v1_finseq_1(C) & v1_funct_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]. 4.60/4.70 3037 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3038 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C ((exists D (m1_subset_1(D,A) & (exists E (m1_subset_1(E,A) & B = k11_finseq_1(C,D,E))))) & m1_subset_1(C,A))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3039 (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]. 4.60/4.70 3040 (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) -> (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_relat_1(D) = k2_finseq_1(A) & C = k5_relat_1(D,B) & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C)))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3041 (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 (k8_finseq_1(B,D,k12_finseq_1(B,E)) = C & m1_subset_1(E,B))) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3042 (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]. 4.60/4.70 3043 (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_relat_1(E) & v1_funct_1(E) & v1_finseq_1(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) -> (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]. 4.60/4.70 3044 (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]. 4.60/4.70 3045 (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,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (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]. 4.60/4.70 3046 (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)) -> k8_finseq_1(B,D,C) = D & D = k8_finseq_1(B,C,D))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3047 (all A (v4_ordinal2(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)) & v1_funct_1(k1_finseq_2(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3048 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(B),A) & m2_relset_1(B,k4_finseq_1(B),A))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3049 (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 (m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_2(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]. 4.60/4.70 3050 (all A all B all C (v4_ordinal2(B) -> ((exists D (m2_finseq_2(D,C,k3_finseq_2(C)) & A = D & B = k3_finseq_1(D))) <-> r2_hidden(A,a_2_0_finseq_2(B,C))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3051 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3052 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C)) = k2_finseq_2(k1_nat_1(A,B),C)))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3053 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (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]. 4.60/4.70 3054 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,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]. 4.60/4.70 3055 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C ((exists D (B = k10_finseq_1(C,D) & m1_subset_1(D,A))) & m1_subset_1(C,A))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3056 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3057 (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]. 4.60/4.70 3058 (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]. 4.60/4.70 3059 (all A all B all C all D (m2_subset_1(C,k1_numbers,k5_numbers) & -v1_xboole_0(D) & 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)) & m2_finseq_2(F,D,k4_finseq_2(C,D)) & A = k8_finseq_1(D,E,F)))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3060 (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) -> -(k3_finseq_1(C) = k1_nat_1(A,B) & (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> -(C = k7_finseq_1(D,E) & B = k3_finseq_1(E) & A = k3_finseq_1(D))))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3061 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3062 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> C = k1_funct_1(k2_finseq_2(A,C),B))))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3063 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3064 (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]. 4.60/4.70 3065 (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 -> k4_funcop_1(H,I,G) = 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))))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3066 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3067 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(B) -> 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(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3068 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (B = k12_finseq_1(A,C) & m1_subset_1(C,A))))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3069 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,np__1))) = k1_finseq_2(k1_nat_1(A,np__1)))) # label(t60_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3070 (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]. 4.60/4.70 3071 (all A (v4_ordinal2(A) -> (all B a_2_0_finseq_2(A,B) = k4_finseq_2(A,B)))) # label(d4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3072 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3073 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (A != np__0 -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> B = k1_funct_1(k1_finseq_2(A),B)))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3074 (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) -> -(D = k8_finseq_1(C,E,F) & k3_finseq_1(F) = B & k3_finseq_1(E) = A))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3075 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_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) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D)) & C = k3_funcop_1(D,A,B) -> 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]. 4.60/4.70 3076 (all A all B (m1_finseq_2(B,A) <-> (all C (r2_hidden(C,B) -> m2_finseq_1(C,A))))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3077 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3078 (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_relat_1(k5_relat_1(C,B)) & v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3079 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & k12_finseq_1(B,C) = A)) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3080 (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) & 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,B) -> (k5_funcop_1(F,D,G) = E -> k3_finseq_1(G) = k3_finseq_1(E)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3081 (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]. 4.60/4.70 3082 (all A (v1_funct_1(A) & v1_finseq_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]. 4.60/4.70 3083 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3084 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k1_funct_2(k2_finseq_1(A),B) = k4_finseq_2(A,B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3085 (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) -> B = k5_relat_1(k1_finseq_2(A),B)))))) # label(t64_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3086 (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]. 4.60/4.70 3087 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3088 (all A (-v1_xboole_0(A) -> a_1_2_finseq_2(A) = k4_finseq_2(np__3,A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3089 (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(C,E) = k1_funct_1(D,E)))) -> D = C))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3090 (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_funct_1(C) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) -> (k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3091 (all A (m1_finseq_2(k3_finseq_2(A),A) & -v1_xboole_0(k3_finseq_2(A)))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3092 (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 (v1_funct_2(J,k2_zfmisc_1(A,B),C) & m2_relset_1(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) -> (K = k11_finseq_1(D,E,F) & L = k11_finseq_1(G,H,I) -> k3_funcop_1(J,K,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))))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3093 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3094 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k3_square_1(np__0,A) = np__0 & k4_square_1(A,np__0) = A & k4_square_1(np__0,A) = A & np__0 = k3_square_1(A,np__0))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3095 (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]. 4.60/4.70 3096 (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_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> 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]. 4.60/4.70 3097 (all A all B (v4_ordinal2(A) & -v1_xboole_0(B) -> -v1_xboole_0(k4_finseq_2(A,B)))) # label(fc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3098 (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]. 4.60/4.70 3099 (all A all B (v1_funct_1(B) & v1_finseq_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),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]. 4.60/4.70 3100 (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)))) & f1_s1_finseq_2 = k3_finseq_1(A))) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3101 (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)) & k1_nat_1(B,np__1) != A & r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3102 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_finseq_2(C,B) -> -v1_xboole_0(C) & m1_finseq_2(C,A))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3103 (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 (k8_finseq_1(C,E,F) = D & 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]. 4.60/4.70 3104 (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) -> (k7_relat_1(C,k2_finseq_1(A)) = B & r1_xreal_0(k3_finseq_1(C),A) -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3105 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (k2_finseq_1(A) = B -> (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]. 4.60/4.70 3106 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3107 (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]. 