0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n007.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1440 0.12/0.33 % WCLimit : 180 0.12/0.33 % DateTime : Mon Jul 3 08:52:43 EDT 2023 0.12/0.33 % CPUTime : 4.66/4.70 ============================== Prover9 =============================== 4.66/4.70 Prover9 (32) version 2009-11A, November 2009. 4.66/4.70 Process 12404 was started by sandbox on n007.cluster.edu, 4.66/4.70 Mon Jul 3 08:52:47 2023 4.66/4.70 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_12251_n007.cluster.edu". 4.66/4.70 ============================== end of head =========================== 4.66/4.70 4.66/4.70 ============================== INPUT ================================= 4.66/4.70 4.66/4.70 % Reading from file /tmp/Prover9_12251_n007.cluster.edu 4.66/4.70 4.66/4.70 set(prolog_style_variables). 4.66/4.70 set(auto2). 4.66/4.70 % set(auto2) -> set(auto). 4.66/4.70 % set(auto) -> set(auto_inference). 4.66/4.70 % set(auto) -> set(auto_setup). 4.66/4.70 % set(auto_setup) -> set(predicate_elim). 4.66/4.70 % set(auto_setup) -> assign(eq_defs, unfold). 4.66/4.70 % set(auto) -> set(auto_limits). 4.66/4.70 % set(auto_limits) -> assign(max_weight, "100.000"). 4.66/4.70 % set(auto_limits) -> assign(sos_limit, 20000). 4.66/4.70 % set(auto) -> set(auto_denials). 4.66/4.70 % set(auto) -> set(auto_process). 4.66/4.70 % set(auto2) -> assign(new_constants, 1). 4.66/4.70 % set(auto2) -> assign(fold_denial_max, 3). 4.66/4.70 % set(auto2) -> assign(max_weight, "200.000"). 4.66/4.70 % set(auto2) -> assign(max_hours, 1). 4.66/4.70 % assign(max_hours, 1) -> assign(max_seconds, 3600). 4.66/4.70 % set(auto2) -> assign(max_seconds, 0). 4.66/4.70 % set(auto2) -> assign(max_minutes, 5). 4.66/4.70 % assign(max_minutes, 5) -> assign(max_seconds, 300). 4.66/4.70 % set(auto2) -> set(sort_initial_sos). 4.66/4.70 % set(auto2) -> assign(sos_limit, -1). 4.66/4.70 % set(auto2) -> assign(lrs_ticks, 3000). 4.66/4.70 % set(auto2) -> assign(max_megs, 400). 4.66/4.70 % set(auto2) -> assign(stats, some). 4.66/4.70 % set(auto2) -> clear(echo_input). 4.66/4.70 % set(auto2) -> set(quiet). 4.66/4.70 % set(auto2) -> clear(print_initial_clauses). 4.66/4.70 % set(auto2) -> clear(print_given). 4.66/4.70 assign(lrs_ticks,-1). 4.66/4.70 assign(sos_limit,10000). 4.66/4.70 assign(order,kbo). 4.66/4.70 set(lex_order_vars). 4.66/4.70 clear(print_given). 4.66/4.70 4.66/4.70 % formulas(sos). % not echoed (4467 formulas) 4.66/4.70 4.66/4.70 ============================== end of input ========================== 4.66/4.70 4.66/4.70 % From the command line: assign(max_seconds, 1440). 4.66/4.70 4.66/4.70 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 4.66/4.70 4.66/4.70 % Formulas that are not ordinary clauses: 4.66/4.70 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 2 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> C = B)) -> (exists A all B (r2_hidden(B,A) <-> (exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 3 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 4 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 5 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 6 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 7 (all A all B ((all C ((exists D (r2_hidden(C,D) & r2_hidden(D,A))) <-> r2_hidden(C,B))) <-> k3_tarski(A) = B)) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 8 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 9 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 10 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 11 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 12 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 13 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 14 (all A all B k2_tarski(k2_tarski(A,B),k1_tarski(A)) = k4_tarski(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 15 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C))))) & (all D all E all F all G (r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) -> (F = D <-> G = E))) & (all D -(r2_hidden(D,A) & (all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 16 (all A all B all C ((all D (r2_hidden(D,C) <-> D = A | D = B)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 17 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 18 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 19 (all A all B (k1_tarski(A) = B <-> (all C (r2_hidden(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 20 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 21 (all A exists B (r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -((all E (r1_tarski(E,C) -> r2_hidden(E,D))) & r2_hidden(D,B))))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 23 (all A all B -(r2_hidden(A,B) & (all C -((all D -(r2_hidden(D,B) & r2_hidden(D,C))) & r2_hidden(C,B))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 24 (all A all B all C ((all D (-r2_hidden(D,A) <-> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 25 (all A all B all C -(r1_xboole_0(A,B) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & -(-r2_hidden(C,B) & r2_hidden(C,A)) & r2_hidden(C,k2_xboole_0(A,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 26 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 27 (all A all B (A = B <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 28 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) | r2_hidden(D,A))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 29 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 30 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 31 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 32 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 33 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 34 (all A all B k3_xboole_0(B,A) = k3_xboole_0(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 35 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 36 (all A all B k3_xboole_0(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 37 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -(-r1_xboole_0(A,B) & (all C -r2_hidden(C,k3_xboole_0(A,B)))))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 38 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 39 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 40 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 41 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (-r2_hidden(D,B) & r2_hidden(D,A) <-> r2_hidden(D,C))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 42 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.70 43 (all A all B (B != A & r1_tarski(A,B) <-> r2_xboole_0(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 44 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 45 (all A all B (-(-r1_xboole_0(A,B) & (all C -(r2_hidden(C,A) & r2_hidden(C,B)))) & -(r1_xboole_0(A,B) & (exists C (r2_hidden(C,A) & r2_hidden(C,B)))))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 46 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 47 (all A all B (k1_xboole_0 = k3_xboole_0(A,B) <-> r1_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 48 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 49 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 50 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 51 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 52 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 53 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 54 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 55 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (r2_hidden(C,B) <-> p1_s3_xboole_0(C))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 56 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 57 (all A all B all C (r2_hidden(A,k5_xboole_0(B,C)) <-> -(r2_hidden(A,C) <-> r2_hidden(A,B)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 58 (all A (A = k1_xboole_0 <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 59 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 60 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 61 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 63 (all A k4_xboole_0(k1_xboole_0,A) = k1_xboole_0) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 64 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 65 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 66 (all A k5_xboole_0(A,k1_xboole_0) = A) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 67 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 68 (all A (v1_xboole_0(A) -> k1_xboole_0 = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 69 (all A all B all C (r1_xboole_0(A,B) & r1_xboole_0(C,B) & k2_xboole_0(C,B) = k2_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 70 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 71 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 72 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 73 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 74 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 75 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 76 (all A all B (k2_xboole_0(A,B) = k1_xboole_0 -> A = k1_xboole_0)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 77 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 78 (all A all B (r1_xboole_0(A,B) -> k4_xboole_0(k2_xboole_0(A,B),B) = A)) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 79 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 80 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 81 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 82 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 83 (all A all B k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 84 (all A all B all C k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k5_xboole_0(A,C),B)) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 85 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 86 (all A all B all C (r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,k2_xboole_0(B,C)) <-> r1_tarski(A,k5_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 87 (all A all B all C all D (k2_xboole_0(C,D) = k2_xboole_0(A,B) & r1_xboole_0(D,B) & r1_xboole_0(C,A) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 88 (all A all B all C (r1_tarski(A,B) & (all D (r1_tarski(A,D) & r1_tarski(C,D) -> r1_tarski(B,D))) & r1_tarski(C,B) -> k2_xboole_0(A,C) = B)) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 89 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 90 (all A all B (-(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 91 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 92 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 93 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 94 (all A all B all C k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A)) = k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 95 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 96 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 97 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 98 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> A = k1_xboole_0)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 99 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 100 (all A (-(k1_xboole_0 = A & -r1_xboole_0(A,A)) & -(k1_xboole_0 != A & r1_xboole_0(A,A)))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 101 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 102 (all A all B all C k3_xboole_0(k4_xboole_0(A,C),B) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 103 (all A all B all C k4_xboole_0(A,k4_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 104 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 105 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 106 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 107 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 108 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 109 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 110 (all A all B k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 111 (all A all B -(r1_xboole_0(k3_xboole_0(A,B),B) & -r1_xboole_0(A,B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 112 (all A all B all C k2_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k2_xboole_0(A,B),C)) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 113 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 114 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 115 (all A all B k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 116 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 117 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 118 (all A all B all C ((all D (r1_tarski(D,C) & r1_tarski(D,B) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> A = k3_xboole_0(B,C))) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 119 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 120 (all A all B all C (-(r1_xboole_0(A,k2_xboole_0(B,C)) & -(r1_xboole_0(A,C) & r1_xboole_0(A,B))) & -(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) & r1_xboole_0(A,B)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 121 (all A all B all C k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 122 (all A all B all C (r1_tarski(A,C) & r1_tarski(A,B) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 123 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 124 (all A all B k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 125 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 126 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 127 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 128 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 129 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(B,D) & r1_xboole_0(C,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 130 (all A all B all C (r1_tarski(B,C) & r2_xboole_0(A,B) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 131 (all A all B all C -(-r1_xboole_0(A,k3_xboole_0(B,C)) & r1_xboole_0(A,B))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 132 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 133 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 134 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 135 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 136 (all A all B (-v1_xboole_0(B) -> -(r1_xboole_0(B,A) & r1_tarski(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 137 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 138 (all A (k1_xboole_0 != A -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 139 (all A all B all C k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),C)) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 140 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 141 (all A all B k4_xboole_0(A,B) = k4_xboole_0(A,k3_xboole_0(A,B))) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 142 (all A all B all C k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) = k3_xboole_0(A,k2_xboole_0(B,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 143 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 144 (all A all B k5_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 145 (all A all B k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 146 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 147 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 148 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 149 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k4_xboole_0(B,A))) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 150 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 151 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 152 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 153 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 154 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 155 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 156 (all A all B all C (r1_tarski(A,C) & r1_xboole_0(B,C) & r1_tarski(A,B) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 157 (all A all B (r1_tarski(A,B) <-> k1_xboole_0 = k4_xboole_0(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 158 (all A all B all C (-v1_xboole_0(C) -> -(r1_xboole_0(A,B) & r1_tarski(C,B) & r1_tarski(C,A)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 159 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 160 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 161 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 162 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 163 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 164 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 165 (all A all B all C (r1_tarski(A,B) -> k2_xboole_0(A,k3_xboole_0(C,B)) = k3_xboole_0(k2_xboole_0(A,C),B))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 166 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 167 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 168 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 169 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 170 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 171 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 172 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 173 (all A all B all C (r1_tarski(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 174 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 175 (all A all B all C all D (r1_tarski(C,D) & r1_xboole_0(B,D) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 176 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 177 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 178 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 179 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 180 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 181 (all A all B -(k4_xboole_0(B,A) = k1_xboole_0 & r2_xboole_0(A,B))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 182 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 183 (all A all B (A != B -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 184 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> B = k1_xboole_0 | A = B | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 185 (all A all B all C all D -(r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F -(r2_hidden(F,C) & D = k4_tarski(E,F) & r2_hidden(E,B))) & r2_hidden(D,A))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 186 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 187 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 188 (all A all B (A = k4_xboole_0(A,k1_tarski(B)) <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 189 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 190 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 191 (all A all B (r1_tarski(k2_xboole_0(k1_tarski(A),B),B) -> r2_hidden(A,B))) # label(t45_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 192 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 193 (all A all B (k1_zfmisc_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 194 (all A all B all C k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 195 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> k1_xboole_0 = B | B = D & C = A | k1_xboole_0 = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 196 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 197 (all A all B (-r2_hidden(A,B) -> B = k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 198 (all A k2_tarski(k1_xboole_0,k1_tarski(A)) = k1_zfmisc_1(k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 199 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & -(C = k1_tarski(A) & k1_tarski(A) = B) & -(B = k1_tarski(A) & k1_xboole_0 = C) & -(B = k1_xboole_0 & C = k1_tarski(A)))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 200 (all A all B all C all D (r1_xboole_0(C,D) | r1_xboole_0(A,B) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 201 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 202 (all A all B -(r1_xboole_0(k1_tarski(A),k1_tarski(B)) & B = A)) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 203 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 204 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> r1_xboole_0(C,D) | D = C)) -> k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 205 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 206 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 207 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 208 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> C = A)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 209 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 210 (all A all B all C (k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 211 (all A exists B (r2_hidden(A,B) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C -(r1_tarski(C,B) & -r2_hidden(C,B) & -r2_tarski(C,B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 212 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 213 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) | k4_xboole_0(k1_tarski(A),B) = k1_xboole_0)) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 214 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> C = A & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 215 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 216 (all A all B (r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 217 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 -> B = A)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 218 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 219 (all A all B r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B))))) # label(t105_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 220 (all A all B all C (k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) & k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) = k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 221 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 222 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)) & k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 223 (all A all B all C all D (r2_hidden(A,C) & B = D <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 224 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> B = A)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 225 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 226 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 227 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 228 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 229 (all A all B all C (r2_hidden(B,C) & r2_hidden(A,C) <-> k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0)) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 230 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 231 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B)))) # label(t81_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 232 (all A all B (B != A -> k2_tarski(A,B) = k5_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 233 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 234 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 235 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 236 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> k2_zfmisc_1(A,C) = k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 237 (all A all B (-r2_hidden(A,B) -> r1_xboole_0(k1_tarski(A),B))) # label(t56_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 238 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 239 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> k1_xboole_0 = k2_zfmisc_1(A,B) | r1_tarski(A,C) & r1_tarski(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 240 (all A all B all C -(r2_hidden(A,C) & r1_xboole_0(k2_tarski(A,B),C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 241 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 242 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> D = B & A = C)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 243 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 244 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 245 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 246 (all A all B -(r2_hidden(A,B) & r1_xboole_0(k1_tarski(A),B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 247 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 248 (all A all B (B != A -> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),k1_tarski(B)))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 249 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 250 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 251 (all A all B (r1_tarski(A,k1_tarski(B)) <-> A = k1_xboole_0 | k1_tarski(B) = A)) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 252 (all A all B all C -(k2_xboole_0(B,C) = k1_tarski(A) & C != B & k1_xboole_0 != B & k1_xboole_0 != C)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 253 (all A all B -(k1_tarski(B) != A & A != k1_xboole_0 & (all C -(r2_hidden(C,A) & B != C)))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 254 (all A all B all C all D (B = D & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 255 (all A all B r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t84_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 256 (all A all B all C (k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C) <-> (B = A | r2_hidden(B,C)) & -r2_hidden(A,C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 257 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 258 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 259 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 260 (all A all B all C (r1_tarski(A,B) -> r2_hidden(C,A) | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 261 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 262 (all A all B k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 263 (all A all B (r2_hidden(A,B) -> k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 264 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 265 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 266 (all A all B all C all D -(k2_tarski(C,D) = k2_tarski(A,B) & D != A & A != C)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 267 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 268 (all A all B all C k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 269 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 270 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 271 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B)))) # label(t86_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 272 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 273 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k2_tarski(A,B) = k1_tarski(C))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 274 (all A all B all C (-(k1_tarski(B) != A & k2_tarski(B,C) != A & k1_tarski(C) != A & k1_xboole_0 != A) <-> r1_tarski(A,k2_tarski(B,C)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 275 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 276 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (k4_tarski(E,F) = D & r2_hidden(F,B) & r2_hidden(E,A))))) <-> C = k2_zfmisc_1(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 277 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 278 (all A all B -(A != k1_xboole_0 & A != k1_tarski(B) & k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 279 (all A all B all C -((all D all E A != k4_tarski(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 280 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> A = D)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 281 (all A all B all C all D k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) = k4_zfmisc_1(A,B,C,D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 282 (all A all B ((all C (r1_tarski(C,A) <-> r2_hidden(C,B))) <-> k1_zfmisc_1(A) = B)) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 283 (all A all B all C (k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 284 (all A all B k1_tarski(k4_tarski(A,B)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 285 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 286 (all A all B (r2_hidden(A,B) <-> r1_tarski(k1_tarski(A),B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 287 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 288 (all A all B (k1_xboole_0 = B | A = k1_xboole_0 <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 289 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k2_xboole_0(k2_tarski(A,C),B) = B)) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 290 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 291 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 292 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 293 (all A all B ((all C (r2_hidden(C,A) -> r1_xboole_0(C,B))) -> r1_xboole_0(k3_tarski(A),B))) # label(t98_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 294 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t95_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 295 (all A all B all C (r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) -> r2_hidden(A,C))) # label(t47_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 296 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 297 (all A all B all C (k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 298 (all A all B all C -(k1_tarski(A) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(B) & k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 299 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 300 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 301 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 302 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 303 (all A all B all C -(-r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(C,B) & -r2_hidden(A,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 304 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 305 (all A all B all C (k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) = k2_zfmisc_1(C,k2_tarski(A,B)) & k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 306 (all A all B all C all D k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D)))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 307 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 308 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 309 (all A all B all C -(r2_hidden(B,C) & A != B & k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 310 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) -> r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)))) # label(t107_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 311 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 312 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 313 (all A all B all C (k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 314 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 315 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 316 (all A all B all C -(A != k1_xboole_0 & -r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 317 (all A all B r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t97_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 318 (all A all B all C all D (r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F (r2_hidden(k4_tarski(E,F),A) -> r2_hidden(k4_tarski(E,F),D))) -> r1_tarski(A,D))) # label(t109_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 319 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 320 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 321 (all A all B (r2_hidden(A,B) <-> k1_xboole_0 = k4_xboole_0(k1_tarski(A),B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 322 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(C,B))) -> r1_tarski(k3_tarski(A),B))) # label(t94_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 323 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 324 (all A all B all C all D k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 325 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 326 (all A all B (r1_xboole_0(k1_tarski(A),B) | k3_xboole_0(k1_tarski(A),B) = k1_tarski(A))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 327 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 328 (all A all B (k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 329 (all A all B all C (-(A != k1_xboole_0 & A != k1_tarski(C) & A != k2_tarski(B,C) & k1_tarski(B) != A) <-> k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0)) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 330 (all A all B all C all D -(A != D & A != C & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 331 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 332 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 333 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 334 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k4_subset_1(A,B,C)) = k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 335 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k3_xboole_0(B,C) = k5_subset_1(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 336 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> B = A))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 337 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 338 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> A = B))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 339 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 340 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))) = k3_subset_1(A,k7_subset_1(A,B,C)))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 341 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 342 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 343 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 344 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 345 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f3_s4_subset_1 = f2_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 346 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 347 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 348 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 349 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k3_subset_1(A,B)))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 350 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 351 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k7_subset_1(A,C,B) = k7_subset_1(A,B,C))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 352 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 353 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> k3_subset_1(A,C) = B))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 354 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 355 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 356 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 357 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 358 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 359 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 360 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 361 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 362 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (A != k1_xboole_0 -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 363 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_xboole_0(A,B) <-> r1_subset_1(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 364 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 365 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)) & (all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_subset_1) & p1_s1_subset_1(B))))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 366 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 367 (all A all B (r2_hidden(A,B) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)))) # label(t63_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 368 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 369 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) | r2_hidden(E,C)))) -> k4_subset_1(A,C,D) = B))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 370 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 371 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 372 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 373 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.71 374 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 375 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 376 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) <-> r1_tarski(B,k3_subset_1(A,C))))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 377 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 378 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 379 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 380 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k2_subset_1(A)))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 381 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)))))) # label(t41_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 382 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,C) <-> r2_hidden(E,D))))) -> k7_subset_1(A,C,D) = B))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 383 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 385 (all A all B (m1_subset_1(B,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 386 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 387 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 388 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 389 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 390 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 391 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 392 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 393 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))))))) # label(t42_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 394 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 395 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_xboole_0(B,k3_subset_1(A,C))))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 396 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 397 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 398 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (-r2_hidden(E,D) & r2_hidden(E,C) <-> r2_hidden(E,B)))) -> B = k6_subset_1(A,C,D)))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 399 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 400 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 401 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 402 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 403 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k2_subset_1(A) = B <-> r1_tarski(k3_subset_1(A,B),B)))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 404 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) -> r2_subset_1(B,A)))) # label(symmetry_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 405 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 406 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)) & (all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 407 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 408 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 409 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> -r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 410 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 411 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 412 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 413 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 414 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 415 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 416 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 417 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 418 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 419 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 420 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 421 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 422 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 423 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> r1_xboole_0(B,k3_subset_1(A,B)))) # label(t26_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 424 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 425 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 426 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 427 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (A != k1_xboole_0 -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 428 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),C) -> r1_tarski(k3_subset_1(A,C),B)))))) # label(t36_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 429 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,k3_subset_1(A,C)) & r2_hidden(B,C)))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 430 (all A all B ((v1_xboole_0(A) -> (v1_xboole_0(B) <-> m1_subset_1(B,A))) & (-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 431 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 432 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 433 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 434 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 435 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 436 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 437 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 438 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 439 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 440 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> C = B))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 441 (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]. 