4.60/4.70 3108 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) = k2_finseq_2(k1_nat_1(A,np__1),B)))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3109 (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) -> A = B))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3110 (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 (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_relat_1(k3_funcop_1(C,A,B)) & v1_funct_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3111 (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]. 4.60/4.70 3112 (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]. 4.60/4.70 3113 (all A (-v1_xboole_0(A) -> a_1_0_finseq_2(A) = k4_finseq_2(np__1,A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3114 (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_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,B) -> (H = k10_finseq_1(E,F) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) = k5_funcop_1(G,D,H)))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3115 (all A exists B (-v1_xboole_0(B) & m1_finseq_2(B,A))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3116 (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) -> k6_finseq_1(C) = k4_funcop_1(E,k6_finseq_1(A),D))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3117 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (A = k3_finseq_1(B) & A = k3_finseq_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)))) -> C = B))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3118 (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]. 4.60/4.70 3119 (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)) -> (r1_xreal_0(A,k3_finseq_1(B)) & k5_relat_1(D,B) = C -> k3_finseq_1(C) = A))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3120 (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]. 4.60/4.70 3121 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers) & m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers))))) # label(t1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3122 (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]. 4.60/4.70 3123 (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]. 4.60/4.70 3124 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_2(C,k2_finseq_1(A),B) & v1_funct_1(C) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3125 (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]. 4.60/4.70 3126 (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)) -> k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)) = k5_relat_1(k10_finseq_1(B,C),A))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3127 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3128 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -((all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D k7_finseq_1(C,k9_finseq_1(D)) != B))) & k1_nat_1(A,np__1) = k3_finseq_1(B)))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3129 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(np__0 != k3_finseq_1(B) & (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))))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3130 (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_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) -> (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]. 4.60/4.70 3131 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3132 (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) -> (k12_finseq_1(B,E) = G -> k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3133 (all A all B all C k1_enumset1(A,B,C) = k2_relat_1(k11_finseq_1(A,B,C))) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3134 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (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) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C))))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3135 (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)) & v3_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]. 4.60/4.70 3136 (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_funct_1(D) & v1_finseq_1(D) -> (k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) -> A = B & D = C))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3137 (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)) -> k4_finseq_1(C) = k2_finseq_1(A))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3138 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> B = k6_finseq_1(A))) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3139 (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) -> k6_xcmplx_0(B,A) = k2_square_1(np__0,k6_xcmplx_0(B,A))))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3140 (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_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (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]. 4.60/4.70 3141 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3142 (all 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) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (C = k5_funcop_1(D,A,B) & 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]. 4.60/4.70 3143 (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) & m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(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]. 4.60/4.70 3144 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (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]. 4.60/4.70 3145 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3146 (all A k3_finseq_2(A) = k13_finseq_1(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3147 (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]. 4.60/4.70 3148 (all A (v4_ordinal2(A) -> k3_finseq_1(k1_finseq_2(A)) = A)) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3149 (all A all B (-v1_xboole_0(B) -> ((exists C (A = k4_finseq_2(C,B) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_3_finseq_2(B))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3150 (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]. 4.60/4.70 3151 (all A k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3152 (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]. 4.60/4.70 3153 (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]. 4.60/4.70 3154 (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 (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 & k4_finseq_1(A) = k2_relat_1(C) -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3155 (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_2(G,D,E) & m2_relset_1(G,D,E) & v1_funct_1(G) -> (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]. 4.60/4.70 3156 (all A all B all C (m2_finseq_1(C,A) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(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]. 4.60/4.70 3157 (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(F) = k3_finseq_1(G) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_finseq_1(G) & k3_finseq_1(D) = k3_finseq_1(F)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3158 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]. 4.60/4.70 3159 (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) & 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,A) -> (all H (m2_finseq_1(H,B) -> (k12_finseq_1(B,E) = H & k12_finseq_1(A,D) = G -> 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]. 4.60/4.70 3160 (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]. 4.60/4.70 3161 (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]. 4.60/4.70 3162 (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)) -> k5_relat_1(k1_finseq_2(A),C) = C)))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3163 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3164 (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 (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(D) -> (r1_xreal_0(B,k3_finseq_1(C)) -> v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)) | np__0 != A & B = np__0))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3165 (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]. 4.60/4.70 3166 (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]. 4.60/4.70 3167 (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]. 4.60/4.70 3168 (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_2(D,k5_numbers,B) & m2_relset_1(D,k5_numbers,B) & v1_funct_1(D) -> (C = k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3169 (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]. 4.60/4.70 3170 (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 (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(A),k1_relat_1(C)) & k5_relat_1(A,C) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3171 (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]. 4.60/4.70 3172 (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]. 4.60/4.70 3173 (all A all B all C all D (v1_funct_1(C) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -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]. 4.60/4.70 3174 (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]. 4.60/4.70 3175 (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]. 4.60/4.70 3176 (all A (v1_funct_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3177 (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]. 4.60/4.70 3178 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3179 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3180 (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]. 4.60/4.70 3181 (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]. 4.60/4.70 3182 (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,D) & r4_pboole(A,B,C)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3183 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)) & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A)))))) # label(t67_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3184 (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]. 4.60/4.70 3185 (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]. 4.60/4.70 3186 (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]. 4.60/4.70 3187 (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]. 4.60/4.70 3188 (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]. 4.60/4.70 3189 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> v1_funcop_1(D))))) # label(cc3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3190 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3191 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3192 (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]. 4.60/4.70 3193 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3194 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (C = B <-> r6_pboole(A,B,C)))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3195 (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]. 4.60/4.70 3196 (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]. 4.60/4.70 3197 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,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]. 4.60/4.70 3198 (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) & r2_pboole(A,B,D) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3199 (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]. 4.60/4.70 3200 (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]. 4.60/4.70 3201 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3202 (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]. 4.60/4.70 3203 (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,C,B),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3204 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.70 3205 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3206 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_xboole_0)) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3207 (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,C) & r2_pboole(A,B,D)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3208 (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) & r4_pboole(A,B,D) & r2_pboole(A,B,C) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3209 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,A) & v2_relat_1(B) & -v1_xboole_0(A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3210 (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]. 4.60/4.71 3211 (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]. 4.60/4.71 3212 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3213 (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]. 4.60/4.71 3214 (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]. 4.60/4.71 3215 (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]. 4.60/4.71 3216 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3217 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3218 (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]. 4.60/4.71 3219 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3220 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k2_pboole(A,B,B) = B)) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3221 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (A = k1_relat_1(B) <-> m1_pboole(B,A)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3222 (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]. 4.60/4.71 3223 (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]. 4.60/4.71 3224 (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]. 4.60/4.71 3225 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> ((all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)))) <-> C = k6_pboole(A,B)))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3226 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & r2_pboole(A,C,B) <-> r6_pboole(A,B,C)))))) # label(d13_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3227 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3228 (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,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3229 (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]. 4.60/4.71 3230 (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]. 4.60/4.71 3231 (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]. 4.60/4.71 3232 (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]. 4.60/4.71 3233 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3234 (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,k4_pboole(A,C,B),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3235 (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]. 4.60/4.71 3236 (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]. 4.60/4.71 3237 (all A -(k1_xboole_0 = f2_s1_pboole(A) & r2_hidden(A,f1_s1_pboole))) -> (exists A (m1_pboole(A,f1_s1_pboole) & (all B (r2_hidden(B,f1_s1_pboole) -> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)))))) # label(s1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3238 (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]. 4.60/4.71 3239 (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]. 4.60/4.71 3240 (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]. 4.60/4.71 3241 (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]. 4.60/4.71 3242 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3243 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> 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]. 4.60/4.71 3244 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B))))) # label(t71_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3245 (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]. 4.60/4.71 3246 (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]. 4.60/4.71 3247 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> -r2_hidden(k1_xboole_0,k2_relat_1(B)))) # label(t149_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3248 (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]. 4.60/4.71 3249 (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]. 4.60/4.71 3250 (exists A (m1_pboole(A,f1_s4_pboole) & (all B (r2_hidden(B,f1_s4_pboole) -> k1_funct_1(A,B) = f2_s4_pboole(B))))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3251 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k3_pboole(A,C,B) = k3_pboole(A,B,C))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3252 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3253 (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]. 4.60/4.71 3254 (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) & (all E (m1_pboole(E,A) -> (r2_pboole(A,E,C) & r2_pboole(A,E,D) -> r2_pboole(A,E,B)))) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3255 (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]. 4.60/4.71 3256 (all A all B (m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_2(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]. 4.60/4.71 3257 (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]. 4.60/4.71 3258 (all A (m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(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]. 4.60/4.71 3259 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k3_pboole(A,B,C),A))) # label(dt_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3260 (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]. 4.60/4.71 3261 (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) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3262 (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))) -> C = B))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3263 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r6_pboole(A,B,B))) # label(reflexivity_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3264 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(r4_pboole(A,B,B) & k1_pboole(A) = B))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3265 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3266 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,C,B) <-> m4_pboole(C,A,B)))))) # label(d23_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3267 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3268 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3269 (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]. 4.60/4.71 3270 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3271 (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]. 4.60/4.71 3272 (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]. 4.60/4.71 3273 (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]. 4.60/4.71 3274 (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]. 4.60/4.71 3275 (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]. 4.60/4.71 3276 (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]. 4.60/4.71 3277 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3278 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3279 (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]. 4.60/4.71 3280 (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]. 4.60/4.71 3281 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3282 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r2_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3283 (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]. 4.60/4.71 3284 (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]. 4.60/4.71 3285 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3286 (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]. 4.60/4.71 3287 (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]. 4.60/4.71 3288 (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]. 4.60/4.71 3289 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (m1_pboole(C,A) & r1_pboole(A,C,B))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3290 (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]. 4.60/4.71 3291 (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]. 4.60/4.71 3292 (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) & r2_pboole(A,B,D) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3293 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (m4_pboole(C,A,B) & v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3294 (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]. 4.60/4.71 3295 (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,k3_pboole(A,D,B),k3_pboole(A,D,C))))))))) # label(t114_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3296 (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) & r2_pboole(A,B,C) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3297 (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]. 4.60/4.71 3298 (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]. 