4.66/4.72 442 (all A all B all C -(v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 443 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 444 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 445 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 446 (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]. 4.66/4.72 447 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> A = k1_relat_1(k7_relat_1(B,A))))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 448 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 449 (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]. 4.66/4.72 450 (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]. 4.66/4.72 451 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) <-> v1_relat_1(A))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 452 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 453 (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]. 4.66/4.72 454 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_tarski(A,B) = k3_relat_1(C)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 455 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 456 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 457 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 458 (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]. 4.66/4.72 459 (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]. 4.66/4.72 460 (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]. 4.66/4.72 461 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 462 (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]. 4.66/4.72 463 (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]. 4.66/4.72 464 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 465 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 466 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 467 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 468 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 469 (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]. 4.66/4.72 470 (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]. 4.66/4.72 471 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) = k3_relat_1(k2_xboole_0(A,B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 472 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 473 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v3_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 474 (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]. 4.66/4.72 475 (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]. 4.66/4.72 476 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k2_xboole_0(A,B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 477 (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]. 4.66/4.72 478 (all A all B (v1_relat_1(B) -> k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 479 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 480 (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]. 4.66/4.72 481 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 482 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k9_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 483 (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]. 4.66/4.72 484 (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]. 4.66/4.72 485 (all A (v1_relat_1(A) -> ((all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B)) <-> v3_relat_1(A)))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 486 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 487 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 488 (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]. 4.66/4.72 489 (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]. 4.66/4.72 490 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 491 (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]. 4.66/4.72 492 (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]. 4.66/4.72 493 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 494 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 495 (all A (A = k1_relat_1(k6_relat_1(A)) & k2_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 496 (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]. 4.66/4.72 497 (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]. 4.66/4.72 498 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 499 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k4_xboole_0(A,B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 500 (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]. 4.66/4.72 501 (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]. 4.66/4.72 502 (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]. 4.66/4.72 503 (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]. 4.66/4.72 504 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 505 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B) <-> r2_hidden(k4_tarski(D,E),C))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 506 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 507 (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]. 4.66/4.72 508 (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]. 4.66/4.72 509 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 510 (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]. 4.66/4.72 511 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 512 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 513 (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]. 4.66/4.72 514 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 515 (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]. 4.66/4.72 516 (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]. 4.66/4.72 517 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 518 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 519 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 520 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k7_relat_1(k7_relat_1(B,A),A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 521 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(B,f1_s1_relat_1) & r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 522 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 523 (all A all B (v1_relat_1(B) -> -(k1_xboole_0 != A & k1_xboole_0 = k9_relat_1(B,A) & r1_tarski(A,k1_relat_1(B))))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 524 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 525 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 526 (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]. 4.66/4.72 527 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 528 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 529 (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]. 4.66/4.72 530 (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]. 4.66/4.72 531 (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]. 4.66/4.72 532 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 533 (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]. 4.66/4.72 534 (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]. 4.66/4.72 535 (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]. 4.66/4.72 536 (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]. 4.66/4.72 537 (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]. 4.66/4.72 538 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 539 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 540 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 541 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 542 (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]. 4.66/4.72 543 (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]. 4.66/4.72 544 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 545 (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]. 4.66/4.72 546 (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]. 4.66/4.72 547 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 548 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 549 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 550 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_relat_1(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 551 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 552 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,k5_relat_1(B,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 553 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B) & r2_hidden(D,k2_relat_1(C)))) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 554 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k5_relat_1(k4_relat_1(B),k4_relat_1(A)) = k4_relat_1(k5_relat_1(A,B)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 555 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 556 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 557 (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]. 4.66/4.72 558 (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]. 4.66/4.72 559 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 560 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 561 (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]. 4.66/4.72 562 (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]. 4.66/4.72 563 (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]. 4.66/4.72 564 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 565 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 566 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 567 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k9_relat_1(C,B)) <-> (exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C)))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 568 (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]. 4.66/4.72 569 (all A (v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 570 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_tarski(A,C) = k1_relat_1(E) & k2_relat_1(E) = k2_tarski(B,D)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 571 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_relat_1(C) = k1_tarski(B) & k1_relat_1(C) = k1_tarski(A)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 572 (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]. 4.66/4.72 573 (all A (v1_relat_1(A) -> k1_xboole_0 = k8_relat_1(k1_xboole_0,A))) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 574 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k2_xboole_0(A,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 575 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 576 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C -r2_hidden(C,k1_relat_1(B)))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 577 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 578 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 579 (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]. 4.66/4.72 580 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 581 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B) <-> r2_hidden(k4_tarski(D,E),C))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 582 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 583 (all A (v1_relat_1(A) -> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A)) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 584 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 585 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k2_relat_1(B)) -> k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A))))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 586 (all A (v1_relat_1(A) -> k1_xboole_0 = k7_relat_1(A,k1_xboole_0))) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 587 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 588 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> (exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))))) <-> C = k5_relat_1(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 589 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 590 (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]. 4.66/4.72 591 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 592 (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]. 4.66/4.72 593 (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]. 4.66/4.72 594 (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]. 4.66/4.72 595 (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]. 4.66/4.72 596 (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]. 4.66/4.72 597 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 598 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,B) = k1_xboole_0))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 599 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 600 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 601 (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]. 4.66/4.72 602 (all A (v1_relat_1(A) -> k1_relat_1(k4_relat_1(A)) = k2_relat_1(A) & k2_relat_1(k4_relat_1(A)) = k1_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 603 (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]. 4.66/4.72 604 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = A <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A)))))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 605 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 606 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k10_relat_1(B,A) = k1_xboole_0))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 607 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k2_xboole_0(B,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 608 (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]. 4.66/4.72 609 (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]. 4.66/4.72 610 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 611 (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]. 4.66/4.72 612 (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]. 4.66/4.72 613 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 614 (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]. 4.66/4.72 615 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 616 (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]. 4.66/4.72 617 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0 & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 618 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 619 (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]. 4.66/4.72 620 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 621 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 622 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_relat_1(A) = k1_xboole_0 -> k1_xboole_0 = A))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 623 (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]. 4.66/4.72 624 (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]. 4.66/4.72 625 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 626 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 627 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 628 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 629 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k2_xboole_0(A,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 630 (all A k6_relat_1(A) = k4_relat_1(k6_relat_1(A))) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 631 (all A (v1_relat_1(A) -> k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) = k3_relat_1(A))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 632 (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]. 4.66/4.72 633 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 634 (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]. 4.66/4.72 635 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 636 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 637 (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]. 4.66/4.72 638 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 639 (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]. 4.66/4.72 640 (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]. 4.66/4.72 641 (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]. 4.66/4.72 642 (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]. 4.66/4.72 643 (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]. 4.66/4.72 644 (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]. 4.66/4.72 645 (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]. 4.66/4.72 646 (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]. 4.66/4.72 647 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 648 (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]. 4.66/4.72 649 (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]. 4.66/4.72 650 (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]. 4.66/4.72 651 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(A,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D))))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 652 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 653 (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]. 4.66/4.72 654 (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]. 4.66/4.72 655 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k1_relat_1(B)) & (all C -r2_hidden(C,k2_relat_1(B)))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.72 656 (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]. 4.66/4.73 657 (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]. 4.66/4.73 658 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k6_relat_1(A),B) = B))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 659 (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]. 4.66/4.73 660 (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]. 4.66/4.73 661 (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]. 4.66/4.73 662 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 663 (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]. 4.66/4.73 664 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D)) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 665 (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]. 4.66/4.73 666 (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]. 4.66/4.73 667 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 668 (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]. 4.66/4.73 669 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 670 (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]. 4.66/4.73 671 (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]. 4.66/4.73 672 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k5_relat_1(B,D) = k6_relat_1(A) & k6_relat_1(k1_relat_1(D)) = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(B) -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 673 (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]. 4.66/4.73 674 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 675 (all A k6_relat_1(A) = k2_funct_1(k6_relat_1(A))) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 676 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 677 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 678 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 679 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 680 (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]. 4.66/4.73 681 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 682 (all A all B (v1_relat_1(B) -> (k10_relat_1(B,k1_tarski(A)) != k1_xboole_0 <-> r2_hidden(A,k2_relat_1(B))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 683 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 684 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 685 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 686 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B -((all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)) & r2_hidden(B,k2_relat_1(A))))))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 687 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 688 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 689 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_funct_1(A) = k4_relat_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 690 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 691 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 692 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 693 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 694 (all A all B -((all C (v1_relat_1(C) & v1_funct_1(C) -> -(B = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A)))) & -(k1_xboole_0 = A & B != k1_xboole_0))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 695 (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]. 4.66/4.73 696 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 697 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 698 (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]. 4.66/4.73 699 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 700 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 701 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 702 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 703 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 704 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 705 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 706 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 707 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k5_relat_1(A,B) = A & k2_relat_1(A) = k1_relat_1(B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 708 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 709 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 710 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 711 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 712 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 713 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_tarski(A) = k2_relat_1(B) & k1_tarski(A) = k2_relat_1(C) & k1_relat_1(C) = k1_relat_1(B) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 714 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 715 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 716 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(k9_relat_1(C,A),B) = k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 717 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 718 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_funct_1(k2_funct_1(A)) = A))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 719 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 720 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 721 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k4_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 722 (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]. 4.66/4.73 723 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 724 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 725 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 726 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 727 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 728 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 729 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 730 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 731 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 732 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A)))) <-> v2_relat_1(A)))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 733 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.66/4.73 734 (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]. 4.72/4.73 735 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 736 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 737 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 738 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 739 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 740 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 741 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 742 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 743 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 744 (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]. 4.72/4.73 745 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 746 (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]. 4.72/4.73 747 (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]. 4.72/4.73 748 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 749 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 750 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 751 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(C) = k1_relat_1(B) & k5_relat_1(B,A) = k5_relat_1(C,A) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> B = C))))) <-> v2_funct_1(A)))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 752 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)))))) <-> k2_relat_1(A) = B)))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 753 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 754 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 755 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 756 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 757 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 758 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 759 (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]. 4.72/4.73 760 (all A all B k6_relat_1(k3_xboole_0(A,B)) = k5_relat_1(k6_relat_1(B),k6_relat_1(A))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 761 (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]. 4.72/4.73 762 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_funct_1(B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 763 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A & k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 764 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 765 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 766 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 767 (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]. 4.72/4.73 768 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(A,k2_funct_1(A))) = k1_relat_1(A) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 769 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 770 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 771 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & k2_relat_1(B) = k1_relat_1(A) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 772 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 773 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k2_relat_1(B) = k1_relat_1(A) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 774 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 775 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 776 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B) & k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 777 (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]. 4.72/4.73 778 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & (all C all D ((k1_funct_1(B,C) = D & r2_hidden(C,k2_relat_1(A)) -> C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A))) & (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> D = k1_funct_1(B,C) & r2_hidden(C,k2_relat_1(A))))) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 779 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B))))))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 780 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 781 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 782 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 783 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> B = C)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_funct_1(B,C) & r2_hidden(B,f1_s1_funct_1))))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 784 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k2_funct_1(A)) = k1_relat_1(A) & k1_relat_1(k2_funct_1(A)) = k2_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 785 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) & r2_hidden(B,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 786 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 787 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 788 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k2_relat_1(B) & k1_relat_1(D) = A & k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(C) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 789 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 790 (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]. 4.72/4.73 791 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 792 (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]. 4.72/4.73 793 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(k1_funct_1(B,D) = C & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 794 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 795 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 796 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k9_relat_1(C,k2_tarski(A,B)) = k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 797 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 798 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(A) = k1_relat_1(B) & (all C all D (r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(B)) -> (C = k1_funct_1(B,D) <-> D = k1_funct_1(A,C)))) & k2_relat_1(B) = k1_relat_1(A) -> B = k2_funct_1(A)))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 799 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 800 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 801 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 802 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k8_relat_1(A,C)))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 803 (exists A (v1_relat_1(A) & v1_funct_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 804 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 805 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C))) & k1_relat_1(B) = A))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 806 (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]. 4.72/4.73 807 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 808 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 809 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 810 (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_relat_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 811 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) & (all B -((all C all D B != k4_tarski(C,D)) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 812 (all A all B (v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & k1_xboole_0 = k10_relat_1(B,k1_tarski(C)))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 813 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k2_relat_1(A) = k1_relat_1(B) & v2_funct_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 814 (exists A (v1_relat_1(A) & v1_funct_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 815 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 816 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 817 (all A (k1_xboole_0 != A -> (all B exists C (v1_funct_1(C) & A = k1_relat_1(C) & k1_tarski(B) = k2_relat_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 818 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 819 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 820 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 821 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 822 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 823 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C)) & k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 824 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A & k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 825 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k5_relat_1(k6_relat_1(A),C),B) = k1_funct_1(C,B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 826 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 827 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,k1_relat_1(A)) & D = k1_funct_1(A,E) & r2_hidden(E,B))) <-> r2_hidden(D,C))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 828 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 829 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 830 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k7_relat_1(C,A) = B <-> k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)))))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 831 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(B,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 832 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 833 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 834 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 835 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (A = k1_relat_1(D) & k5_relat_1(B,D) = k5_relat_1(B,C) & A = k1_relat_1(C) -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 836 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 837 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(A,k9_relat_1(C,B)) = k9_relat_1(k8_relat_1(A,C),B))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 838 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 839 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 840 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 841 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 842 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 843 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 844 (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]. 