4.60/4.71 3299 (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,C) & r1_pboole(A,E,B) <-> r1_pboole(A,E,D)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3300 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,C,B) = k2_pboole(A,B,C))) # label(commutativity_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3301 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3302 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> (r3_pboole(A,B,C) <-> r1_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3303 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3304 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3305 (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]. 4.60/4.71 3306 (all A all B (m1_pboole(B,A) -> ((all C -(v1_xboole_0(k1_funct_1(B,C)) & r2_hidden(C,A))) <-> v2_relat_1(B)))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3307 (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]. 4.60/4.71 3308 (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]. 4.60/4.71 3309 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k3_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3310 (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) -> r2_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t19_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3311 (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]. 4.60/4.71 3312 (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]. 4.60/4.71 3313 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3314 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) & r2_hidden(D,A)))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3315 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funcop_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)))) & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) <-> C = k13_pboole(A,B)))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3316 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3317 (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]. 4.60/4.71 3318 (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)) -> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A))))))))) # label(t52_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3319 (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]. 4.60/4.71 3320 (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]. 4.60/4.71 3321 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3322 (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]. 4.60/4.71 3323 (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]. 4.60/4.71 3324 (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)) <-> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,C,E) -> r2_pboole(A,B,E)))) & r2_pboole(A,D,B) & r2_pboole(A,C,B)))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3325 (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,D,C) & r6_pboole(A,E,B)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3326 (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]. 4.60/4.71 3327 (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]. 4.60/4.71 3328 (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]. 4.60/4.71 3329 (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]. 4.60/4.71 3330 (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]. 4.60/4.71 3331 (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]. 4.60/4.71 3332 (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]. 4.60/4.71 3333 (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]. 4.60/4.71 3334 (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]. 4.60/4.71 3335 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3336 (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]. 4.60/4.71 3337 (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]. 4.60/4.71 3338 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r5_pboole(A,C,D) & r2_pboole(A,B,D) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3339 (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]. 4.60/4.71 3340 (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,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3341 (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]. 4.60/4.71 3342 (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]. 4.60/4.71 3343 (all A k2_funcop_1(A,k1_xboole_0) = k1_pboole(A)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3344 (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]. 4.60/4.71 3345 (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]. 4.60/4.71 3346 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) = k1_funct_1(k5_pboole(A,B,C),D))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3347 (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]. 4.60/4.71 3348 (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) -> k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) <-> k14_pboole(A,B,C) = D))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3349 (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]. 4.60/4.71 3350 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & (all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B))))))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3351 (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,C,B),C) & r6_pboole(A,k2_pboole(A,B,C),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3352 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3353 (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]. 4.60/4.71 3354 (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]. 4.60/4.71 3355 (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) & r2_pboole(A,D,E) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3356 (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]. 4.60/4.71 3357 (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]. 4.60/4.71 3358 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v3_relat_1(B) & m1_pboole(B,A))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3359 (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]. 4.60/4.71 3360 (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]. 4.60/4.71 3361 (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]. 4.60/4.71 3362 (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]. 4.60/4.71 3363 (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]. 4.60/4.71 3364 (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]. 4.60/4.71 3365 (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_1(k1_funct_1(D,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)))) <-> m3_pboole(D,A,B,C)))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3366 (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]. 4.60/4.71 3367 (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]. 4.60/4.71 3368 (all A all B all C (m1_pboole(C,A) & v1_funcop_1(C) & m1_pboole(B,A) -> m1_pboole(k14_pboole(A,B,C),A))) # label(dt_k14_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3369 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r7_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t145_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3370 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k12_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3371 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k11_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3372 (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]. 4.60/4.71 3373 (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]. 4.60/4.71 3374 (all A -((all B -p1_s3_pboole(A,B)) & r2_hidden(A,f1_s3_pboole))) -> (exists A ((all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))) & m1_pboole(A,f1_s3_pboole))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3375 (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]. 4.60/4.71 3376 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (p1_s2_pboole(B,C) & r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3377 (exists A ((all B (m1_subset_1(B,f1_s5_pboole) -> k1_funct_1(A,B) = f2_s5_pboole(B))) & m1_pboole(A,f1_s5_pboole))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3378 (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]. 4.60/4.71 3379 (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)) & r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3380 (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]. 4.60/4.71 3381 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) <-> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3382 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & 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]. 4.60/4.71 3383 (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]. 4.60/4.71 3384 (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]. 4.60/4.71 3385 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r5_pboole(A,B,C)))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3386 (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]. 4.60/4.71 3387 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 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,C) & r2_pboole(A,C,D) & r5_pboole(A,B,D)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3389 (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]. 4.60/4.71 3390 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) -> k5_relat_1(C,D) = k7_pboole(A,B,C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3391 (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]. 4.60/4.71 3392 (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,D,B),k2_pboole(A,D,C)) & r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3393 (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) & r2_pboole(A,D,E) -> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D))))))))))) # label(t61_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3394 (all A all B (m1_pboole(B,A) -> -(r5_pboole(A,B,B) & B != k1_pboole(A)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3395 (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,C,B),B) & r6_pboole(A,k3_pboole(A,B,C),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3396 (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]. 4.60/4.71 3397 (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]. 4.60/4.71 3398 (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,D) & k3_pboole(A,C,D) = k1_pboole(A) & r3_pboole(A,B,C)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3399 (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]. 4.60/4.71 3400 (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]. 