4.72/4.73 845 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 846 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 847 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 848 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> A = k1_xboole_0)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 849 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 850 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> C = k1_xboole_0)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 851 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 852 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k6_relat_1(k2_relat_1(A)) = k5_relat_1(k2_funct_1(A),A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 853 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 854 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 855 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 856 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k9_relat_1(B,k10_relat_1(B,A))))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 857 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 858 (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]. 4.72/4.73 859 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 860 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(A,D)) = k1_funct_1(C,D))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 861 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 862 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 863 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 864 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k4_xboole_0(A,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 865 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 866 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k8_relat_1(A,C) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C)) <-> r2_hidden(D,k1_relat_1(B))))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 867 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 868 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 869 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 870 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 871 (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]. 4.72/4.73 872 (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]. 4.72/4.73 873 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 874 (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]. 4.72/4.73 875 (all A (v1_relat_1(A) -> (k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) <-> v7_relat_2(A)))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 876 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 877 (all A (v1_relat_1(A) -> (r7_relat_2(A,k3_relat_1(A)) <-> v7_relat_2(A)))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 878 (all A (v1_relat_1(A) -> (r5_relat_2(A,k3_relat_1(A)) <-> v5_relat_2(A)))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 879 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 880 (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]. 4.72/4.73 881 (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]. 4.72/4.73 882 (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]. 4.72/4.73 883 (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]. 4.72/4.73 884 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 885 (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]. 4.72/4.73 886 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k4_xboole_0(A,B)) & v4_relat_2(k3_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 887 (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]. 4.72/4.73 888 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v3_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 889 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 890 (all A (v1_relat_1(A) -> (r8_relat_2(A,k3_relat_1(A)) <-> v8_relat_2(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 891 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 892 (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]. 4.72/4.73 893 (all A (v4_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 894 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 895 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 896 (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]. 4.72/4.73 897 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k3_xboole_0(A,B)) & v1_relat_2(k2_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.73 898 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 899 (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]. 4.72/4.74 900 (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]. 4.72/4.74 901 (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]. 4.72/4.74 902 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 903 (all A (v3_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 904 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r2_relat_2(A,k3_relat_1(A))))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 905 (all A (v1_relat_1(A) -> (all 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))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 906 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 907 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 908 (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]. 4.72/4.74 909 (all A (v1_relat_1(A) -> (all B (r7_relat_2(A,B) <-> (all C all D -(-r2_hidden(k4_tarski(C,D),A) & -r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 910 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r1_xboole_0(k6_relat_1(k3_relat_1(A)),A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 911 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 912 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 913 (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(k4_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 914 (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]. 4.72/4.74 915 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> r3_relat_2(A,k3_relat_1(A))))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 916 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 917 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(B) & v8_relat_2(A) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 918 (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]. 4.72/4.74 919 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(E,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 920 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k1_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k2_relat_1(A) = k2_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 921 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r4_relat_2(A,k3_relat_1(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 922 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 923 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v2_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 924 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 925 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(C,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 926 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> A = k4_relat_1(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 927 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & C != D & r2_hidden(D,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 928 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(C,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 929 (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]. 4.72/4.74 930 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 931 (all A all B (v1_relat_1(B) -> (r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A) <-> r4_relat_2(B,A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 932 (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]. 4.72/4.74 933 (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]. 4.72/4.74 934 (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]. 4.72/4.74 935 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 936 (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]. 4.72/4.74 937 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 938 (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]. 4.72/4.74 939 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A) & v3_ordinal1(B))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 940 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 941 (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]. 4.72/4.74 942 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 943 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_xboole_0(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 944 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 945 (all A all B all C all D -(r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 946 (all A ((all B (r2_hidden(B,A) -> v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v1_relat_1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 947 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 948 (all A (v3_ordinal1(A) -> -v1_xboole_0(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 949 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 950 (all A ((all B all C -(r2_hidden(B,A) & r2_hidden(C,A) & -r2_hidden(B,C) & -r2_hidden(C,B) & B != C)) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 951 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 952 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 953 (all A (v1_ordinal1(A) & v2_ordinal1(A) <-> v3_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 954 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 955 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 956 (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]. 4.72/4.74 957 (all A all B (v3_ordinal1(B) -> -(k1_xboole_0 != A & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & r1_tarski(A,B)))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 958 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 959 (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) & (all A (v3_ordinal1(A) -> (all B ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_relat_1(C) = A & f3_s5_ordinal1(C) = B & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> f2_s5_ordinal1(A) = B)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A))))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 960 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 961 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 962 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 963 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 964 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 965 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(B,A) | r1_ordinal1(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 966 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(B,A) & A != B & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 967 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 968 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r2_hidden(A,k1_ordinal1(B))))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 969 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 970 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 971 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 972 (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]. 4.72/4.74 973 (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]. 4.72/4.74 974 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(B,A) & B != A & -r2_xboole_0(A,B)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 975 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 976 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 977 (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]. 4.72/4.74 978 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 979 (all A (v3_ordinal1(A) -> -(v4_ordinal1(A) & (exists B (A = k1_ordinal1(B) & v3_ordinal1(B)))) & -((all B (v3_ordinal1(B) -> A != k1_ordinal1(B))) & -v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 980 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 981 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 982 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) -> k2_ordinal1(A,B) = k7_relat_1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 983 (all A all B (v5_ordinal1(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 984 (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]. 4.72/4.74 985 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 986 (all A all B all C all D all E -(r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,A) & r2_hidden(A,B))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 987 (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]. 4.72/4.74 988 (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]. 4.72/4.74 989 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 990 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 991 (all A all B (m1_ordinal1(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 992 (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]. 4.72/4.74 993 (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]. 4.72/4.74 994 (exists A (v1_relat_1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k2_ordinal1(A,B) = C & r2_hidden(B,f1_s4_ordinal1) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v5_ordinal1(A) & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 995 (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]. 4.72/4.74 996 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 997 (all A (k3_tarski(A) = A <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 998 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 999 (all A all B all C all D all E all F -(r2_hidden(B,C) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(D,E) & r2_hidden(C,D) & r2_hidden(A,B))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1000 (all A all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1001 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1002 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1003 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1004 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1005 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A (p1_s1_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & v3_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1006 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1007 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1008 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1009 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1010 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1011 (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]. 4.72/4.74 1012 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(A,B) & r2_hidden(C,A) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1013 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1014 f1_s3_ordinal1 = k1_relat_1(f4_s3_ordinal1) & (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k2_ordinal1(f4_s3_ordinal1,A) = B & r2_hidden(A,f1_s3_ordinal1) -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) & (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (B = k2_ordinal1(f3_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & f1_s3_ordinal1 = k1_relat_1(f3_s3_ordinal1) -> f3_s3_ordinal1 = f4_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1015 (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]. 4.72/4.74 1016 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1017 (all A all B all C (m2_relset_1(C,A,B) -> k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1018 (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]. 4.72/4.74 1019 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> D = k9_relset_1(A,B,C,D)))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1020 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k5_relat_1(E,F) = k7_relset_1(A,B,C,D,E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1021 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1022 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1023 (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]. 4.72/4.74 1024 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,D) = k3_xboole_0(C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1025 (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]. 4.72/4.74 1026 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1027 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1028 (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]. 4.72/4.74 1029 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1030 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1031 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(A,B) & r1_tarski(C,D) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1032 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(D,E),C)))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1033 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> B = k5_relset_1(A,B,C) & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1034 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1035 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,D,C) = k1_relset_1(A,B,C,D))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1036 (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]. 4.72/4.74 1037 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(k4_tarski(E,F) = C & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1038 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,D,C) = k2_relset_1(A,B,C,D))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1039 (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]. 4.72/4.74 1040 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1041 (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]. 4.72/4.74 1042 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> D = k8_relset_1(B,A,D,C)))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1043 (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]. 4.72/4.74 1044 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1045 (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]. 4.72/4.74 1046 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> k1_xboole_0 = C))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1047 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1048 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C) & k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1049 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1050 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1051 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1052 (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]. 4.72/4.74 1053 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1054 (all A all B all C (m1_relset_1(C,A,B) -> k4_relat_1(C) = k6_relset_1(A,B,C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1055 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1056 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> B = k4_relset_1(B,A,C) & r1_tarski(B,k5_relset_1(B,A,C))))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1057 (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]. 4.72/4.74 1058 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1059 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1060 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1061 (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]. 4.72/4.74 1062 (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]. 4.72/4.74 1063 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relset_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1064 (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]. 4.72/4.74 1065 (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]. 4.72/4.74 1066 (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]. 4.72/4.74 1067 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1068 (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]. 4.72/4.74 1069 (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]. 4.72/4.74 1070 (all A all B all C (m2_relset_1(C,B,A) -> k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) & k4_relset_1(B,A,C) = k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1071 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> k1_xboole_0 = C))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1072 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1073 (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]. 4.72/4.74 1074 (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]. 4.72/4.74 1075 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1076 (all A all B all C (m1_relset_1(C,A,B) -> k2_relat_1(C) = k5_relset_1(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1077 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1078 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1079 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> C = k1_relset_1(A,B,C,C))) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1080 (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]. 4.72/4.74 1081 (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]. 4.72/4.74 1082 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1083 (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]. 4.72/4.74 1084 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1085 (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]. 4.72/4.74 1086 (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]. 4.72/4.74 1087 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1088 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1089 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1090 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1091 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1092 (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]. 4.72/4.74 1093 (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]. 4.72/4.74 1094 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1095 (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]. 4.72/4.74 1096 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1097 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C)))) & r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1098 (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]. 4.72/4.74 1099 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1100 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1101 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k4_relset_1(A,B,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C))))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1102 (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]. 4.72/4.74 1103 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k2_relset_1(A,B,C,D),A,B))) # label(dt_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1104 (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]. 4.72/4.74 1105 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1106 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1107 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1108 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1109 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1110 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1111 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1112 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1113 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1114 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1115 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1116 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1117 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)) & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1118 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1119 (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]. 4.72/4.74 1120 (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]. 4.72/4.74 1121 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1122 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1123 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1124 (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]. 4.72/4.74 1125 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1126 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k1_tarski(C) = k5_partfun1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1127 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1128 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & r2_hidden(A,k1_relat_1(D)) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1129 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1130 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1131 (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]. 4.72/4.74 1132 (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]. 4.72/4.74 1133 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1134 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1135 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1136 (all A exists B (m1_relset_1(B,A,A) & v1_relat_1(B) & v1_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1137 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1138 (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]. 4.72/4.74 1139 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1140 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),B) & r1_tarski(A,k1_relat_1(C)) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.74 1141 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1142 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k2_relat_1(C) = k9_relat_1(C,A))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1143 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),C,B))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1144 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1145 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B)))) & r1_partfun1(C,D) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1146 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k2_relat_1(B) = k1_xboole_0 & k4_relset_1(A,k1_xboole_0,B) = k1_xboole_0)) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1147 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1148 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1149 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1150 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1151 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1152 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(k1_xboole_0,A,B))) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1153 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,E) = k1_funct_1(C,D) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1154 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1155 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1156 (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]. 4.72/4.75 1157 (exists A (v1_funct_1(A) & f1_s1_partfun1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> k1_funct_1(A,B) = f3_s1_partfun1(B)) & (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1158 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1159 (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]. 4.72/4.75 1160 (all A all B all C all D (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) -> C = D)) & (all A all B all C (p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> r2_hidden(B,f1_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1))) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1161 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1162 (all A (v1_relat_1(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1163 (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]. 4.72/4.75 1164 (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]. 4.72/4.75 1165 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1166 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1167 (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]. 4.72/4.75 1168 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1169 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1170 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1171 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1172 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> D = C)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1173 (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]. 4.72/4.75 1174 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1175 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D)) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1176 (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]. 4.72/4.75 1177 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1178 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1179 (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]. 4.72/4.75 1180 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1181 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1182 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1183 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1184 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & B = k1_xboole_0 -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1185 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1186 (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]. 4.72/4.75 1187 (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]. 4.72/4.75 1188 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1189 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1190 (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]. 4.72/4.75 1191 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k10_relat_1(C,B))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1192 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1193 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1194 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & v1_partfun1(E,A,B) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1195 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1196 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1197 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1198 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1199 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1200 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1201 (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]. 4.72/4.75 1202 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & r1_partfun1(C,D)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1203 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (v1_relat_1(C) & r1_tarski(A,C) & r1_tarski(B,C) & v1_funct_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1204 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1205 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m2_relset_1(k2_partfun1(A,B,C,D),A,B) & v1_funct_1(k2_partfun1(A,B,C,D)))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1206 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1207 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1208 (all A all B (v1_funct_1(k1_xboole_0) & m2_relset_1(k1_xboole_0,A,B))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1209 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)) = k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1210 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1211 (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]. 4.72/4.75 1212 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (k5_partfun1(A,B,C) = D <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & E = F & r1_partfun1(C,F) & v1_partfun1(F,A,B))) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1213 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1214 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1215 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1216 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> k1_funct_1(D,C) = B))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1217 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1218 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1219 (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]. 4.72/4.75 1220 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1221 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_1(D) & m2_relset_1(D,A,B))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1222 (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]. 4.72/4.75 1223 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1224 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1225 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1226 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1227 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1228 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1229 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1230 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.72/4.75 1231 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1232 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1233 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1234 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1235 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1236 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) & v1_funct_1(F) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1237 (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]. 4.74/4.75 1238 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1239 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1240 (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]. 4.74/4.75 1241 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,C) = k1_funct_1(A,C))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1242 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1243 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1244 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1245 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1246 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1247 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1248 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> k1_xboole_0 = A)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1249 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (C = k2_xboole_0(A,B) & v1_funct_1(C) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1250 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1251 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k1_tarski(A) & r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1252 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k9_relset_1(B,C,A,k3_partfun1(D,B,C)) = k3_partfun1(D,B,k3_xboole_0(A,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1253 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1254 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1255 (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]. 4.74/4.75 1256 (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]. 4.74/4.75 1257 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(A,C) & r1_tarski(B,D) -> v1_funct_1(E) & m2_relset_1(E,C,D)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1258 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,E) = k4_relset_1(k2_zfmisc_1(A,B),C,D) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1259 (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]. 4.74/4.75 1260 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1261 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1262 (all A all B all C ((all D ((exists E (r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k4_partfun1(A,B))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1263 (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]. 4.74/4.75 1264 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1265 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1266 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1267 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1268 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1269 (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]. 4.74/4.75 1270 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1271 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1272 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1273 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1274 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(k6_relat_1(A),C) = C)) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1275 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1276 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1277 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A (m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) <-> p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1))) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1278 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1279 (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]. 4.74/4.75 1280 (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]. 4.74/4.75 1281 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1282 (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]. 4.74/4.75 1283 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1284 (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]. 4.74/4.75 1285 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1286 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1287 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1288 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1289 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1290 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1291 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1292 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1293 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1294 (all A (v1_relat_1(A) & v8_relat_2(A) & v3_relat_2(A) -> v1_relat_1(A) & v1_relat_2(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1295 (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]. 4.74/4.75 1296 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1297 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1298 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1299 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1300 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1301 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> B = k1_xboole_0)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1302 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) & p1_s2_partfun1(A,C) -> B = C)) & (all A all B (p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1303 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1304 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1305 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1306 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1307 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> k3_partfun1(C,A,B) = C))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1308 (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]. 4.74/4.75 1309 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1310 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1311 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1312 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1313 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k1_xboole_0,B) & v1_funct_1(D) -> C = D)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1314 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1315 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1316 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1317 (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]. 4.74/4.75 1318 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1319 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1320 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(C)) & r4_wellord1(A,k1_wellord2(B)) -> B = C))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1321 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1322 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(k1_wellord2(A),k1_wellord2(B)) -> A = B))))) # label(t11_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1323 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1324 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1325 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> A = k3_relat_1(k2_wellord1(B,A)) & v2_wellord1(k2_wellord1(B,A))))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1326 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1327 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (r1_wellord2(A,B) <-> k2_wellord2(B) = A))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1328 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1329 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1330 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1331 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1332 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1333 (all A all B all C (r2_wellord2(A,B) & r2_wellord2(B,C) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1334 (all A all B (r1_tarski(A,B) -> k1_wellord2(A) = k2_wellord1(k1_wellord2(B),A))) # label(t8_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1335 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1336 (all A exists B (v1_relat_1(B) & r2_wellord1(B,A))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1337 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B (v3_ordinal1(B) -> (B = k2_wellord2(A) <-> r4_wellord1(A,k1_wellord2(B)))))))) # label(d2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1338 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1339 (all A -((all B -(r2_hidden(B,f2_s1_wellord2) & p1_s1_wellord2(A,B))) & r2_hidden(A,f1_s1_wellord2))) -> (exists A (v1_funct_1(A) & r1_tarski(k2_relat_1(A),f2_s1_wellord2) & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & f1_s1_wellord2 = k1_relat_1(A) & v1_relat_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1340 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1341 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v2_wellord1(k1_wellord2(B)))))) # label(t9_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1342 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1343 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1344 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1345 (all A (-v1_xboole_0(A) -> -((all B -(k1_xboole_0 = B & r2_hidden(B,A))) & (all B (v1_relat_1(B) & v1_funct_1(B) -> -(A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))))))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1346 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1347 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1348 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,B) -> r1_ordinal1(k2_wellord2(k1_wellord2(A)),B)))) # label(t17_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1349 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1350 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1351 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1352 (all A all B (v1_relat_1(B) -> (k1_wellord2(A) = B <-> (all C all D (r2_hidden(D,A) & r2_hidden(C,A) -> (r1_tarski(C,D) <-> r2_hidden(k4_tarski(C,D),B)))) & A = k3_relat_1(B)))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1353 (all A (-v1_xboole_0(A) -> -((all B exists C ((all D k3_xboole_0(B,C) != k1_tarski(D)) & r2_hidden(C,A))) & (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r1_xboole_0(B,C) | C = B)) & (all B -(B = k1_xboole_0 & r2_hidden(B,A)))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1354 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> A = k1_wellord1(k1_wellord2(B),A)))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.75 1355 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & B = k2_relat_1(C) & k1_relat_1(C) = A)) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1356 (all A -(r2_hidden(A,f1_s2_wellord2) & (all B all C -(r2_hidden(B,f2_s2_wellord2) & p1_s2_wellord2(A,B,C) & r2_hidden(C,f3_s2_wellord2))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (exists B (v1_relat_1(B) & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & f1_s2_wellord2 = k1_relat_1(B) & k1_relat_1(A) = f1_s2_wellord2 & v1_funct_1(B))))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1357 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & (all B -((all C (v3_ordinal1(C) -> -r4_wellord1(k2_wellord1(A,k1_wellord1(A,B)),k1_wellord2(C)))) & r2_hidden(B,k3_relat_1(A)))) & v2_wellord1(A)))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1358 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1359 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1360 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1361 (all A all B (m1_relset_1(B,A,A) -> (v1_partfun1(B,A,A) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_funct_1(B) -> v1_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v2_funct_1(B)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1362 (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]. 4.74/4.76 1363 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (v1_relat_1(E) & D = E & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1364 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D)) & r2_hidden(D,B)))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1365 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1366 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k1_tarski(C) = k5_partfun1(A,B,k3_partfun1(C,A,B))))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1367 (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]. 4.74/4.76 1368 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1369 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1370 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1371 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1372 (all A all B all C (v1_funct_1(B) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> v1_funct_1(k5_funct_2(A,B,C)) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1373 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1374 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1375 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1376 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1377 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1378 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | B = k1_xboole_0))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1379 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1380 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1381 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1382 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1383 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1384 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> -(k1_xboole_0 != B & -v2_funct_1(C) & (exists D (v1_funct_2(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & m2_relset_1(D,B,A) & v1_funct_1(D)))))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1385 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1386 (all A all B all C all D (v1_funct_2(D,k1_tarski(A),B) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1387 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1388 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1389 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k4_funct_2(A,B,C) = B & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1390 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1391 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1392 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1393 (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]. 4.74/4.76 1394 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1395 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1396 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1397 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1398 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,D) = k2_funct_2(A,B,C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1399 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1400 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1401 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1402 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> v2_funct_1(C) & k2_relat_1(D) = A | k1_xboole_0 = B))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1403 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1404 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (B != k1_xboole_0 -> ((all D (k1_xboole_0 != D -> (all E (v1_funct_2(E,B,D) & m2_relset_1(E,B,D) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> E = F))))))) <-> B = k2_relat_1(C))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1405 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1406 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1407 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1408 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1409 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A ((all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1410 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,k10_relat_1(D,C)) <-> r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C)))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1411 (all A all B all C all D (m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1412 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1413 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1414 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (k5_partfun1(A,B,C) = k5_partfun1(A,B,D) & (all E B != k1_tarski(E)) -> D = C))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1415 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (-(B = k1_xboole_0 & A != k1_xboole_0 & C != k1_xboole_0) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1416 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1417 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))))) -> D = E))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1418 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> B = k1_xboole_0 & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1419 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1420 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (k2_relat_1(C) = B & v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> k1_xboole_0 = B | k2_funct_1(C) = D | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1421 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1422 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k2_relat_1(B) = k2_funct_2(A,A,B,A))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1423 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1424 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1425 (all A all B k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B)) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1426 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1427 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1428 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1429 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1430 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & B = k2_relat_1(C) -> k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k5_relat_1(k2_funct_1(C),C) = k6_partfun1(B) | B = k1_xboole_0))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1431 f3_s11_funct_2 != f4_s11_funct_2 -> (exists A (v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(f7_s11_funct_2(B) != k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) & B != f4_s11_funct_2 & B != f3_s11_funct_2))) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_1(A))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1432 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1433 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1434 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1435 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1436 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1437 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1438 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1439 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(C),B) & k1_relat_1(C) = A))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1440 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1441 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_xboole_0 -> v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1442 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1443 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1444 (all A all B all C all D all E (v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) & -v1_xboole_0(B) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1445 (all A all B all C (v1_funct_1(B) & v1_funct_1(C) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) -> v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_1(k4_funct_2(A,B,C)))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1446 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & B = k3_funct_2(A,A,C,k2_funct_2(A,A,C,B))))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1447 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (k1_xboole_0 != B -> (all E ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1448 (all A all B -(r2_hidden(A,f1_s5_funct_2) & (all C -(r2_hidden(C,f3_s5_funct_2) & p1_s5_funct_2(A,B,C))) & r2_hidden(B,f2_s5_funct_2))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1449 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) -> k2_funct_2(k1_xboole_0,A,C,B) = k1_xboole_0)) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1450 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1451 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1452 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1453 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (r2_hidden(C,A) & r2_hidden(D,A) & k1_funct_1(B,C) = k1_funct_1(B,D) -> D = C))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1454 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(C,A) -> k1_xboole_0 = B & A != k1_xboole_0 | v1_funct_1(k2_partfun1(A,B,D,C)) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & m2_relset_1(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1455 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> -(r2_hidden(C,B) & B = k2_relat_1(D) & (all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C))))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1456 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | k1_xboole_0 = B))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1457 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1458 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1459 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1460 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1461 (all A all B all C (m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1462 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1463 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1464 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1465 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k4_funct_2(A,C,B) = B & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1466 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1467 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1468 (all A all B all C (v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1469 (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]. 4.74/4.76 1470 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_funct_1(D,C) = B))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1471 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1472 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D -((all E -(D = k1_funct_1(C,E) & r2_hidden(E,A))) & r2_hidden(D,B))) -> k1_xboole_0 = B | k2_relat_1(C) = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1473 (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]. 4.74/4.76 1474 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1475 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & -v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1476 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (B = k2_relat_1(D) & k2_relat_1(E) = C -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | k1_xboole_0 = B))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1477 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C & C = k7_relset_1(A,A,A,B,k6_partfun1(A),C))) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1478 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1479 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> v1_partfun1(C,A,B) | A != k1_xboole_0 & k1_xboole_0 = B))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1480 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k4_relset_1(A,A,B) = A & r1_tarski(k2_relat_1(B),A))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1481 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1482 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1483 (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]. 4.74/4.76 1484 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1485 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & k1_xboole_0 != A | C = D))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1486 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1487 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> k2_relat_1(C) = B))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1488 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1489 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1490 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1491 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1492 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1493 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,k2_funct_2(A,B,C,A)) = A))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1494 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A ((all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1495 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1496 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1497 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1498 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1499 (exists A ((all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> f4_s8_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1500 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1501 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1502 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) & v2_funct_1(D) -> B = k1_xboole_0 | C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C))))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1503 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (A = k2_relat_1(B) & k2_relat_1(C) = A -> k2_relat_1(k4_funct_2(A,B,C)) = A))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1504 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (C = k5_funct_2(A,B,C) -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1505 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1506 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1507 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1508 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1509 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1510 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1511 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1512 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1513 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> k1_xboole_0 != A & k1_xboole_0 = B | v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1514 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1515 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1516 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1517 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -(-r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A) & (k1_xboole_0 = C -> k1_xboole_0 = B)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1518 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> -(A != k1_xboole_0 & k1_xboole_0 != B & -(v2_funct_1(C) <-> (all D all E (v1_funct_2(E,D,A) & m2_relset_1(E,D,A) & v1_funct_1(E) -> (all F (m2_relset_1(F,D,A) & v1_funct_2(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,E,C) = k1_partfun1(D,A,A,B,F,C) -> E = F))))))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1519 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1520 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> k1_xboole_0 != A & k1_xboole_0 = B | r1_partfun1(C,D)))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1521 (all A (r2_hidden(A,f1_s9_funct_2) -> (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)) & (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> f4_s9_funct_2(B) = k1_funct_1(A,B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1522 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k1_xboole_0 = C | B = k2_relat_1(D)))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1523 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F -(r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1524 (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]. 4.74/4.76 1525 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> B = k1_xboole_0 & k1_xboole_0 != A | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1526 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1527 (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]. 4.74/4.76 1528 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (v2_funct_1(C) <-> (all D all E (r2_hidden(D,A) & k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,A) -> E = D)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1529 (exists A (k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2 & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> f5_s10_funct_2(B) = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1530 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1531 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k2_relat_1(C) = k2_funct_2(A,B,C,A)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1532 (all A exists B (m1_relset_1(B,A,A) & v1_relat_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A) & v2_funct_1(B) & v1_funct_1(B))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1533 (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]. 4.74/4.76 1534 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1535 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1536 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1537 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_2(D,A,B) & v1_funct_1(D) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1538 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> B = k1_xboole_0 & A != k1_xboole_0 | v2_funct_1(D) | B != k1_xboole_0 & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1539 (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]. 4.74/4.76 1540 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1541 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1542 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) & B = k2_relat_1(D) -> k1_xboole_0 = C & k1_xboole_0 != B | v2_funct_1(D) & v2_funct_1(E)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1543 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (v2_funct_1(B) & A = k2_relat_1(B) -> v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1544 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1545 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A)))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1546 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_xboole_0 = B | k1_funct_1(E,C) = k1_funct_1(k9_relset_1(A,B,D,E),C)))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1547 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((B = k1_xboole_0 -> k1_xboole_0 = A) & (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E)))))))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1548 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> (k4_relset_1(A,B,C) = A <-> v1_funct_2(C,A,B))) & (k1_xboole_0 = B -> (C = k1_xboole_0 <-> v1_funct_2(C,A,B)) | k1_xboole_0 = A))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1549 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1550 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_1(C) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1551 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1552 (all A all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> k1_xboole_0 = C | r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C)))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1553 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B & B = k7_relset_1(A,A,A,A,k6_partfun1(A),B))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1554 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1555 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1556 (exists A (v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_1(A))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1557 (all A (A != k1_xboole_0 -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1558 (all A all B all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1559 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.76 1560 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> ((all C all D (k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1561 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1562 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & v2_funct_1(C) & (all E all F ((k1_funct_1(C,F) = E & r2_hidden(F,A) -> k1_funct_1(D,E) = F & r2_hidden(E,B)) & (r2_hidden(E,B) & F = k1_funct_1(D,E) -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) -> A = k1_xboole_0 | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1563 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1564 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1565 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1566 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1567 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A ((all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))) & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1568 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1569 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1570 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1571 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1572 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1573 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1574 (all A all B (A != k1_xboole_0 -> k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1575 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1576 (all A all B all C (v1_relat_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(A) -> v1_funct_1(k5_funcop_1(A,B,C)) & v1_relat_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1577 (all A all B all C all D all E (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1578 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1579 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_binop_1(B,k1_funct_1(A,C),D) = k1_funct_1(k4_funcop_1(B,A,D),C))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1580 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1581 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1582 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1583 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1584 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k5_funcop_1(C,E,D)) & m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1585 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(B) -> k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)) = D)) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1586 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1587 (all A (k1_xboole_0 = k1_relat_1(k2_funcop_1(k1_xboole_0,A)) & k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1588 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1589 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1590 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1591 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(A) = k1_relat_1(B) -> k1_relat_1(k5_relat_1(C,B)) = k1_relat_1(k5_relat_1(C,A))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1592 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1593 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1594 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1595 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1596 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B k1_funcop_1(k7_relat_1(A,B)) = k7_relat_1(k1_funcop_1(A),B)))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1597 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1598 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1599 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0 & k1_xboole_0 != B)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1600 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) = k5_funcop_1(A,B,C))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1601 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,B) & v1_funct_2(E,B,B) -> k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1602 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1603 (all A (v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1604 (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]. 4.74/4.77 1605 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1606 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1607 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k3_funcop_1(k5_relat_1(D,A),B,C) = k5_relat_1(k3_funcop_1(D,B,C),A))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1608 (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]. 4.74/4.77 1609 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k1_relat_1(A) -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1610 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1611 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1612 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1613 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1614 (all A all B (v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1615 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1616 (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]. 4.74/4.77 1617 (all A all B all C (r2_hidden(B,A) -> C = k1_funct_1(k2_funcop_1(A,C),B))) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1618 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1619 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1620 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k13_funct_3(B,C),A) = k3_funcop_1(A,B,C))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1621 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1622 (all A all B all C k2_funcop_1(k3_xboole_0(A,C),B) = k7_relat_1(k2_funcop_1(A,B),C)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1623 (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]. 4.74/4.77 1624 (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]. 4.74/4.77 1625 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1626 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1627 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1628 (all A all B (A = k1_relat_1(k2_funcop_1(A,B)) & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1629 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1630 (all A all B all C all D all E (-v1_xboole_0(A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) -> k4_funcop_1(C,D,E) = k7_funcop_1(A,B,C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1631 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F) = k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F))))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1632 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1633 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1634 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1635 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1636 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> v1_funct_1(k3_funcop_1(C,D,E)) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & m2_relset_1(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1637 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1638 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1639 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k10_funcop_1(A,B,C,D) = k1_funcop_1(D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1640 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1641 (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]. 4.74/4.77 1642 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B) & v1_funct_1(k4_funcop_1(C,D,E)))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1643 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1644 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & v1_funct_1(k10_funcop_1(A,B,C,D)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1645 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k8_funcop_1(B,A,C,E,D) = k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1646 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1647 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1648 (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]. 4.74/4.77 1649 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1650 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1651 (all A all B all C (r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = A)) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1652 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1653 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1654 (all A all B (v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1655 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k13_funct_3(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1656 (all A all B all C (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1657 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1658 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))) = k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1659 (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]. 4.74/4.77 1660 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1661 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k1_funct_1(A,C) = k4_tarski(D,E) -> k4_tarski(E,D) = k1_funct_1(B,C))) & -((all D all E k1_funct_1(A,C) != k4_tarski(D,E)) & k1_funct_1(A,C) != k1_funct_1(B,C)))) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1662 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1663 (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]. 