4.60/4.71 3401 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3402 (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]. 4.60/4.71 3403 (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) & r2_pboole(A,C,D) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3404 (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]. 4.60/4.71 3405 (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]. 4.60/4.71 3406 (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]. 4.60/4.71 3407 (all A (v1_finset_1(A) -> (-r1_xreal_0(np__2,k4_card_1(A)) <-> v1_realset1(A)))) # label(t13_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3408 (all A (-(v1_realset1(A) & (exists B exists C (B != C & r2_hidden(C,A) & r2_hidden(B,A)))) & -((all B all C -(r2_hidden(B,A) & r2_hidden(C,A) & C != B)) & -v1_realset1(A)))) # label(t14_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3409 (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) -> (exists C m1_realset1(C,A,B)))) # label(existence_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3410 (all A all B (m1_subset_1(B,A) -> (exists 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) & v1_funct_1(C))))) # label(t10_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3411 (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]. 4.60/4.71 3412 $T # label(dt_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3413 (all A (v1_realset1(A) <-> -(-v1_xboole_0(A) & (all B A != k1_tarski(B))))) # label(d4_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3414 (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)) -> (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]. 4.60/4.71 3415 (all A all B (v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)))) # label(fc1_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3416 (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]. 4.60/4.71 3417 (all A (-v1_realset1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (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_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))) & v1_funct_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C))) & m1_realset1(k4_xboole_0(A,k1_tarski(C)),A,B) <-> r2_realset1(A,B,C)))))))) # label(d5_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3418 (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]. 4.60/4.71 3419 (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]. 4.60/4.71 3420 (all A all B (m1_subset_1(B,A) -> (all C (m3_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_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3421 (all A all B all C (-v1_realset1(A) & m3_realset1(C,A,B) & m1_subset_1(B,A) -> 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))) & 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))) & v1_funct_1(k4_realset1(A,B,C)))) # label(dt_k4_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3422 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(C,B) & r2_hidden(D,B) & D != C))))) & -v1_realset1(B)) & -(v1_realset1(B) & (exists C ((exists D (m1_subset_1(D,A) & r2_hidden(C,B) & r2_hidden(D,B) & C != D)) & m1_subset_1(C,A)))))) # label(t15_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3423 (exists A (-v1_xboole_0(A) & v1_realset1(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3424 (all A all B (m1_subset_1(B,A) & -v1_realset1(A) -> k5_realset1(A,B) = k1_tarski(B))) # label(redefinition_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3425 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> v1_funct_1(k1_realset1(C,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_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))))))))) # label(t11_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3426 (all A all 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) -> (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]. 4.60/4.71 3427 (all A (-v1_realset1(A) -> (exists B m4_realset1(B,A)))) # label(existence_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3428 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3429 (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) -> (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]. 4.60/4.71 3430 (all A (v1_relat_1(A) -> (all B k1_realset1(A,B) = k7_relat_1(A,k2_zfmisc_1(B,B))))) # label(d3_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3431 (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) -> v1_funct_1(k1_realset1(B,C)) & 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))))) # label(t3_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3432 $T # label(dt_k1_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3433 (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]. 4.60/4.71 3434 (all A all B (v1_funct_1(A) & v1_relat_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]. 4.60/4.71 3435 (all A (-v1_realset1(A) -> (all B ((exists C (m1_subset_1(C,A) & k1_tarski(C) = B)) <-> m4_realset1(B,A))))) # label(d10_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3436 (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]. 4.60/4.71 3437 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m2_realset1(C,A,B) -> v1_funct_1(k3_realset1(A,B,C)) & m2_relset_1(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & v1_funct_2(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B))) # label(dt_k3_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3438 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_1(k1_realset1(C,B)) & m2_relset_1(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & v1_funct_2(k1_realset1(C,B),k2_zfmisc_1(B,B),B))))) # label(t9_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3439 (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)) -> (r1_realset1(A,B,C) <-> (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C)))))))) # label(d1_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3440 (exists A ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) & -v1_xboole_0(A))) # label(t5_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3441 (all A (-v1_xboole_0(A) -> ((all B -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))) <-> -v1_realset1(A)))) # label(t4_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3442 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_realset1(C,A,B) & m1_relset_1(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]. 4.60/4.71 3443 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C (v1_funct_1(C) & v1_funct_2(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))) & m2_relset_1(C,k2_zfmisc_1(A,A),A))))) # label(t8_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3444 (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]. 4.60/4.71 3445 (all A (-v1_realset1(A) -> (exists B (-v1_xboole_0(B) & m4_realset1(B,A))))) # label(rc3_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.71 3446 (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]. 4.60/4.71 3447 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (m3_realset1(C,A,B) <-> (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)))))))))) # label(d8_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3448 (all A (v1_realset1(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc3_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3449 (all A all B all C (m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_realset1(C,A,B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> k1_realset1(B,C) = k2_realset1(A,B,C))) # label(redefinition_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3450 (all A all B (m1_subset_1(B,k1_zfmisc_1(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) -> (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]. 4.60/4.72 3451 (exists A (-v1_xboole_0(A) & -v1_realset1(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3452 (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]. 4.60/4.72 3453 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C))))) # label(dt_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3454 (all A (v1_relat_1(A) -> v1_relat_1(k1_sysrel(A)))) # label(dt_k1_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3455 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),k2_xboole_0(B,k4_relat_1(B))) -> r1_tarski(k6_relat_1(A),k4_relat_1(B)) & r1_tarski(k6_relat_1(A),B)))) # label(t36_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3456 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B)) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k1_relat_1(B))) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)))) # label(t46_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3457 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(B,k4_xboole_0(B,k6_relat_1(A))) & r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k2_relat_1(B)))) = k1_xboole_0) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),B) & r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0))) # label(t42_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3458 (all A (v1_relat_1(A) -> (k5_relat_1(A,A) = A & k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) -> k2_relat_1(A) = k2_relat_1(k1_sysrel(A)) & k2_relat_1(A) = k1_relat_1(k1_sysrel(A))) & (k5_relat_1(A,A) = A & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 -> k1_relat_1(A) = k1_relat_1(k1_sysrel(A)) & k2_relat_1(k1_sysrel(A)) = k1_relat_1(A)))) # label(t50_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3459 (all A all B all C (r2_hidden(k4_tarski(A,B),k6_relat_1(C)) <-> r2_hidden(k4_tarski(B,A),k6_relat_1(C)))) # label(t31_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3460 $T # label(t9_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3461 (all A all B all C (v1_relat_1(C) -> r1_tarski(k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),B) & r1_tarski(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),A))) # label(t13_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3462 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) -> r1_tarski(k7_relat_1(C,A),k2_zfmisc_1(A,B))))) # label(t26_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3463 $T # label(t10_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3464 $T # label(t4_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3465 (all A (v1_relat_1(A) -> k1_relat_1(k1_sysrel(A)) = k2_relat_1(k1_sysrel(A)))) # label(t45_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3466 $T # label(t6_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3467 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))))) # label(t52_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3468 (all A k6_relat_1(A) = k5_relat_1(k6_relat_1(A),k6_relat_1(A))) # label(t29_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3469 $T # label(t11_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3470 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) & k1_xboole_0 = k5_relat_1(C,k4_xboole_0(C,k6_relat_1(k1_relat_1(C)))) & k5_relat_1(C,C) = C -> r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(B,k1_relat_1(k1_sysrel(C))) | B = A) & (C = k5_relat_1(C,C) & k5_relat_1(k4_xboole_0(C,k6_relat_1(k1_relat_1(C))),C) = k1_xboole_0 & r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(A,k1_relat_1(k1_sysrel(C))) | A = B))) # label(t49_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3471 (all A k1_tarski(k4_tarski(A,A)) = k6_relat_1(k1_tarski(A))) # label(t30_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3472 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 & A = k5_relat_1(B,A) -> k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),A) = k1_xboole_0) & (A = k5_relat_1(A,B) & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 -> k5_relat_1(A,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0))))) # label(t57_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3473 $T # label(t28_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3474 (all A (v1_relat_1(A) -> k1_sysrel(A) = k3_xboole_0(A,k6_relat_1(k1_relat_1(A))))) # label(d1_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3475 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k4_relat_1(C),k2_zfmisc_1(B,A))))) # label(t16_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3476 $T # label(t23_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3477 $T # label(t19_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3478 $T # label(t2_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3479 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k4_relat_1(A),k4_relat_1(B))))))) # label(t27_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3480 $T # label(t3_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3481 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B)))) # label(t15_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3482 (all A (v1_relat_1(A) -> (r1_tarski(A,k5_relat_1(A,A)) & k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) -> r1_tarski(k6_relat_1(k1_relat_1(A)),A)) & (k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) = k1_xboole_0 & r1_tarski(A,k5_relat_1(A,A)) -> r1_tarski(k6_relat_1(k2_relat_1(A)),A)))) # label(t40_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3483 (all A all B (r1_tarski(A,B) -> r1_tarski(k6_relat_1(A),k6_relat_1(B)))) # label(t33_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3484 (all A all B all C all D all E (v1_relat_1(E) -> (k2_xboole_0(C,D) = A & r1_tarski(E,k2_zfmisc_1(A,B)) -> E = k2_xboole_0(k7_relat_1(E,C),k7_relat_1(E,D))))) # label(t25_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3485 $T # label(t8_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3486 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(B,A) = A & B = k5_relat_1(A,B) & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 & k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 -> k1_sysrel(B) = k1_sysrel(A)) & (k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) = k1_xboole_0 & k5_relat_1(B,A) = B & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 & k5_relat_1(A,B) = A -> k1_sysrel(B) = k1_sysrel(A)))))) # label(t59_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3487 $T # label(t7_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3488 $T # label(t17_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3489 (all A all B k2_zfmisc_1(B,A) = k4_relat_1(k2_zfmisc_1(A,B))) # label(t18_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3490 (all A all B all C (v1_relat_1(C) -> (r1_xboole_0(A,B) -> r1_xboole_0(k1_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B)))) & r1_xboole_0(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))))))) # label(t14_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3491 (all A all B all C (v1_relat_1(C) -> (C = k5_relat_1(C,C) & k1_xboole_0 = k5_relat_1(k4_xboole_0(C,k1_sysrel(C)),C) & r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(k1_sysrel(C))) & r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) | A = B) & (k5_relat_1(C,C) = C & r2_hidden(k4_tarski(A,B),C) & k5_relat_1(C,k4_xboole_0(C,k1_sysrel(C))) = k1_xboole_0 -> r2_hidden(B,k1_relat_1(k1_sysrel(C))) & r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) | B = A))) # label(t48_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3492 (all A all B (k6_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k6_relat_1(A),k6_relat_1(B)) & k6_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k6_relat_1(A),k6_relat_1(B)) & k6_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k6_relat_1(A),k6_relat_1(B)))) # label(t32_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3493 (all A all B k4_xboole_0(k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(A)) = k1_xboole_0) # label(t34_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3494 $T # label(t21_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3495 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_sysrel(C)) -> A = B & r2_hidden(A,k1_relat_1(k1_sysrel(C)))))) # label(t44_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3496 (all A all B (v1_relat_1(B) -> (k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) = k1_xboole_0 -> k2_relat_1(k4_xboole_0(B,k6_relat_1(A))) = k4_xboole_0(k2_relat_1(B),k2_relat_1(k6_relat_1(A)))) & (k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) = k1_xboole_0 -> k1_relat_1(k4_xboole_0(B,k6_relat_1(A))) = k4_xboole_0(k1_relat_1(B),k1_relat_1(k6_relat_1(A)))))) # label(t39_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3497 $T # label(t5_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3498 (all A all B all C all D all E (v1_relat_1(E) -> (r1_xboole_0(A,B) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(C,A) & r2_hidden(k4_tarski(C,D),E) -> r2_hidden(D,B) & -r2_hidden(D,A) & -r2_hidden(C,B)) & (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),E) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) -> -r2_hidden(D,A) & r2_hidden(C,A) & -r2_hidden(C,B)) & (r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(D,A) & r1_xboole_0(A,B) -> -r2_hidden(C,A) & r2_hidden(C,B) & -r2_hidden(D,B)) & (r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(C,B) & r1_xboole_0(A,B) -> -r2_hidden(D,B) & r2_hidden(D,A) & -r2_hidden(C,A)))) # label(t22_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3499 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),B) -> r1_tarski(k6_relat_1(A),k4_relat_1(B))))) # label(t37_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3500 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(fc1_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3501 (all A (v1_relat_1(A) -> r1_tarski(k1_sysrel(A),k6_relat_1(k1_relat_1(A))) & r1_tarski(k1_sysrel(A),A))) # label(t43_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3502 (all A (v1_relat_1(A) -> (k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 -> k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A)))),k6_relat_1(k1_relat_1(k1_sysrel(A)))) = k1_xboole_0) & (k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) -> k1_xboole_0 = k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A)))))))) # label(t56_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3503 (all A (v1_relat_1(A) -> (k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 & r1_tarski(A,k5_relat_1(A,A)) -> k3_xboole_0(A,k6_relat_1(k1_relat_1(A))) = k6_relat_1(k1_relat_1(A))) & (k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) & r1_tarski(A,k5_relat_1(A,A)) -> k3_xboole_0(A,k6_relat_1(k2_relat_1(A))) = k6_relat_1(k2_relat_1(A))))) # label(t41_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3504 (all A (v1_relat_1(A) -> (r1_tarski(A,k6_relat_1(k1_relat_1(A))) -> k6_relat_1(k1_relat_1(A)) = A))) # label(t35_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3505 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A))))) -> k7_relat_1(A,k1_relat_1(k1_sysrel(A))) = k6_relat_1(k1_relat_1(k1_sysrel(A))) & k7_relat_1(A,k2_relat_1(k1_sysrel(A))) = k6_relat_1(k1_relat_1(k1_sysrel(A)))) & (k5_relat_1(k4_xboole_0(A,k6_relat_1(k2_relat_1(k1_sysrel(A)))),k6_relat_1(k2_relat_1(k1_sysrel(A)))) = k1_xboole_0 -> k6_relat_1(k2_relat_1(k1_sysrel(A))) = k8_relat_1(k2_relat_1(k1_sysrel(A)),A) & k8_relat_1(k1_relat_1(k1_sysrel(A)),A) = k6_relat_1(k1_relat_1(k1_sysrel(A)))))) # label(t55_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3506 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (A = k5_relat_1(A,B) & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 -> r1_tarski(k1_sysrel(A),k1_sysrel(B))) & (k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 & A = k5_relat_1(B,A) -> r1_tarski(k1_sysrel(A),k1_sysrel(B))))))) # label(t58_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3507 (all A all B (v1_relat_1(B) -> (r1_tarski(B,k2_zfmisc_1(A,A)) -> k4_xboole_0(B,k6_relat_1(k1_relat_1(B))) = k4_xboole_0(B,k6_relat_1(A)) & k4_xboole_0(B,k6_relat_1(A)) = k4_xboole_0(B,k6_relat_1(k2_relat_1(B)))))) # label(t38_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3508 (all A all B all C all D (v1_relat_1(D) -> (r1_tarski(C,B) & r1_tarski(D,k2_zfmisc_1(A,B)) -> k8_relat_1(C,D) = k3_xboole_0(D,k2_zfmisc_1(A,C))) & (r1_tarski(D,k2_zfmisc_1(A,B)) & r1_tarski(C,A) -> k7_relat_1(D,C) = k3_xboole_0(D,k2_zfmisc_1(C,B))))) # label(t24_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3509 (all A (v1_relat_1(A) -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k1_sysrel(A))) # label(t47_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3510 (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,C),k5_relat_1(B,C)) = k5_relat_1(k2_xboole_0(A,B),C) & k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t20_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3511 $T # label(t1_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3512 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) & r1_tarski(k6_relat_1(A),B) -> k7_relat_1(B,A) = k6_relat_1(A)) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) & r1_tarski(k6_relat_1(A),B) -> k6_relat_1(A) = k8_relat_1(A,B)))) # label(t54_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3513 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(k1_sysrel(A)),k1_relat_1(A)) & r1_tarski(k1_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k1_relat_1(k1_sysrel(A)),k1_relat_1(A)))) # label(t51_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3514 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),A) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),A))) # label(t53_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3515 (all A all B -(B != k1_xboole_0 & -(B = k2_relat_1(k2_zfmisc_1(A,B)) & k1_relat_1(k2_zfmisc_1(A,B)) = A) & k1_xboole_0 != A)) # label(t12_sysrel) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3516 (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]. 