4.74/4.77 1664 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1665 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1666 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1667 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> v1_funct_1(k8_funcop_1(A,B,C,D,E)) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1668 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1669 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1670 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1671 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) = k8_funct_2(A,B,F,G))) -> F = k6_funcop_1(B,A,C,D,E)))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1672 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1673 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1674 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1675 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1676 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1677 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(B) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1678 (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]. 4.74/4.77 1679 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1680 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k2_funcop_1(k10_relat_1(A,B),C) = k5_relat_1(A,k2_funcop_1(B,C))))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1681 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1682 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1683 (all A all B k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B))) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1684 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1685 (all A (v1_relat_1(A) -> (all B all C (A = k2_zfmisc_1(B,C) -> k1_xboole_0 = C | C = k2_relat_1(A) & k1_relat_1(A) = B | B = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1686 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1687 (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]. 4.74/4.77 1688 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1689 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1690 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(B,D),k1_relat_1(F)) & r2_hidden(k4_tarski(A,C),k1_relat_1(E)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1691 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = k2_funct_4(k2_funct_4(C))))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1692 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1693 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1694 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1695 (all A all B all C all D k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D))) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1696 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1697 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1698 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_funcop_1(A,C),k2_funcop_1(B,C)))) # label(t5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1699 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))) = k5_relat_1(B,A))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1700 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1701 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(B,C) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1702 (all A all B all C all D all E all F (k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) -> D = F & C = E | A = B)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1703 (all A all B all C all D all E all F all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1704 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> r1_tarski(A,k1_funct_4(A,B))))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1705 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(A,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1706 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1707 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1708 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(B) = k1_relat_1(C) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1709 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(B,A) = k1_funct_4(A,B)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1710 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1711 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_funct_4(A,B)) & v1_funct_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1712 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> v1_funct_1(k5_funct_4(A,B,C,D,E)) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1713 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1714 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),E) & v1_funct_2(G,k2_zfmisc_1(A,B),E) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) -> v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1715 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1716 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(k1_relat_1(B),C) -> A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1717 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1718 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k1_funct_4(C,D),A,B) & v1_funct_1(k1_funct_4(C,D)))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1719 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(B),D) -> k7_relat_1(k1_funct_4(A,B),C) = A & k7_relat_1(k1_funct_4(A,B),D) = B)))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1720 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_funct_1(E,A) = C & D = k1_funct_1(E,B) & k1_relat_1(E) = k2_tarski(A,B) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.77 1721 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(A,D)) & (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))) & k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) <-> C = k1_funct_4(A,B)))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1722 (all A all B all C all D (B != A -> k1_funct_1(k4_funct_4(A,B,C,D),B) = D & C = k1_funct_1(k4_funct_4(A,B,C,D),A))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1723 (all A -((all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1724 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1725 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1726 (all A all B (r1_tarski(k6_partfun1(A),k6_partfun1(B)) <-> r1_tarski(A,B))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1727 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1728 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(k2_funct_4(C),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(B,A))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1729 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_4(A)) & v1_funct_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1730 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(A,B) & B = k1_funct_4(B,A)))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1731 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k3_funct_4(A,B) = C <-> (all D ((exists E exists F exists G exists H (k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)))) <-> r2_hidden(D,k1_relat_1(C)))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),k1_relat_1(B)) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) -> k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))) = k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G)))))))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1732 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funct_4(A,k1_xboole_0))) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1733 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> v1_funct_1(k2_funct_4(D)) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1734 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k2_xboole_0(A,B) = k1_funct_4(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1735 (all A (v1_funct_1(A) & v1_relat_1(A) -> (exists B exists C r1_tarski(k1_relat_1(k2_funct_4(A)),k2_zfmisc_1(B,C))))) # label(t45_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1736 (all A all B all C all D (v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1737 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_funct_4(A,k1_funct_4(B,C)) = k1_funct_4(k1_funct_4(A,B),C))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1738 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1739 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)) = B)))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1740 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k1_funct_4(B,C))) <-> r2_hidden(A,k1_relat_1(C)) | r2_hidden(A,k1_relat_1(B))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1741 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1742 (all A all B all C all D (r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) & k2_tarski(A,B) = k1_relat_1(k4_funct_4(A,B,C,D)))) # label(t65_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1743 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1744 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1745 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> B = D | A = k1_xboole_0)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1746 (all A all B all C all D (A != C -> k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = k4_funct_4(A,C,B,D))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1747 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k2_funct_4(C)),k2_zfmisc_1(B,A))))) # label(t46_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1748 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k2_funct_4(C)) = k2_zfmisc_1(B,A)))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1749 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1750 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1751 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> k1_funct_4(A,A) = A)) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1752 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = k7_relat_1(A,k2_xboole_0(B,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1753 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (C = k4_tarski(E,D) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)))))) & (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(B,k4_tarski(D,C)) = k1_funct_1(A,k4_tarski(C,D)))) <-> k2_funct_4(A) = B))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1754 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1755 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F))) -> k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1756 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (k1_xboole_0 != C -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1757 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1758 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1759 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1760 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) = k7_relat_1(k1_funct_4(A,B),C)))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1761 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_1(k2_funct_4(D)) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1762 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(k1_xboole_0,A) = A)) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1763 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_partfun1(A,B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1764 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (k1_xboole_0 != C -> D = k2_funct_4(k2_funct_4(D))))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1765 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> r1_tarski(A,C))) # label(t6_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1766 (all A all B all C all D (B != A -> k2_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(C,D))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1767 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1768 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1769 (all A all B k6_partfun1(k2_xboole_0(A,B)) = k1_funct_4(k6_partfun1(A),k6_partfun1(B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1770 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_xboole_0(A,B) = k1_funct_4(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.74/4.78 1771 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1772 (all A all B all C k4_funct_4(A,B,C,C) = k2_funcop_1(k2_tarski(A,B),C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1773 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1774 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1775 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> A = k7_relat_1(k1_funct_4(A,B),k1_relat_1(A))))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1776 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1777 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_4(A,B)) & v1_relat_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1778 (all A all B all C all D all E all F all G (v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) -> -(F != k1_xboole_0 & -(v1_funct_1(k3_funct_4(G,H)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F))) & k1_xboole_0 != C))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1779 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (k2_zfmisc_1(C,D) = k1_relat_1(F) & k2_zfmisc_1(A,B) = k1_relat_1(E) -> k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k1_relat_1(k3_funct_4(E,F))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1780 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1781 (all A all B k1_tarski(k4_tarski(A,B)) = k2_funcop_1(k1_tarski(A),B)) # label(t70_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1782 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1783 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1784 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1785 (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]. 4.87/4.89 1786 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1787 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> k1_xboole_0 = A | (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k15_ordinal2(A,B) = k3_tarski(k8_ordinal2(C)))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1788 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D))))) & f4_s12_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = f2_s12_ordinal2(A)))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> k1_xboole_0 = A | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> f4_s12_ordinal2 = k1_funct_1(f1_s12_ordinal2,k1_xboole_0)) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1789 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1790 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k16_ordinal2(B,D) = k1_funct_1(C,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1791 (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]. 4.87/4.89 1792 (all A all B (v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v1_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1793 (all A (v3_ordinal1(A) -> A = k3_tarski(k1_ordinal1(A)))) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1794 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k4_ordinal2 & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> E = k1_xboole_0 | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal1(B) = k1_relat_1(D) & k1_ordinal2(D) = C & v5_ordinal1(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1795 (all A all B (v3_ordinal1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1796 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & k1_ordinal1(A) = k1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k1_funct_1(D,k1_ordinal1(E)) = k14_ordinal2(k1_funct_1(D,E),B)))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1797 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1798 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1799 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1800 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.89 1801 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t50_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1802 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s5_ordinal2 & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> f2_s5_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> B = k1_xboole_0 | f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1803 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1804 (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]. 4.87/4.91 1805 (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]. 4.87/4.91 1806 (all A all B (B = k2_ordinal2(A) <-> (all C (v3_ordinal1(C) & r2_hidden(C,A) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1807 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & f1_s9_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s9_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v5_ordinal1(C))) <-> B = f4_s9_ordinal2(A))))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1808 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | A = k1_xboole_0))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1809 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1810 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1811 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1812 (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]. 4.87/4.91 1813 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A))))) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1814 (all A (v3_ordinal1(A) -> A = k2_ordinal2(A))) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1815 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1816 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1817 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1818 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1819 (all A all B (v1_relat_1(A) & v3_ordinal1(B) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1820 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = A -> (r1_ordinal2(A,B) <-> (exists C (v3_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) & r1_ordinal1(C,D) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)))))) & (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(C,k1_funct_1(B,F)) & r2_hidden(k1_funct_1(B,F),D)))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1821 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(A,k1_xboole_0))) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1822 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1823 (all A (v3_ordinal1(A) -> (all B ((exists C (k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s8_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = f1_s8_ordinal2(A))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1824 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (B = k10_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & B = k9_ordinal2(C) & v1_ordinal2(C) & v5_ordinal1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1825 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k1_ordinal2(A) = k1_funct_1(A,k3_tarski(k1_relat_1(A))))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1826 (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]. 4.87/4.91 1827 (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]. 4.87/4.91 1828 (all A (v4_ordinal2(A) <-> r2_hidden(A,k5_ordinal2))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1829 (exists A (v1_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1830 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k1_funct_1(A,B) & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> k1_xboole_0 = B | r1_ordinal2(C,k2_ordinal1(A,B)))))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1831 k1_xboole_0 != f2_s10_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & f2_s10_ordinal2 = k1_relat_1(f1_s10_ordinal2) & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B (f3_s10_ordinal2(A) = B <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & k1_relat_1(C) = k1_ordinal1(A))))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1832 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1833 (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]. 4.87/4.91 1834 (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]. 4.87/4.91 1835 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1836 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_ordinal1(k14_ordinal2(A,B)) = k14_ordinal2(A,k1_ordinal1(B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1837 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1838 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k14_ordinal2(A,B) = C <-> (exists D (v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> E = k1_xboole_0 | k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E))))) & A = k1_funct_1(D,k1_xboole_0) & k1_ordinal1(B) = k1_relat_1(D) & k1_ordinal2(D) = C & v1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1839 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1840 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s14_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1841 (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]. 4.87/4.91 1842 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.91 1843 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (v2_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C)))))))))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1844 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1845 (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]. 4.87/4.93 1846 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1847 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (B = k12_ordinal2(A) <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1848 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1849 (all A (v3_ordinal1(A) -> (exists B (v4_ordinal1(B) & r2_hidden(A,B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1850 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1851 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1852 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1853 (exists A (v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v5_ordinal1(A) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1854 (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]. 4.87/4.93 1855 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(k4_ordinal2,A) & A = k16_ordinal2(A,k4_ordinal2))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1856 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> k1_xboole_0 = k2_ordinal2(B) | r1_ordinal1(A,k6_ordinal2(B)))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1857 (all A (v3_ordinal1(A) -> (all B all C (r1_tarski(B,C) & r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1858 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v1_funct_1(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | C = k1_xboole_0))) & A = k1_ordinal2(B) & v1_ordinal2(B) & v5_ordinal1(B))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.87/4.93 1859 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_xboole_0 = D | f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & v1_ordinal2(C))) & B != A & (exists C (v1_relat_1(C) & v5_ordinal1(C) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> D = k1_xboole_0 | f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & A = k1_ordinal2(C) & v1_ordinal2(C) & v1_funct_1(C)))))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1860 (exists A (v1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1861 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1862 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k7_ordinal2(B)) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & r1_ordinal1(A,C)))))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1863 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1864 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1865 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & A = k1_ordinal2(B) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s7_ordinal2(C,k1_funct_1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | C = k1_xboole_0))) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(B))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1866 (all A all B -((exists C (v1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_ordinal2(C) = A & v5_ordinal1(C) & v1_funct_1(C))) & A != B & (exists C (k1_ordinal2(C) = B & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1867 (all A (v3_ordinal1(A) -> k15_ordinal2(k1_xboole_0,A) = k1_xboole_0)) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1868 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> k1_xboole_0 = A | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1869 (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]. 4.87/4.94 1870 (all A all B (v3_ordinal1(B) -> (r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) <-> B = k7_ordinal2(A)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1871 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1872 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.94 1873 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1874 (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]. 4.87/4.95 1875 (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]. 4.87/4.95 1876 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1877 (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]. 4.87/4.95 1878 (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]. 4.87/4.95 1879 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(A,k16_ordinal2(A,B)) = k16_ordinal2(A,k1_ordinal1(B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1880 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (B = k11_ordinal2(A) <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & B = k8_ordinal2(C) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1881 (all A all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1882 (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]. 4.87/4.95 1883 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1884 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1885 (all A (A = k5_ordinal2 <-> v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v4_ordinal1(A) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1886 (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]. 4.87/4.95 1887 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1888 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1889 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.87/4.95 1890 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f3_s16_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s16_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & v1_ordinal2(C)))))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & v4_ordinal1(f2_s16_ordinal2) & k1_xboole_0 != f2_s16_ordinal2 -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1891 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1892 (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_funct_1(C,k1_xboole_0) = f4_s6_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> f2_s6_ordinal2(A) = k1_funct_1(f1_s6_ordinal2,A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1893 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1894 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_relat_1(C))) <-> B = f4_s15_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1895 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s11_ordinal2 & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> B = k1_xboole_0 | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & v5_ordinal1(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1896 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1897 (all A all B ((all C (r2_hidden(C,A) & (exists D (v3_ordinal1(D) & v4_ordinal1(D) & D = C)) <-> r2_hidden(C,B))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1898 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)) & k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1899 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1900 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1901 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A)) | k1_xboole_0 = A))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1902 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1903 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & A = k14_ordinal2(B,C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1904 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1905 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1906 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1907 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1908 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1909 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1910 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1911 (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]. 4.98/5.00 1912 (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]. 4.98/5.00 1913 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1914 (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]. 4.98/5.00 1915 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & (all C -((all D (r2_hidden(D,B) & r1_tarski(C,D) -> C = D)) & r2_hidden(C,B)))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1916 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1917 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1918 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1919 (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]. 4.98/5.00 1920 (all A exists B (v1_xboole_0(B) & v1_relat_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1921 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1922 (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]. 4.98/5.00 1923 (all A -((all B -((all C (r2_hidden(C,A) -> r1_tarski(B,C))) & r2_hidden(B,A))) & v6_ordinal1(A) & A != k1_xboole_0 & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1924 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1925 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1926 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1927 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1928 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(D) & v1_finset_1(C) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1929 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1930 (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]. 4.98/5.00 1931 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1932 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1933 (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]. 4.98/5.00 1934 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> A = k1_xboole_0 | v1_finset_1(B))) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1935 (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]. 4.98/5.00 1936 (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]. 4.98/5.00 1937 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1938 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1939 v1_finset_1(f1_s2_finset_1) & (all A all B (r2_hidden(A,f1_s2_finset_1) & r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & p1_s2_finset_1(k1_xboole_0) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1940 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1941 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(C,B))))) & v6_ordinal1(A) & k1_xboole_0 != A & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1942 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1943 (all A (v1_finset_1(A) & (all B (r2_hidden(B,A) -> v1_finset_1(B))) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1944 (exists A (v1_relat_1(A) & f1_s1_finset_1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (-p1_s1_finset_1(B) -> f3_s1_finset_1(B) = k1_funct_1(A,B)) & (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B))))) & v1_funct_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1945 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1946 (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]. 4.98/5.00 1947 (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]. 4.98/5.00 1948 (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]. 4.98/5.00 1949 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1950 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1951 (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]. 4.98/5.00 1952 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1953 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1954 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(A) <-> v1_finset_1(k1_relat_1(A))))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1955 (all A (v1_finset_1(A) <-> (exists B (r2_hidden(k1_relat_1(B),k5_ordinal2) & k2_relat_1(B) = A & v1_funct_1(B) & v1_relat_1(B))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1956 (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]. 4.98/5.00 1957 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> v1_finset_1(B) | k1_xboole_0 = A)) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1958 (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]. 4.98/5.00 1959 (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]. 4.98/5.00 1960 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1961 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1962 (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]. 4.98/5.00 1963 (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]. 4.98/5.00 1964 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1965 (all A ((exists B (np__0 = k1_funct_1(B,k13_arytm_3) & A = B & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))) <-> r2_hidden(A,a_0_0_numbers))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1966 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1967 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1968 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1969 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1970 (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]. 4.98/5.00 1971 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-r1_xreal_0(B,A) <-> r2_hidden(k1_card_1(A),k1_card_1(B))))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1972 (all A (v3_ordinal1(A) -> k3_card_1(k1_ordinal1(A)) = k2_card_1(k3_card_1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1973 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1974 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v2_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1975 (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]. 4.98/5.00 1976 (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]. 4.98/5.00 1977 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = k1_card_1(k5_numbers) & B = k1_ordinal2(C) & v5_ordinal1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1978 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1979 (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]. 4.98/5.00 1980 (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]. 4.98/5.00 1981 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> k2_card_1(B) != A)) <-> v2_card_1(A)))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1982 (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]. 4.98/5.00 1983 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1984 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1985 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1986 (all A all B (k1_card_1(A) = k1_card_1(B) -> k2_card_1(B) = k2_card_1(A))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1987 (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]. 4.98/5.00 1988 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1989 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1990 (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]. 4.98/5.00 1991 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1992 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (r1_tarski(A,k2_relat_1(C)) & B = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1993 (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]. 4.98/5.00 1994 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) & r2_wellord2(A,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1995 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1996 (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]. 4.98/5.00 1997 (all A (v1_card_1(A) -> v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1998 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 1999 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2000 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2001 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2002 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2003 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2004 (all A (m1_subset_1(A,k5_numbers) -> v2_ordinal1(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2005 (all A (v3_ordinal1(A) -> v2_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v3_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2006 (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]. 4.98/5.00 2007 (exists A (v1_finset_1(A) & v1_card_1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2008 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2009 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2010 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2011 (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]. 4.98/5.00 2012 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2013 (all A all B (v1_card_1(B) -> (B = k1_card_1(A) <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2014 (all A k4_card_1(k1_tarski(A)) = np__1) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2015 (all A all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) & (all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2016 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2017 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2018 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> k1_xboole_0 = A | p1_s1_card_1(A)))) & (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & p1_s1_card_1(k1_xboole_0) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2019 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k1_card_1(A))) # label(t66_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2020 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2021 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2022 (all A all B all C (r1_tarski(A,B) & r2_wellord2(A,C) & r1_tarski(B,C) -> r2_wellord2(A,B) & r2_wellord2(B,C))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2023 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2024 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2025 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2026 (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]. 4.98/5.00 2027 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_ordinal1(A,B) <-> r1_xreal_0(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2028 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2029 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (A = B <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2030 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2031 (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]. 4.98/5.00 2032 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2033 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k3_card_1(C)))) & A = k1_relat_1(B) -> k3_card_1(A) = k1_card_1(k8_ordinal2(B)))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2034 (all A (v1_finset_1(A) -> v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2035 (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]. 4.98/5.00 2036 (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]. 4.98/5.00 2037 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2038 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k4_card_1(A) = B <-> k1_card_1(A) = k1_card_1(B)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2039 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2040 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2041 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(A) = k3_card_1(B) -> A = B))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2042 (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]. 4.98/5.00 2043 (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]. 4.98/5.00 2044 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2045 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2046 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2047 (all A (v1_card_1(A) <-> (exists B ((all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))) & B = A & v3_ordinal1(B))))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2048 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2049 (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]. 4.98/5.00 2050 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2051 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2052 (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]. 4.98/5.00 2053 (all A (v1_finset_1(A) -> k4_card_1(A) = k1_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2054 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2055 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2056 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2057 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2058 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r1_tarski(A,B) & B != A <-> r2_hidden(A,B)))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2059 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2060 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2061 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2062 (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]. 4.98/5.00 2063 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2064 (all A all B all C all D (r1_xboole_0(A,B) & r1_xboole_0(C,D) & r2_wellord2(B,D) & r2_wellord2(A,C) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2065 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2066 (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]. 4.98/5.00 2067 (all A (r2_wellord2(A,k1_xboole_0) <-> k1_xboole_0 = A)) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2068 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2069 (all A all B (r2_wellord2(A,B) -> k2_card_1(A) = k2_card_1(B))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2070 (all A all B (k1_card_1(k1_tarski(B)) = k1_card_1(A) <-> (exists C A = k1_tarski(C)))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2071 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2072 (all A all B (r2_wellord2(A,B) <-> k1_card_1(A) = k1_card_1(B))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2073 (all A all B all C all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (np__3 = k3_finseq_1(D) & B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & A = k1_funct_1(D,np__1) <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2074 (all A (v1_relat_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2075 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2076 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2077 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> B = A))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2078 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k5_finseq_1(B) = k12_finseq_1(A,B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2079 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2080 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -((all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A))) & A != k1_xboole_0))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2081 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B))) & r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))))) -> (exists A (k2_finseq_1(f2_s5_finseq_1) = k4_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & m2_finseq_1(A,f1_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2082 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2083 (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]. 4.98/5.00 2084 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2085 (all A (v4_ordinal2(A) -> k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(A))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2086 (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]. 4.98/5.00 2087 (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]. 4.98/5.00 2088 (all A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2089 (all A all B all C (m1_finseq_1(B,A) & v4_ordinal2(C) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2090 (exists A all B ((exists C (v1_relat_1(C) & v1_finseq_1(C) & r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & B = C & p1_s4_finseq_1(C) & v1_funct_1(C))) <-> r2_hidden(B,A))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2091 (all A all B (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2092 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) = A)))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2093 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2094 (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]. 4.98/5.00 2095 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2096 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)) = A)) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2097 (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]. 4.98/5.00 2098 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2099 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(B) = k2_finseq_1(A) -> B = A))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2100 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(A,C) & m2_finseq_1(B,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2101 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2102 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (k4_finseq_1(A) = k1_xboole_0 <-> k1_xboole_0 = A))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2103 (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> k1_funct_1(A,B) = f2_s2_finseq_1(B)))) & f1_s2_finseq_1 = k3_finseq_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2104 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2105 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.00 2106 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) & p1_s3_finseq_1(k1_xboole_0) -> (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2107 (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]. 4.98/5.01 2108 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2109 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2110 (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]. 4.98/5.01 2111 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) = k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2112 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2113 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2114 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2115 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k2_relat_1(A) & v2_funct_1(B) & v2_funct_1(A) -> k3_finseq_1(A) = k3_finseq_1(B)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2116 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2117 (all A all B (m1_finseq_1(B,A) -> v1_xboole_0(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2118 (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]. 4.98/5.01 2119 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k6_finseq_1(B) = A <-> np__0 = k3_finseq_1(A))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2120 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2121 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (k3_finseq_1(C) = A & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2122 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2123 (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]. 4.98/5.01 2124 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_finseq_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2125 (all A (-v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2126 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2127 (all A (v1_funct_1(k9_finseq_1(A)) & v1_relat_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2128 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2129 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> r1_xreal_0(C,k3_finseq_1(A)) | k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2130 (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]. 4.98/5.01 2131 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) -> k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,C)))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2132 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2133 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2134 (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]. 4.98/5.01 2135 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2136 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (C = k7_relat_1(B,k2_finseq_1(A)) & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C) & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2137 (all A exists B (v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_relat_1(B) & m1_finseq_1(B,A))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2138 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2139 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k2_relat_1(k14_finseq_1(k1_relat_1(A))) = k1_relat_1(A))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2140 (all A (v4_ordinal2(A) -> k4_card_1(k2_finseq_1(A)) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2141 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_card_1(A) = A & k4_card_1(k1_card_1(A)) = A)) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2142 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k2_finseq_1(np__1) & A = k1_funct_1(B,np__1) <-> k9_finseq_1(A) = B))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2143 (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]. 4.98/5.01 2144 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2145 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k7_finseq_1(A,k1_xboole_0) = A & k7_finseq_1(k1_xboole_0,A) = A)) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2146 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (np__1 = k3_finseq_1(B) & A = k1_funct_1(B,np__1) <-> B = k9_finseq_1(A)))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2147 (exists A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2148 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2149 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A))))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2150 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2151 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2152 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2153 (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]. 4.98/5.01 2154 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2155 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2156 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) <-> C = k7_finseq_1(A,B)))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2157 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> -(r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> k7_finseq_1(A,E) != C)) & k7_finseq_1(C,D) = k7_finseq_1(A,B)))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2158 (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]. 4.98/5.01 2159 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,k3_relat_1(A)) & (exists E (v1_relat_1(E) & v1_funct_1(E) & r1_xreal_0(np__1,k3_finseq_1(E)) & k1_funct_1(E,np__1) = C & k1_funct_1(E,k3_finseq_1(E)) = D & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r1_xreal_0(k3_finseq_1(E),F) | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A)))) & v1_finseq_1(E))) & r2_hidden(D,k3_relat_1(A))))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2160 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -(r2_hidden(A,B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k4_tarski(C,k1_funct_1(B,C)) = A & r2_hidden(C,k4_finseq_1(B)))))))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2161 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_finseq_1(B)) <-> (exists C (r1_xreal_0(C,B) & r1_xreal_0(np__1,C) & A = C & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2162 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2163 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(np__1,A) & r1_xreal_0(A,B) <-> r2_hidden(A,k2_finseq_1(B))))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2164 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2165 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(D = A & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B)))))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2166 (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]. 4.98/5.01 2167 (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]. 4.98/5.01 2168 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2169 (all A k6_finseq_1(A) = k1_xboole_0) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2170 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k3_finseq_1(A) = k3_finseq_1(B) -> A = B))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2171 (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]. 4.98/5.01 2172 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2173 (all A all B all C (v1_funct_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2174 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & (all B -p1_s1_finseq_1(A,B))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) -> C = B)))) -> (exists A (v1_relat_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1) & v1_funct_1(A))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2175 (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]. 4.98/5.01 2176 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2177 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2178 (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]. 4.98/5.01 2179 (all A all B all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k1_funct_1(C,np__1) & k1_funct_1(C,np__2) = B & k3_finseq_1(C) = np__2 <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2180 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k7_finseq_1(A,B) -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2181 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2182 (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]. 4.98/5.01 2183 (all A all B all C k11_finseq_1(A,B,C) = k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C))) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2184 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2185 (all A (v4_ordinal2(A) -> r2_hidden(A,k2_finseq_1(A)) | np__0 = A)) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2186 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2187 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(k7_finseq_1(A,B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2188 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_relat_1(A) = k2_finseq_1(B) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2189 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (k7_finseq_1(B,A) = k7_finseq_1(B,C) | k7_finseq_1(C,B) = k7_finseq_1(A,B) -> C = A))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2190 (all A (v1_finset_1(A) <-> (exists B (v1_funct_1(B) & A = k2_relat_1(B) & v1_finseq_1(B) & v1_relat_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2191 (all A all B (m2_finseq_1(B,A) -> v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) & v1_funct_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2192 (exists A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2193 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k9_finseq_1(A) = B <-> k2_relat_1(B) = k1_tarski(A) & k2_finseq_1(np__1) = k4_finseq_1(B)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2194 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_relat_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2195 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2196 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2197 (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]. 4.98/5.01 2198 (all A (v1_funct_1(A) & v1_relat_1(A) -> -((all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -r1_tarski(A,B))) & (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B))))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2199 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (k1_xboole_0 = k14_finseq_1(A) <-> A = k1_xboole_0))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2200 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2201 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2202 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> A = k1_xboole_0))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2203 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1))) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2204 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> k1_card_1(A) = k3_finseq_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2205 (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]. 4.98/5.01 2206 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2207 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k3_finseq_1(A) = np__0 <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2208 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) = k2_finseq_1(A) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2209 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2210 (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]. 4.98/5.01 2211 (all A (v4_ordinal2(A) -> a_1_0_finseq_1(A) = k1_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2212 (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]. 4.98/5.01 2213 (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]. 4.98/5.01 2214 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2215 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2216 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2217 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (B = k9_finseq_1(A) <-> np__1 = k3_finseq_1(B) & k1_tarski(A) = k2_relat_1(B)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2218 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2219 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2220 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) = k15_finseq_1(A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2221 (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]. 4.98/5.01 2222 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2223 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_finseq_1(A) -> v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2224 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k14_finseq_1(A) = B <-> k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(-r1_xreal_0(D,C) & F = k1_funct_1(B,D) & r1_xreal_0(F,E) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,C))))))))))))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2225 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2226 (all A all B ((all C (r2_hidden(C,B) <-> m2_finseq_1(C,A))) <-> k13_finseq_1(A) = B)) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2227 (exists A (v1_xboole_0(A) & v2_funct_1(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2228 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2229 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> r1_tarski(k2_finseq_1(A),k2_finseq_1(B))))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2230 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2231 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2232 (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]. 4.98/5.01 2233 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(-r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(D,k4_finseq_1(B)) & k1_nat_1(k3_finseq_1(A),D) = C))) & r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B)))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2234 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2235 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2236 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2237 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v3_orders_1(A) & v2_orders_1(A) & v1_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2238 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2239 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2240 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) <-> r1_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2241 (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]. 4.98/5.01 2242 (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]. 4.98/5.01 2243 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2244 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v1_orders_1(A) & v2_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2245 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2246 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2247 (all A (v1_relat_1(A) -> (all B (v4_relat_2(A) & r9_orders_1(A,B) -> r7_orders_1(A,B))))) # label(t157_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2248 (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) -> k3_relat_1(B) = A)) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2249 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2250 (all A -((all B -((all C -(r1_tarski(C,B) & C != B & r2_hidden(C,A))) & r2_hidden(B,A))) & (all B -(v6_ordinal1(B) & (all C -((all D (r2_hidden(D,B) -> r1_tarski(C,D))) & r2_hidden(C,A))) & r1_tarski(B,A))) & k1_xboole_0 != A)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2251 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2252 (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]. 4.98/5.01 2253 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2254 (all A all B all C all D (v4_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) & v1_relat_2(D) -> (r2_hidden(B,A) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(C,A) -> C = B))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2255 (all A (v1_relat_1(A) -> (all B (r9_orders_1(k4_relat_1(A),B) <-> r8_orders_1(A,B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2256 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2257 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2258 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(B,C),A) & C != B & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A)) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2259 (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]. 4.98/5.01 2260 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2261 (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)) -> r2_hidden(k4_tarski(C,B),A) | B = C)))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2262 (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]. 4.98/5.01 2263 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) & r6_relat_2(A,B) & r4_relat_2(A,B) & r1_relat_2(A,B) <-> r3_orders_1(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2264 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2265 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2266 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2267 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2268 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & r1_tarski(B,C) & B != C)))) & (all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k3_tarski(B),A) | B = k1_xboole_0)))) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2269 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2270 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2271 (all A (v1_relat_1(A) -> (all B all C (r8_orders_1(A,B) & v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r2_hidden(B,C) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2272 (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]. 4.98/5.01 2273 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2274 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2275 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2276 (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]. 4.98/5.01 2277 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r2_orders_1(A,B) & r3_orders_1(A,B) & r1_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2278 (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]. 4.98/5.01 2279 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2280 (all A (v1_relat_1(A) -> (v3_orders_1(A) <-> v1_relat_2(A) & v6_relat_2(A) & v4_relat_2(A) & v8_relat_2(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2281 (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]. 4.98/5.01 2282 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2283 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2284 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2285 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2286 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2287 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) <-> (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A) | B = C)) & r2_hidden(B,k3_relat_1(A)))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2288 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2289 (all A (v1_relat_1(A) -> (all B (r7_orders_1(k4_relat_1(A),B) <-> r6_orders_1(A,B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2290 (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]. 4.98/5.01 2291 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & k3_relat_1(A) = B & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2292 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2293 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2294 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) & v6_relat_2(A) -> r9_orders_1(A,B))))) # label(t159_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2295 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2296 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2297 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2298 (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]. 4.98/5.01 2299 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2300 (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]. 4.98/5.01 2301 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2302 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2303 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> k3_relat_1(B) = A)) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2304 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2305 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2306 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2307 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2308 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2309 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2310 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2311 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C (v1_relat_1(C) -> -(r1_tarski(A,C) & k3_relat_1(C) = B & r3_orders_1(C,B)))) & r2_orders_1(A,B))))) # label(t179_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2312 (all A (v1_relat_1(A) -> (v2_orders_1(A) <-> v4_relat_2(A) & v8_relat_2(A) & v1_relat_2(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2313 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2314 (all A (v1_relat_1(A) -> (all B (r8_orders_1(k4_relat_1(A),B) <-> r9_orders_1(A,B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.01 2315 (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]. 4.98/5.02 2316 (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]. 4.98/5.02 2317 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2318 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2319 (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]. 4.98/5.02 2320 (all A all B all C (v4_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & 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]. 4.98/5.02 2321 (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]. 4.98/5.02 2322 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2323 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2324 (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]. 4.98/5.02 2325 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2326 (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]. 4.98/5.02 2327 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> k5_relset_1(A,A,B) = A & k4_relset_1(A,A,B) = A)) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2328 (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]. 4.98/5.02 2329 (all A (v1_relat_1(A) -> (all B -(B = k1_xboole_0 & r4_orders_1(A,B))))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2330 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2331 (all A all B (v1_relat_1(B) -> (r7_relat_2(B,A) <-> r1_relat_2(B,A) & r6_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2332 (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) -> r1_orders_1(B,A))) # label(t139_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2333 (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]. 4.98/5.02 2334 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2335 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2336 (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]. 4.98/5.02 2337 (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]. 4.98/5.02 2338 (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]. 4.98/5.02 2339 (all A (v1_relat_1(A) -> (all B all C (r2_hidden(B,C) & r9_orders_1(A,B) & r1_tarski(C,k3_relat_1(A)) & v1_relat_2(A) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2340 (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]. 4.98/5.02 2341 (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]. 4.98/5.02 2342 (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]. 4.98/5.02 2343 (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]. 4.98/5.02 2344 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2345 (all A (r2_orders_1(k6_partfun1(A),A) & r1_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2346 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2347 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2348 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2349 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2350 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2351 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2352 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2353 (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]. 4.98/5.02 2354 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2355 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2356 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2357 (all A (v1_relat_1(A) -> (all B (r4_orders_1(k4_relat_1(A),B) <-> r5_orders_1(A,B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2358 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2359 (all A (-((exists B (r2_hidden(B,A) & k1_xboole_0 != B)) & k1_xboole_0 = k3_tarski(A)) & -((all B -(B != k1_xboole_0 & r2_hidden(B,A))) & k3_tarski(A) != k1_xboole_0))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2360 (all A (v2_orders_1(k6_partfun1(A)) & v1_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2361 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2362 (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]. 4.98/5.02 2363 (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]. 4.98/5.02 2364 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) & r1_relat_2(A,B) <-> r1_orders_1(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2365 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2366 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2367 (all A (v1_relat_1(A) -> (all B ((all C -((all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))) & r2_hidden(D,B))) & v3_orders_1(k2_wellord1(A,C)) & r1_tarski(C,B))) <-> r5_orders_1(A,B))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2368 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v1_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)) & v4_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2369 (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]. 4.98/5.02 2370 (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]. 4.98/5.02 2371 (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]. 4.98/5.02 2372 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2373 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2374 (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]. 4.98/5.02 2375 (all A all B (v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2376 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2377 (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]. 4.98/5.02 2378 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2379 (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]. 4.98/5.02 2380 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2381 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2382 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2383 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2384 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2385 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2386 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> k4_relset_1(A,A,B) = A & k3_relat_1(B) = A))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2387 (all A -((all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & r1_tarski(B,C) & B != C)))) & (all B -(v6_ordinal1(B) & (all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & r1_tarski(B,A))) & k1_xboole_0 != A)) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2388 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & (all D -(r2_hidden(D,B) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))))) & v3_orders_1(k2_wellord1(A,C)))) <-> r4_orders_1(A,B))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2389 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & C != B & r1_tarski(C,B))))) & (all B (r1_tarski(B,A) & v6_ordinal1(B) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)))) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2390 (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]. 4.98/5.02 2391 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2392 (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]. 