4.60/4.72 3517 (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]. 4.60/4.72 3518 (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]. 4.60/4.72 3519 (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]. 4.60/4.72 3520 (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]. 4.60/4.72 3521 (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]. 4.60/4.72 3522 (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]. 4.60/4.72 3523 (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) -> k8_setfam_1(A,B) = k5_subset_1(A,C,D)))))))) # label(t10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3524 (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]. 4.60/4.72 3525 (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]. 4.60/4.72 3526 (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]. 4.60/4.72 3527 (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]. 4.60/4.72 3528 (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]. 4.60/4.72 3529 (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)) -> (B = k1_tarski(C) -> k8_setfam_1(A,B) = C))))) # label(t9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3530 (all A all B (m1_pboole(B,A) -> v2_mssubfam(k7_mssubfam(A,B),A,B) & v5_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)) & v4_mssubfam(k7_mssubfam(A,B),A,B) & v3_mssubfam(k7_mssubfam(A,B),A,B) & v1_mssubfam(k7_mssubfam(A,B),A,B))) # label(dt_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3531 (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]. 4.60/4.72 3532 (all A all B all C (m4_pboole(C,A,k1_mboolean(A,B)) & m1_pboole(B,A) -> m4_pboole(k6_mssubfam(A,B,C),A,B))) # label(dt_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3533 (all A all B all C (v1_pre_circ(B,A) & m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,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]. 4.60/4.72 3534 (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_pre_circ(k12_pboole(A,B,C),A) & v1_funct_1(k12_pboole(A,B,C)) & v1_relat_1(k12_pboole(A,B,C)))) # label(fc9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3535 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) -> v1_relat_1(k4_pboole(A,C,B)) & v1_pre_circ(k4_pboole(A,C,B),A) & v1_funct_1(k4_pboole(A,C,B)))) # label(fc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3536 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r2_pboole(A,C,k2_mssubfam(A,B)) & (all D (m1_pboole(D,A) -> -(r2_pboole(A,D,k1_mssubfam(A,B)) & v1_pre_circ(D,A) & r6_pboole(A,k14_pboole(A,D,B),C)))) & v1_pre_circ(C,A)))))) # label(t30_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3537 (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]. 4.60/4.72 3538 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_funct_1(C,A) = D & r2_hidden(A,B) -> k1_funct_1(k1_mssubfam(B,C),A) = k1_relat_1(D)))))) # label(t14_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3539 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) & v2_relat_1(C) -> r2_pboole(A,k6_mssubfam(A,B,C),k2_mboolean(A,C)))))) # label(t42_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3540 (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]. 4.60/4.72 3541 (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]. 4.60/4.72 3542 (all A all B all C (v1_funcop_1(B) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_funct_1(k14_pboole(A,C,B)) & v1_pre_circ(k14_pboole(A,C,B),A) & v1_relat_1(k14_pboole(A,C,B)))) # label(fc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3543 $T # label(d1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3544 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v1_pre_circ(k11_pboole(A,C,B),A) & v2_relat_1(B) -> v1_pre_circ(C,A)))))) # label(t19_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.60/4.72 3545 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (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]. 4.60/4.72 3546 (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]. 4.70/4.72 3547 (all A (v3_relat_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A) & v1_funct_1(k1_pboole(A)) & v1_relat_1(k1_pboole(A)))) # label(fc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3548 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v1_mssubfam(C,A,B) & v2_mssubfam(C,A,B) & v4_mssubfam(C,A,B) & v6_mssubfam(C,A,B) & v5_mssubfam(C,A,B) & v3_mssubfam(C,A,B) & v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C))))) # label(rc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3549 (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]. 4.70/4.72 3550 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) -> v1_relat_1(k3_pboole(A,C,B)) & v1_pre_circ(k3_pboole(A,C,B),A) & v1_funct_1(k3_pboole(A,C,B)))) # label(fc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3551 (all A all B (m1_pboole(B,A) -> k3_mssubfam(A,B) = k1_mboolean(A,B))) # label(redefinition_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3552 (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]. 4.70/4.72 3553 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> k6_mssubfam(A,B,C) = k5_mssubfam(A,B,C))) # label(redefinition_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3554 (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 (m3_pboole(A,f1_s1_mssubfam,f2_s1_mssubfam,f3_s1_mssubfam) & (all B -((all C (m2_relset_1(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & v1_funct_2(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & v1_funct_1(C) -> -(C = k1_funct_1(A,B) & (all D (r2_hidden(D,k1_funct_1(f2_s1_mssubfam,B)) -> p1_s1_mssubfam(k1_funct_1(C,D),D,B)))))) & r2_hidden(B,f1_s1_mssubfam))))) # label(s1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3555 (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]. 4.70/4.72 3556 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & v1_pre_circ(k11_pboole(A,B,C),A) -> v1_pre_circ(C,A)))))) # label(t20_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3557 (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]. 4.70/4.72 3558 (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]. 4.70/4.72 3559 (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))) -> (B = k4_subset_1(k1_zfmisc_1(A),C,D) -> 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]. 4.70/4.72 3560 (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]. 4.70/4.72 3561 (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]. 4.70/4.72 3562 (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]. 4.70/4.72 3563 (all A all B all C (v1_pre_circ(B,A) & m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,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]. 4.70/4.72 3564 (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]. 4.70/4.72 3565 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> v1_relat_1(k1_mboolean(A,B)) & v2_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)) & v1_pre_circ(k1_mboolean(A,B),A))) # label(fc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3566 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3567 (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]. 4.70/4.72 3568 (all A all B (v2_relat_1(B) & v1_pre_circ(B,A) & m1_pboole(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,C,D))))))) & (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(t28_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3569 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> v1_pre_circ(C,A))))) # label(cc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3570 (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]. 4.70/4.72 3571 (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]. 4.70/4.72 3572 (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]. 4.70/4.72 3573 (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]. 4.70/4.72 3574 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v6_mssubfam(C,A,B) <-> r1_pboole(A,k1_pboole(A),C)))))) # label(d8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3575 (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]. 4.70/4.72 3576 (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]. 4.70/4.72 3577 (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) & v1_pre_circ(C,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))))))))) # label(t27_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3578 (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]. 4.70/4.72 3579 (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]. 4.70/4.72 3580 (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]. 4.70/4.72 3581 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_funct_1(C,A) = D & r2_hidden(A,B) -> k1_funct_1(k2_mssubfam(B,C),A) = k2_relat_1(D)))))) # label(t13_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3582 (all A all B all C (v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_pre_circ(k3_pboole(A,B,C),A) & v1_funct_1(k3_pboole(A,B,C)) & v1_relat_1(k3_pboole(A,B,C)))) # label(fc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3583 (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]. 4.70/4.72 3584 (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]. 4.70/4.72 3585 (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]. 