4.98/5.02 2393 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2394 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2395 (all A (v1_relat_1(A) -> (all B (r3_orders_1(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)) & v1_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2396 (all A all B (v1_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v4_relat_2(B) -> v1_orders_1(B))) # label(t111_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2397 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r1_orders_1(A,B) -> r1_orders_1(A,C))))) # label(t128_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2398 (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]. 4.98/5.02 2399 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2400 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2401 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2402 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2403 (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]. 4.98/5.02 2404 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r4_relat_2(C,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2405 (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]. 4.98/5.02 2406 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2407 (all A (v1_relat_1(A) -> (all B (v4_relat_2(A) & r8_orders_1(A,B) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2408 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2409 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(k4_tarski(C,B),A) & C != B & r2_hidden(C,k3_relat_1(A)))))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2410 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2411 (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]. 4.98/5.02 2412 (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]. 4.98/5.02 2413 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2414 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2415 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2416 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2417 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2418 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2419 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2420 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r8_relat_2(C,A) -> r8_relat_2(C,B)))) # label(t95_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2421 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 4.98/5.02 2422 (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]. 4.98/5.02 2423 (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]. 5.04/5.07 2424 (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]. 5.04/5.07 2425 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2426 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2427 (all A (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,A) -> A = B))))) & (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 -(r1_tarski(A,f1_s2_orders_1) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (r2_hidden(C,A) & -p1_s2_orders_1(B,C) & m1_subset_1(C,f1_s2_orders_1))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(r2_hidden(B,A) & r2_hidden(C,A) & -p1_s2_orders_1(B,C) & -p1_s2_orders_1(C,B)))))))) -> (exists 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) & A != B))))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2428 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2429 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2430 (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(B,A) & p1_s1_orders_1(A,B) -> B = A))))) & (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) -> (exists C (m1_subset_1(C,f1_s1_orders_1) & r2_hidden(C,A) & -p1_s1_orders_1(C,B))))) & (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(B,C) & -p1_s1_orders_1(C,B)))))))) -> (exists A ((all B (m1_subset_1(B,f1_s1_orders_1) -> -(A != B & p1_s1_orders_1(A,B)))) & m1_subset_1(A,f1_s1_orders_1))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2431 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2432 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2433 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2434 (all A all B all C all D all E (v1_relat_2(E) & v4_relat_2(E) & v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(B,A) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2435 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -(r1_tarski(B,k2_relat_1(A)) & (all C -(r1_tarski(C,k1_relat_1(A)) & B = k9_relat_1(A,C) & v1_finset_1(C))) & v1_finset_1(B))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2436 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2437 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2438 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> m1_subset_1(A,k1_zfmisc_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2439 (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]. 5.04/5.07 2440 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2441 (all A (v1_relat_1(A) -> (all B -(r5_orders_1(A,B) & B = k1_xboole_0)))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2442 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2443 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2444 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2445 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2446 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2447 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2448 (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]. 5.04/5.07 2449 (all A all B (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2450 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (k1_xboole_0 = A -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2451 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> k5_eqrel_1(A,B,B) = B)) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2452 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & 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) -> v3_relat_2(k5_eqrel_1(A,B,C)) & v8_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))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2453 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2454 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (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 (D = k6_eqrel_1(A,B,E) & r2_hidden(E,A))))))))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2455 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2456 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> B = k3_eqrel_1(A,B,B))) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2457 (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) & (all D -r2_hidden(C,k6_eqrel_1(A,B,D))))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2458 (all A all B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2459 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2460 (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(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2461 (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(B,k6_eqrel_1(A,D,C)) <-> r2_hidden(k4_tarski(B,C),D)))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2462 (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) -> -((all D (m1_subset_1(D,B) -> A != k6_eqrel_1(B,C,D))) & r2_hidden(A,k7_eqrel_1(B,C))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2463 (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]. 5.04/5.07 2464 (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 all D -(-r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & k6_eqrel_1(A,B,C) != k6_eqrel_1(A,B,D) & r2_hidden(D,A) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2465 (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]. 5.04/5.07 2466 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> m2_relset_1(k2_eqrel_1(A,B,C),A,A))) # label(dt_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2467 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2468 (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]. 5.04/5.07 2469 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2470 (all A all B all C all D (v1_partfun1(D,B,B) & m2_relset_1(D,B,B) & v8_relat_2(D) & v3_relat_2(D) -> (all E (v1_partfun1(E,B,B) & m2_relset_1(E,B,B) & v8_relat_2(E) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_funct_1(F) & v1_finseq_1(F) & r1_xreal_0(np__1,k3_finseq_1(F)) & k1_funct_1(F,np__1) = A & C = k1_funct_1(F,k3_finseq_1(F)) & (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_relat_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2471 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2472 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2473 (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]. 5.04/5.07 2474 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,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]. 5.04/5.07 2475 (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) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B)))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2476 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v3_relat_2(C) & v3_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2477 (all A (v3_relat_2(k1_eqrel_1(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))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2478 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2479 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2480 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,B,B) = B)) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2481 (all A all B all C (v3_relat_2(B) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2482 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_eqrel_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2483 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2484 (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]. 5.04/5.07 2485 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2486 (all A (r1_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2487 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2488 (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) & v8_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) -> (r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v3_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E)))) <-> D = k5_eqrel_1(A,B,C)))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2489 (all A all B all C all D all E (m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) & v3_relat_2(E) & v1_relat_2(E) -> (r2_hidden(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]. 5.04/5.07 2490 (all A all B all C (v8_relat_2(B) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> v8_relat_2(k4_eqrel_1(A,B,C)) & m2_relset_1(k4_eqrel_1(A,B,C),A,A) & v1_partfun1(k4_eqrel_1(A,B,C),A,A) & v3_relat_2(k4_eqrel_1(A,B,C)))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2491 (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 A = k6_eqrel_1(A,B,C)) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2492 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (v3_relat_2(D) & v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) -> (k3_eqrel_1(A,B,C) = D -> (all E -(r2_hidden(E,A) & k6_eqrel_1(A,C,E) != k6_eqrel_1(A,D,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,E)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2493 (all A all B (m2_relset_1(B,A,A) -> (A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B) & v1_relat_2(B) <-> v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2494 (all A k1_eqrel_1(A) = k2_zfmisc_1(A,A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2495 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> -(B = k1_xboole_0 & (exists C r2_hidden(C,A))))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2496 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_relat_2(C) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2497 (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) -> m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))) -> k1_xboole_0 = B | v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B))))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2498 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2499 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2500 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2501 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(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) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & D != C & -r1_xboole_0(C,D)))) & C != k1_xboole_0))))) & (A = k1_xboole_0 -> (k1_xboole_0 = B <-> m1_eqrel_1(B,A))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2502 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2503 (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) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2504 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2505 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2506 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2507 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) -> 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]. 5.04/5.07 2508 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & v3_relat_2(B) -> k4_eqrel_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2509 (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 (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> -(B != k1_eqrel_1(A) & k1_eqrel_1(A) != C & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2510 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(B) -> k7_eqrel_1(A,B) = k8_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2511 (all A all B all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D) <-> r2_hidden(k4_tarski(D,B),C)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2512 (all A all B all C (v1_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2513 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & 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,B,k4_eqrel_1(A,B,C)) = B)))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2514 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (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]. 5.04/5.07 2515 (all A all B (m1_eqrel_1(B,A) -> (exists C (v8_relat_2(C) & m2_relset_1(C,A,A) & k7_eqrel_1(A,C) = B & v1_partfun1(C,A,A) & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2516 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2517 (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]. 5.04/5.07 2518 (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]. 5.04/5.07 2519 (all A (v1_relat_1(k1_eqrel_1(A)) & v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2520 (all A all B (r2_hidden(B,A) -> A = k6_eqrel_1(A,k1_eqrel_1(A),B))) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2521 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B all C (p1_s1_eqrel_1(A,B) & p1_s1_eqrel_1(B,C) -> p1_s1_eqrel_1(A,C))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) -> (exists A (v3_relat_2(A) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & (all B all C (p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) & r2_hidden(B,f1_s1_eqrel_1) <-> r2_hidden(k4_tarski(B,C),A))) & v8_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2522 (all A all B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)) & v1_setfam_1(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2523 (all A all B all C (v8_relat_2(B) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> B = k4_eqrel_1(A,B,B))) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2524 (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]. 5.04/5.07 2525 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(B) -> k4_eqrel_1(A,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2526 (all A all B (m2_relset_1(B,A,A) -> (exists C (v8_relat_2(C) & (all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2527 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2528 (all A all B ((all C (r2_hidden(C,B) -> m2_finseq_1(C,A))) <-> m1_finseq_2(B,A))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2529 (all A (v4_ordinal2(A) -> (all B k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2530 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_finseq_2(k1_nat_1(A,np__1)) = k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,np__1))))) # label(t60_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2531 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2532 (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]. 5.04/5.07 2533 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2534 (all A all B (-v1_xboole_0(B) & v4_ordinal2(A) -> -v1_xboole_0(k4_finseq_2(A,B)))) # label(fc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2535 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_xreal_0(k3_finseq_1(B),A) -> k5_relat_1(k1_finseq_2(A),B) = B))))) # label(t64_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2536 (all A all B all C all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m2_finseq_1(F,D) -> (all G (v1_funct_1(G) & v1_funct_2(G,D,E) & m2_relset_1(G,D,E) -> (k11_finseq_1(A,B,C) = F -> k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) = k1_partfun1(k5_numbers,D,D,E,F,G)))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2537 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2538 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2539 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2540 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,A) -> (all H (m2_finseq_1(H,B) -> (G = k12_finseq_1(A,D) & H = k12_finseq_1(B,E) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k3_funcop_1(F,G,H)))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2541 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_square_1(A,k3_finseq_1(C)) = k3_finseq_1(B)))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2542 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A)) & v1_relat_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2543 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B)) & v1_relat_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2544 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> k6_finseq_1(A) = B)) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2545 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funcop_1(D,B,A) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2546 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m1_subset_1(D,B) -> k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,np__1)) = D)))))))) # label(t136_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2547 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> (all J (m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_2(J,k2_zfmisc_1(A,B),C) & v1_funct_1(J) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (k11_finseq_1(D,E,F) = K & k11_finseq_1(G,H,I) = L -> k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) = k3_funcop_1(J,K,L)))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2548 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (k4_finseq_2(B,C) = k4_finseq_2(A,C) -> B = A))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2549 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,k6_finseq_1(A),F))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2550 (all A (-v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2551 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -(k3_finseq_1(B) = k1_nat_1(A,np__1) & (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D k7_finseq_1(C,k9_finseq_1(D)) != B)))))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2552 (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]. 5.04/5.07 2553 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (m2_finseq_1(H,B) -> (k10_finseq_1(E,F) = H -> k5_funcop_1(G,D,H) = k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F))))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2554 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2555 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> np__0 = k2_square_1(np__0,k6_xcmplx_0(A,B))))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2556 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (k1_partfun1(k5_numbers,A,A,B,D,E) = C -> k3_finseq_1(C) = k3_finseq_1(D)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2557 (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]. 5.04/5.07 2558 (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]. 5.04/5.07 2559 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & v1_funct_1(H) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (I = k10_finseq_1(D,E) & k10_finseq_1(F,G) = J -> k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G))))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2560 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (k11_finseq_1(D,E,F) = I -> k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) = k4_funcop_1(H,I,G)))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.07 2561 (all A (v4_ordinal2(A) -> (all B k4_finseq_2(A,B) = a_2_0_finseq_2(A,B)))) # label(d4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2562 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)))))))))) # label(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2563 (exists A (m2_finseq_1(A,f2_s1_finseq_2) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> k1_funct_1(A,B) = f3_s1_finseq_2(B)))) & k3_finseq_1(A) = f1_s1_finseq_2)) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2564 (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]. 5.04/5.08 2565 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k2_finseq_2(k1_nat_1(A,B),C) = k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C))))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2566 (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]. 5.04/5.08 2567 (all A (v4_ordinal2(A) -> (all B k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A)))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2568 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__3,A) = a_1_2_finseq_2(A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2569 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_2(B,k4_finseq_1(B),A) & m2_relset_1(B,k4_finseq_1(B),A) & v1_funct_1(B))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2570 (all A all B all C (v4_ordinal2(B) -> (r2_hidden(A,a_2_0_finseq_2(B,C)) <-> (exists D (m2_finseq_2(D,C,k3_finseq_2(C)) & A = D & k3_finseq_1(D) = B))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2571 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_finseq_2(B)) <-> (exists C exists D exists E (m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,B) & k11_finseq_1(C,D,E) = A))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2572 (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]. 5.04/5.08 2573 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (D = k9_finseq_1(A) -> k9_finseq_1(k1_funct_1(E,A)) = k1_partfun1(k5_numbers,B,B,C,D,E)))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2574 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2575 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (m2_finseq_1(H,A) -> (H = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) = k4_funcop_1(G,H,F)))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2576 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) & v1_relat_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2577 (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]. 5.04/5.08 2578 (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]. 5.04/5.08 2579 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_square_1(np__0,A) = A & k4_square_1(A,np__0) = A & k3_square_1(A,np__0) = np__0 & k3_square_1(np__0,A) = np__0)) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2580 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k2_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))) & k3_finseq_1(C) = A & k3_finseq_1(B) = A -> C = B))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2581 (all A k2_finseq_2(np__0,A) = k1_xboole_0) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2582 (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]. 5.04/5.08 2583 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_finseq_2(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & k4_finseq_2(C,B) = A))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2584 (all A (v4_ordinal2(A) -> k3_finseq_1(k1_finseq_2(A)) = A)) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2585 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (C = k5_relat_1(D,B) & r1_xreal_0(A,k3_finseq_1(B)) -> k3_finseq_1(C) = A))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2586 (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]. 5.04/5.08 2587 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]. 5.04/5.08 2588 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2589 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k5_funcop_1(E,D,F),C))))))))))))) # label(t91_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2590 (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]. 5.04/5.08 2591 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2592 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2593 (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]. 5.04/5.08 2594 (all A (v4_ordinal2(A) -> v1_funct_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)) & v1_relat_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2595 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> -((all E (m2_finseq_1(E,C) -> (all F (m2_finseq_1(F,C) -> -(A = k3_finseq_1(E) & B = k3_finseq_1(F) & k8_finseq_1(C,E,F) = D))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2596 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2597 (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]. 5.04/5.08 2598 (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]. 5.04/5.08 2599 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2600 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k3_funcop_1(D,E,F),C))))))))))))) # label(t84_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2601 (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]. 5.04/5.08 2602 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(k1_nat_1(A,np__1),B)) -> (exists D ((exists E (m1_subset_1(E,B) & C = k8_finseq_1(B,D,k12_finseq_1(B,E)))) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2603 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k5_funcop_1(C,A,B)) & v1_finseq_1(k5_funcop_1(C,A,B)) & v1_relat_1(k5_funcop_1(C,A,B))))))) # label(t80_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2604 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(B) -> v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2605 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D (r2_hidden(B,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) = k5_relat_1(k11_finseq_1(B,C,D),A))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2606 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2607 (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]. 5.04/5.08 2608 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2609 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(D) -> (r1_xreal_0(B,k3_finseq_1(C)) -> np__0 = B & A != np__0 | v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C))))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2610 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(E) -> (r1_xreal_0(B,k3_finseq_1(D)) -> np__0 != A & B = np__0 | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C)))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2611 (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]. 5.04/5.08 2612 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k3_funcop_1(D,A,B) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_square_1(k3_finseq_1(A),k3_finseq_1(B))))))))))) # label(t79_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2613 (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]. 5.04/5.08 2614 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (k7_finseq_1(D,k9_finseq_1(B)) = k7_finseq_1(C,k9_finseq_1(A)) -> B = A & D = C))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2615 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers) & m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers))))) # label(t1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2616 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2617 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> A = k3_finseq_1(C))))))) # label(t109_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2618 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r2_hidden(A,k2_finseq_1(B)) & A != k1_nat_1(B,np__1) & r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2619 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_tarski(A,C) & r1_tarski(B,C) & k3_finseq_1(A) = k3_finseq_1(B) -> A = B))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2620 (all A all B (-v1_xboole_0(B) -> ((exists C (A = k12_finseq_1(B,C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2621 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,B) -> (E = k5_funcop_1(F,D,G) -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2622 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (m1_subset_1(C,A) & k12_finseq_1(A,C) = B)))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2623 (all A all B all C (m2_finseq_1(C,A) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2624 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)))))))))))) # label(t133_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2625 (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]. 5.04/5.08 2626 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (B = k5_relat_1(C,A) & k4_finseq_1(A) = k2_relat_1(C) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2627 (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]. 5.04/5.08 2628 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2629 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k1_funct_1(B,C) = A & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,k2_relat_1(B))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2630 (all A k10_finseq_1(A,A) = k2_finseq_2(np__2,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2631 (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]. 5.04/5.08 2632 (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]. 5.04/5.08 2633 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> C = k5_relat_1(k1_finseq_2(A),C))))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2634 (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]. 5.04/5.08 2635 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_2(C,k2_finseq_1(A),B) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2636 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (B = k2_finseq_1(A) -> (all D (m2_finseq_1(D,C) -> (all E (m2_finseq_1(E,B) -> (r1_xreal_0(A,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k5_numbers,B,k5_numbers,C,E,D),C))))))))))))) # label(t35_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2637 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_finseq_2(B)) <-> (exists C exists D (m1_subset_1(C,B) & A = k10_finseq_1(C,D) & m1_subset_1(D,B)))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2638 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m1_finseq_2(C,B) & -v1_xboole_0(C) -> m1_finseq_2(C,A) & -v1_xboole_0(C))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2639 (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]. 5.04/5.08 2640 (all A all B all C all D (-v1_xboole_0(D) & m2_subset_1(C,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_3_0_finseq_2(B,C,D)) <-> (exists E exists F (m2_finseq_2(E,D,k4_finseq_2(B,D)) & k8_finseq_1(D,E,F) = A & m2_finseq_2(F,D,k4_finseq_2(C,D))))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2641 (all A all B (v4_ordinal2(A) -> v1_finseq_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_relat_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2642 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_finseq_1(A) = k2_relat_1(D) & k5_relat_1(D,B) = C & r1_xreal_0(A,k3_finseq_1(B)) -> k3_finseq_1(C) = A))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2643 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2644 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (E = k4_funcop_1(F,G,D) -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2645 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k2_finseq_2(k1_nat_1(A,np__1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B))))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2646 (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]. 5.04/5.08 2647 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,B) -> (k11_finseq_1(E,F,G) = I -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2648 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2649 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_relat_1(C,k2_finseq_1(A)) = B & r1_xreal_0(k3_finseq_1(C),A) -> C = B))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2650 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(np__0,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> D = k8_finseq_1(B,C,D) & D = k8_finseq_1(B,D,C))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2651 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k2_square_1(np__0,k6_xcmplx_0(B,A)) = k6_xcmplx_0(B,A)))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2652 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k5_numbers,B) & v1_funct_2(D,k5_numbers,B) -> (k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) = C -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2653 (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]. 5.04/5.08 2654 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2655 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(B,C),D) & m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_1(E) -> (all F (m2_finseq_2(F,B,k4_finseq_2(A,B)) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t140_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2656 (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]. 5.04/5.08 2657 (all A (v4_ordinal2(A) -> v1_funct_1(k1_finseq_2(A)) & v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2658 (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]. 5.04/5.08 2659 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t129_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2660 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__1,A) = a_1_0_finseq_2(A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2661 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2662 (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]. 5.04/5.08 2663 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(A,C) = B & r1_tarski(k2_relat_1(A),k1_relat_1(C)) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2664 (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]. 5.04/5.08 2665 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2666 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2667 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_finseq_1(A) = k2_relat_1(D) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B))))))))))) # label(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2668 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C (m1_subset_1(C,A) & (exists D (B = k10_finseq_1(C,D) & m1_subset_1(D,A))))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2669 (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]. 5.04/5.08 2670 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2671 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k6_finseq_1(B) = k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2672 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & (exists E (k11_finseq_1(C,D,E) = B & m1_subset_1(E,A))))))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2673 (all A all B all C k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C)) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2674 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -((all C (m2_finseq_1(C,A) -> (all D (m1_subset_1(D,A) -> B != k8_finseq_1(A,C,k12_finseq_1(A,D)))))) & np__0 != k3_finseq_1(B)))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2675 (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]. 5.04/5.08 2676 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -((all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> -(k3_finseq_1(E) = B & k7_finseq_1(D,E) = C & k3_finseq_1(D) = A))))) & k3_finseq_1(C) = k1_nat_1(A,B)))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2677 (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]. 5.04/5.08 2678 (all A k9_finseq_1(A) = k2_finseq_2(np__1,A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2679 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (np__0 != A -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> k1_funct_1(k1_finseq_2(A),B) = B))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2680 (all A k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2681 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k2_finseq_1(A) = k4_finseq_1(C))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2682 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & m2_relset_1(F,k2_zfmisc_1(B,C),D) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t141_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2683 (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]. 