4.70/4.72 3586 (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) -> (all F (m1_pboole(F,A) -> -(v1_pre_circ(F,A) & r2_pboole(A,F,D) & r2_pboole(A,B,k11_pboole(A,E,F)) & r2_pboole(A,E,C) & v1_pre_circ(E,A)))))) & r2_pboole(A,B,k11_pboole(A,C,D)) & v1_pre_circ(B,A)))))))) # label(t26_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3587 (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]. 4.70/4.72 3588 (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]. 4.70/4.72 3589 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(k1_xboole_0,B) -> k8_setfam_1(A,B) = k1_xboole_0))) # label(t3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3590 (all A all B all C all D (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k1_funct_1(C,D) = k4_mssubfam(A,B,C,D))) # label(redefinition_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3591 (all A all B (m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v1_pre_circ(C,A) & v1_funct_1(C) & v3_relat_1(C) & m4_pboole(C,A,B))))) # label(rc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3592 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v2_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(rc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3593 (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)) | k1_xboole_0 = C))) # label(t5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3594 (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)))) -> -(F = k1_funct_1(C,E) & k1_funct_1(D,E) = k8_setfam_1(k1_funct_1(B,E),F)))))) <-> D = k5_mssubfam(A,B,C)))))))) # label(d2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3595 (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]. 4.70/4.72 3596 (all A all B all C all D (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & -v1_xboole_0(A) -> 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]. 4.70/4.72 3597 (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_funct_1(k11_pboole(A,B,C)) & v1_pre_circ(k11_pboole(A,B,C),A) & v1_relat_1(k11_pboole(A,B,C)))) # label(fc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3598 (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]. 4.70/4.72 3599 (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]. 4.70/4.72 3600 (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]. 4.70/4.72 3601 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v1_funcop_1(D) & m1_pboole(D,A) -> (r1_pzfmisc1(A,B,C) & m3_pboole(D,A,B,C) -> r2_pboole(A,k2_mssubfam(A,D),C) & r6_pboole(A,k1_mssubfam(A,D),B)))))))) # label(t17_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3602 (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]. 4.70/4.72 3603 (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]. 4.70/4.72 3604 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> (r2_pboole(A,B,k2_mssubfam(A,C)) & (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(D,A) & E = k1_funct_1(C,D) -> v1_finset_1(k10_relat_1(E,k1_funct_1(B,D)))))) -> v1_pre_circ(B,A)))))) # label(t25_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3605 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> m1_pboole(k13_pboole(B,C),A) & v1_funcop_1(k13_pboole(B,C)))))) # label(t15_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3606 (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]. 4.70/4.72 3607 (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]. 4.70/4.72 3608 (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) -> m4_pboole(k2_pzfmisc1(A,B,D),A,k1_mboolean(A,C))))))))) # label(t39_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3609 (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]. 4.70/4.72 3610 (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]. 4.70/4.72 3611 (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]. 4.70/4.72 3612 (all A all B (m1_pboole(B,A) -> (exists C (v3_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v1_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3613 (all A all B (v2_relat_1(B) & v1_pre_circ(B,A) & m1_pboole(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]. 4.70/4.72 3614 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (all C (m1_struct_0(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3615 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_struct_0(C,A,B) -> m1_subset_1(C,u1_struct_0(A)))))) # label(dt_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3616 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3617 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> C = A & B = D)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3618 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3619 (all A all B (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3620 (all A (v1_struct_0(g1_struct_0(A)) & l1_struct_0(g1_struct_0(A)))) # label(dt_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3621 (all A all B (g1_struct_0(B) = g1_struct_0(A) -> A = B)) # label(free_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3622 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3623 (all A (l2_struct_0(A) -> m1_subset_1(u2_struct_0(A),u1_struct_0(A)))) # label(dt_u2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3624 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3625 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3626 (all A all B (m1_subset_1(B,A) -> v2_struct_0(g2_struct_0(A,B)) & l2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3627 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3628 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3629 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3630 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3631 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3632 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_struct_0(A,C,B) = k2_struct_0(A,B,C))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3633 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> k1_tarski(B) = k1_struct_0(A,B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3634 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3635 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3636 (exists A (v2_struct_0(A) & l2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3637 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> g1_struct_0(u1_struct_0(A)) = A))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3638 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3639 (all A (l2_struct_0(A) -> (v2_struct_0(A) -> A = g2_struct_0(u1_struct_0(A),u2_struct_0(A))))) # label(abstractness_v2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3640 (all A (l1_struct_0(A) -> (v3_struct_0(A) <-> v1_xboole_0(u1_struct_0(A))))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3641 (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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t41_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3642 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> k10_finseq_1(B,C) = k7_rlvect_1(A,B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3643 (all A (-v3_struct_0(A) & v3_rlvect_1(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)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3644 (all A (-v3_struct_0(A) & v3_rlvect_1(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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t86_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3645 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(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) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) = k3_rlvect_1(B,k6_rlvect_1(B,C,D),A))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3646 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = B -> B = k1_rlvect_1(A)))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3647 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3648 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3649 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(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)) -> (np__3 = k3_finseq_1(B) & k1_funct_1(B,np__1) = C & E = k1_funct_1(B,np__3) & D = k1_funct_1(B,np__2) -> 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]. 4.70/4.72 3650 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.72 3651 (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]. 4.70/4.73 3652 (all A (l1_rlvect_1(A) & -v3_struct_0(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)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B)))))))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3653 (all A (l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_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)) -> (v2_funct_1(C) & v2_funct_1(B) & k2_relat_1(B) = k2_relat_1(C) -> k9_rlvect_1(A,B) = k9_rlvect_1(A,C)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3654 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3655 (exists A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3656 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3657 (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)) -> k2_rlvect_1(A,C,k5_rlvect_1(A,B)) = k5_rlvect_1(A,k6_rlvect_1(A,B,C)))))))) # label(t47_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3658 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (np__1 = k3_finseq_1(B) -> k1_funct_1(B,np__1) = k9_rlvect_1(A,B)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3659 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3660 (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) -> k2_rlvect_1(A,B,C) = k4_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3661 (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)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3662 (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]. 4.70/4.73 3663 (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)) -> (k1_nat_1(k3_finseq_1(C),np__1) = k3_finseq_1(B) & k1_funct_1(B,k3_finseq_1(B)) = D & 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]. 4.70/4.73 3664 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))))) # label(abstractness_v2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.70/4.73 3665 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) Alarm clock 119.87/120.09 Prover9 interrupted 119.87/120.09 EOF