5.04/5.08 2684 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_funcop_1(D,A,B) = C & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2685 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k7_relat_1(B,k2_finseq_1(A)) = k5_relat_1(k1_finseq_2(A),B))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2686 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_square_1(B,C) = A -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A)))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2687 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,B) -> (G = k12_finseq_1(B,E) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k5_funcop_1(F,D,G)))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2688 (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]. 5.04/5.08 2689 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G))))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2690 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_finseq_1(G) = k3_finseq_1(F) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(F) = k3_finseq_1(D) & k3_finseq_1(G) = k3_finseq_1(D)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2691 (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]. 5.04/5.08 2692 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C)) -> (exists E ((exists F (D = k8_finseq_1(C,E,F) & m2_finseq_2(F,C,k4_finseq_2(B,C)))) & m2_finseq_2(E,C,k4_finseq_2(A,C)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2693 (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]. 5.04/5.08 2694 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k2_finseq_1(A)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2695 (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]. 5.04/5.08 2696 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> k1_funct_1(k2_finseq_2(A,C),B) = C)))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2697 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> -r2_hidden(k1_xboole_0,k2_relat_1(B)))) # label(t149_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2698 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k3_pboole(A,C,D)) -> r4_pboole(A,B,C) & r4_pboole(A,B,D)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2699 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) & p1_s2_pboole(B,C) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2700 (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]. 5.04/5.08 2701 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2702 (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]. 5.04/5.08 2703 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2704 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & (all E (m1_pboole(E,A) -> (r2_pboole(A,E,D) & r2_pboole(A,E,C) -> r2_pboole(A,E,B)))) & r2_pboole(A,B,D) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2705 (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]. 5.04/5.08 2706 (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]. 5.04/5.08 2707 (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]. 5.04/5.08 2708 (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]. 5.04/5.08 2709 (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]. 5.04/5.08 2710 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B)))) & r4_pboole(A,B,C)))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2711 (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]. 5.04/5.08 2712 (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]. 5.04/5.08 2713 (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]. 5.04/5.08 2714 (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]. 5.04/5.08 2715 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (m4_pboole(C,A,B) <-> r2_pboole(A,C,B)))))) # label(d23_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2716 (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]. 5.04/5.08 2717 (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]. 5.04/5.08 2718 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) -> v1_relat_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2719 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,D) & r2_pboole(A,B,C)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2720 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2721 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2722 (all A all B all C (-v1_xboole_0(A) & v2_relat_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2723 (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]. 5.04/5.08 2724 (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]. 5.04/5.08 2725 (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]. 5.04/5.08 2726 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2727 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2728 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r2_pboole(A,B,C) -> r2_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t19_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2729 (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]. 5.04/5.08 2730 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C) & m4_pboole(C,A,B))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2731 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> v2_relat_1(C)))))) # label(t145_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2732 (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]. 5.04/5.08 2733 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k11_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.08 2734 (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]. 5.04/5.09 2735 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2736 (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]. 5.04/5.09 2737 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (all D (m3_pboole(D,A,B,C) -> v1_funcop_1(D))))) # label(cc3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2738 (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]. 5.04/5.09 2739 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r4_pboole(A,B,C) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2740 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D))))))))))) # label(t61_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2741 (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]. 5.04/5.09 2742 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2743 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) & r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2744 (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]. 5.04/5.09 2745 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> k3_pboole(A,B,C) = D))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2746 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2747 (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]. 5.04/5.09 2748 (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]. 5.04/5.09 2749 (all A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) -> (k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> C = k13_pboole(A,B)))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2750 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r6_pboole(A,B,C) <-> C = B))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2751 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)))))) # label(t67_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2752 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2753 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2754 (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]. 5.04/5.09 2755 (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]. 5.04/5.09 2756 (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]. 5.04/5.09 2757 (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]. 5.04/5.09 2758 (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]. 5.04/5.09 2759 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D)) & r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2760 (exists A (v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2761 (all A all B (m1_pboole(B,A) -> -(B != k1_pboole(A) & r5_pboole(A,B,B)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2762 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),B) <-> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2763 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2764 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (m1_pboole(B,A) <-> A = k1_relat_1(B)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2765 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (m1_pboole(C,A) & r1_pboole(A,C,B))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2766 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & v2_relat_1(B) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2767 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),B) & r6_pboole(A,k3_pboole(A,C,B),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2768 (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]. 5.04/5.09 2769 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k3_pboole(A,B,C),A))) # label(dt_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2770 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r2_pboole(A,B,C)))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2771 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> v1_funct_1(k6_pboole(A,B)) & -v3_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & v1_relat_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2772 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2773 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2774 (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]. 5.04/5.09 2775 (all A all B all C (-v1_xboole_0(A) & m1_pboole(C,A) & m1_pboole(B,A) -> (r3_pboole(A,B,C) <-> r1_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2776 (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]. 5.04/5.09 2777 (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]. 5.04/5.09 2778 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,B,C) = k2_pboole(A,C,B))) # label(commutativity_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2779 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2780 (all A -(f2_s1_pboole(A) = k1_xboole_0 & r2_hidden(A,f1_s1_pboole))) -> (exists A ((all B (r2_hidden(B,f1_s1_pboole) -> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)))) & m1_pboole(A,f1_s1_pboole))) # label(s1_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2781 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2782 (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]. 5.04/5.09 2783 (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]. 5.04/5.09 2784 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2785 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2786 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r2_hidden(D,A) & r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2787 (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]. 5.04/5.09 2788 (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]. 5.04/5.09 2789 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k3_pboole(A,B,C) = k3_pboole(A,C,B))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2790 (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]. 5.04/5.09 2791 (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]. 5.04/5.09 2792 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2793 (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]. 5.04/5.09 2794 (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]. 5.04/5.09 2795 (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]. 5.04/5.09 2796 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k2_pboole(A,B,B))) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2797 (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]. 5.04/5.09 2798 (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]. 5.04/5.09 2799 (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]. 5.04/5.09 2800 (all A -(r2_hidden(A,f1_s3_pboole) & (all B -p1_s3_pboole(A,B)))) -> (exists A (m1_pboole(A,f1_s3_pboole) & (all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2801 (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]. 5.04/5.09 2802 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(B = k1_pboole(A) & r4_pboole(A,B,B)))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2803 (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]. 5.04/5.09 2804 (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]. 5.04/5.09 2805 (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]. 5.04/5.09 2806 (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]. 5.04/5.09 2807 (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]. 5.04/5.09 2808 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2809 (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]. 5.04/5.09 2810 (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]. 5.04/5.09 2811 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r2_pboole(A,C,D) & r5_pboole(A,B,D) & -r5_pboole(A,B,C)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2812 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r6_pboole(A,B,B))) # label(reflexivity_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2813 (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]. 5.04/5.09 2814 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2815 (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]. 5.04/5.09 2816 (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]. 5.04/5.09 2817 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,B,C) <-> r2_pboole(A,B,C) & r2_pboole(A,C,B)))))) # label(d13_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2818 (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]. 5.04/5.09 2819 (all A all B (m1_pboole(B,A) -> ((all C -(r2_hidden(C,A) & v1_xboole_0(k1_funct_1(B,C)))) <-> v2_relat_1(B)))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2820 (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]. 5.04/5.09 2821 (all A (v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(k9_pboole(A)))) # label(dt_k9_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2822 (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]. 5.04/5.09 2823 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r7_pboole(A,B,C) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2824 (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]. 5.04/5.09 2825 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)))) <-> k14_pboole(A,B,C) = D))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2826 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) & -r4_pboole(A,B,C)))))))) # label(t114_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2827 (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]. 5.04/5.09 2828 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r4_pboole(A,B,C) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2829 (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]. 5.04/5.09 2830 (all A all B all C all D (v2_relat_1(D) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k5_relat_1(C,D) = k8_pboole(A,B,C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2831 (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]. 5.04/5.09 2832 (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]. 5.04/5.09 2833 (all A all B all C all D (v1_funct_2(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A))) # label(dt_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2834 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k1_funct_1(k5_pboole(A,B,C),D) = k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2835 (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]. 5.04/5.09 2836 (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]. 5.04/5.09 2837 (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]. 5.04/5.09 2838 (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]. 5.04/5.09 2839 (all A exists B (v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & m1_pboole(B,A))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2840 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r4_pboole(A,B,D) & r2_pboole(A,D,E) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2841 (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]. 5.04/5.09 2842 (exists A ((all B (r2_hidden(B,f1_s4_pboole) -> k1_funct_1(A,B) = f2_s4_pboole(B))) & m1_pboole(A,f1_s4_pboole))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2843 (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]. 5.04/5.09 2844 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(C,A,B) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k7_pboole(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2845 (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]. 5.04/5.09 2846 (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]. 5.04/5.09 2847 (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]. 5.04/5.09 2848 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2849 (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]. 5.04/5.09 2850 (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]. 5.04/5.09 2851 (all A all B (v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_1(k10_pboole(A,B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2852 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,C),C) & r6_pboole(A,k2_pboole(A,C,B),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2853 (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]. 5.04/5.09 2854 (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]. 5.04/5.09 2855 (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]. 5.04/5.09 2856 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2857 (all A k2_funcop_1(A,k1_xboole_0) = k1_pboole(A)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2858 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2859 (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]. 5.04/5.09 2860 (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]. 5.04/5.09 2861 (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]. 5.04/5.09 2862 (all A (v1_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2863 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2864 (all A all B all C (m1_pboole(B,A) & v1_funcop_1(C) & m1_pboole(C,A) -> m1_pboole(k14_pboole(A,B,C),A))) # label(dt_k14_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2865 (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]. 5.04/5.09 2866 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2867 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2868 (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]. 5.04/5.09 2869 (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]. 5.04/5.09 2870 (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]. 5.04/5.09 2871 (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]. 5.04/5.09 2872 (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]. 5.04/5.09 2873 (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]. 5.04/5.09 2874 (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]. 5.04/5.09 2875 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2876 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,C,D) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2877 (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]. 5.04/5.09 2878 (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]. 5.04/5.09 2879 (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]. 5.04/5.09 2880 (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]. 5.04/5.09 2881 (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]. 5.04/5.09 2882 (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]. 5.04/5.09 2883 (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]. 5.04/5.09 2884 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2885 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_funct_1(B,D))) -> B = C))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2886 (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]. 5.04/5.09 2887 (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]. 5.04/5.09 2888 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,C,B),D) & r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2889 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_xboole_0 = k1_funct_1(B,C))) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2890 (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]. 5.04/5.09 2891 (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]. 5.04/5.09 2892 (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]. 5.04/5.09 2893 (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]. 5.04/5.09 2894 (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]. 5.04/5.09 2895 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r5_pboole(A,E,C) & r5_pboole(A,D,B) & r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) -> r6_pboole(A,E,B) & r6_pboole(A,D,C)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2896 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> D = k12_pboole(A,B,C)))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2897 (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]. 5.04/5.09 2898 (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]. 5.04/5.09 2899 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,C,D) & r4_pboole(A,B,C) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2900 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,B,D) & r5_pboole(A,C,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2901 (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]. 5.04/5.09 2902 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2903 (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]. 5.04/5.09 2904 (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]. 5.04/5.09 2905 (exists A (m1_pboole(A,f1_s5_pboole) & (all B (m1_subset_1(B,f1_s5_pboole) -> k1_funct_1(A,B) = f2_s5_pboole(B))))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2906 (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]. 5.04/5.09 2907 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,B) & r1_pboole(A,E,C) <-> r1_pboole(A,E,D)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2908 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2909 (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]. 5.04/5.09 2910 (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]. 5.04/5.09 2911 (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]. 5.04/5.09 2912 (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]. 5.04/5.09 2913 (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]. 5.04/5.09 2914 (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]. 5.04/5.09 2915 (all A (m1_pboole(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2916 (all A all B all C all D (-v1_xboole_0(B) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2917 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & v1_funct_1(k1_funct_1(D,E)))) <-> m3_pboole(D,A,B,C)))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2918 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> (C = k6_pboole(A,B) <-> (all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k4_card_3(k5_relat_1(D,B)) = k1_funct_1(C,D)))))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2919 (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]. 5.04/5.09 2920 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k2_pboole(A,C,D)) <-> r2_pboole(A,C,B) & (all E (m1_pboole(E,A) -> (r2_pboole(A,C,E) & r2_pboole(A,D,E) -> r2_pboole(A,B,E)))) & r2_pboole(A,D,B)))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2921 (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]. 5.04/5.09 2922 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2923 (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]. 5.04/5.09 2924 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2925 (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]. 5.04/5.09 2926 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A))))))))) # label(t52_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2927 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r3_pboole(A,B,C) & k1_pboole(A) = k3_pboole(A,C,D) & r3_pboole(A,B,D)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2928 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2929 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2930 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B))))) # label(t71_pboole) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2931 (all A (l1_struct_0(A) -> (v1_xboole_0(u1_struct_0(A)) <-> v3_struct_0(A)))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2932 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (all C (m1_subset_1(C,B) <-> m1_struct_0(C,A,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2933 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> k2_struct_0(A,B,C) = k2_struct_0(A,C,B))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2934 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2935 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2936 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2937 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2938 (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]. 5.04/5.09 2939 (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]. 5.04/5.09 2940 (exists A (-v3_struct_0(A) & l1_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2941 (all A all B (m1_subset_1(B,A) -> l2_struct_0(g2_struct_0(A,B)) & v2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2942 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2943 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2944 (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]. 5.04/5.09 2945 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2946 (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]. 5.04/5.09 2947 (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]. 5.04/5.09 2948 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2949 (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]. 5.04/5.09 2950 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2951 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2952 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2953 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2954 (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]. 5.04/5.09 2955 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) & -v3_struct_0(A) -> (all C (m1_struct_0(C,A,B) -> m1_subset_1(C,u1_struct_0(A)))))) # label(dt_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2956 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k1_struct_0(A,B) = k1_tarski(B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2957 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(A,B) = g2_struct_0(C,D) -> C = A & D = B)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2958 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2959 (all A all B all C (v4_lattices(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k3_lattices(A,B,C) = k1_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2960 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k3_lattices(A,B,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2961 (all A (l1_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,C) & k2_lattices(A,C,B) = B)) <-> B = k5_lattices(A))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2962 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2963 (all A all B all C (v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) & -v3_struct_0(A) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2964 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_lattices(A) -> k3_lattices(A,B,C) = k3_lattices(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2965 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v2_lattices(g2_lattices(A,B)) & l2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2966 (all A (l1_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2967 (exists A (l1_lattices(A) & -v3_struct_0(A) & v1_lattices(A) & v7_lattices(A) & v6_lattices(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.09 2968 (all A (-v3_struct_0(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v6_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_lattices(A,B,B) = B)))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2969 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v15_lattices(A) <-> v13_lattices(A) & v14_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2970 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,k7_lattices(A,C)) <-> k4_lattices(A,B,C) = k5_lattices(A)))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2971 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> k2_lattices(A,B,C) = k4_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2972 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)) = k4_lattices(A,B,k3_lattices(A,C,D)))))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t19_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2973 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2974 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)))))))) <-> v11_lattices(A)))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2975 (exists A (-v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v2_lattices(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2976 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2977 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & v16_lattices(A) & l3_lattices(A) & v11_lattices(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,C,B) <-> k7_lattices(A,B) = C)))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2978 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2979 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> v3_lattices(g3_lattices(A,B,C)) & l3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2980 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2981 (all A (l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = k1_lattices(A,B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2982 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v8_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_lattices(A,k2_lattices(A,B,C),C)))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2983 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2984 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v11_lattices(A) & v13_lattices(A) & v15_lattices(A) & v17_lattices(A) & v16_lattices(A) & v14_lattices(A) & v10_lattices(A) & v9_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2985 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_lattices(A,B,C) = k5_lattices(A) & k2_lattices(A,C,B) = k5_lattices(A) & k6_lattices(A) = k1_lattices(A,C,B) & k1_lattices(A,B,C) = k6_lattices(A) <-> r2_lattices(A,B,C)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2986 (all A (l1_lattices(A) -> (v1_lattices(A) -> g1_lattices(u1_struct_0(A),u1_lattices(A)) = A))) # label(abstractness_v1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2987 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2988 (all A (l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k1_lattices(A,B,C) <-> r1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2989 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2990 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2991 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2992 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2993 (all A (v4_lattices(A) & l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,C,B) & r1_lattices(A,B,C) -> C = B))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2994 (all A all B (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v2_lattices(g2_lattices(A,B)) & -v3_struct_0(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2995 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_lattices(A,C,B))))) <-> v6_lattices(A)))) # label(d6_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2996 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_lattices(A) = k4_lattices(A,k7_lattices(A,B),B))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2997 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattices(A,C,B))))) <-> v16_lattices(A)))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2998 (all A (l1_lattices(A) -> m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 2999 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3000 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3001 (all A (l2_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,C,D) & r1_lattices(A,B,C) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3002 (exists A (-v3_struct_0(A) & v3_lattices(A) & l3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3003 (all A (-v3_struct_0(A) & v8_lattices(A) & l3_lattices(A) & v9_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> k2_lattices(A,B,C) = B))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3004 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_lattices(A,C,B) & k1_lattices(A,B,C) = B)) <-> B = k6_lattices(A))))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3005 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3006 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = B & k2_lattices(A,C,B) = B)) & m1_subset_1(B,u1_struct_0(A)))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3007 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3008 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3009 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3010 (exists A (l3_lattices(A) & v3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3011 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v9_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,k1_lattices(A,B,C))))))))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3012 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3013 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3014 (all A (l3_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3015 (exists A (l1_lattices(A) & v1_lattices(A) & -v3_struct_0(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3016 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g2_lattices(A,B) = g2_lattices(C,D) -> D = B & C = A)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3017 (exists A (-v3_struct_0(A) & v3_lattices(A) & v6_lattices(A) & v7_lattices(A) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v12_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A) & v4_lattices(A) & l3_lattices(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3018 (all A (l2_lattices(A) -> v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3019 (all A (l3_lattices(A) -> (v11_lattices(A) & v15_lattices(A) & v16_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3020 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A) <-> v17_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3021 (all A (l3_lattices(A) -> (v17_lattices(A) & -v3_struct_0(A) -> v11_lattices(A) & v13_lattices(A) & v15_lattices(A) & v16_lattices(A) & v14_lattices(A) & -v3_struct_0(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3022 (exists A (l2_lattices(A) & v2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3023 (all A (-v3_struct_0(A) & l1_lattices(A) -> m1_subset_1(k5_lattices(A),u1_struct_0(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3024 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3025 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) -> -v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3026 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3027 (all A (l3_lattices(A) -> (v3_lattices(A) -> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3028 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> v1_lattices(g1_lattices(A,B)) & -v3_struct_0(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3029 (all A (-v3_struct_0(A) & l2_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k1_lattices(A,B,C),D))))))) <-> v5_lattices(A)))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3030 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A) -> -v3_struct_0(A) & v10_lattices(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3031 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k5_lattices(A),B) = B)))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3032 (all A all B all C (l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3033 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k6_lattices(A),B) = k6_lattices(A))))) # label(t44_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3034 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3035 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v4_lattices(A) & v5_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & v8_lattices(A) <-> v10_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3036 (all A all B all C (v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v6_lattices(A) & -v3_struct_0(A) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3037 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3038 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,D) -> k2_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k2_lattices(A,C,D))))))))) <-> v12_lattices(A)))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3039 (all A (l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,B,B))))) # label(t18_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3040 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v15_lattices(A) -> v14_lattices(A) & v13_lattices(A) & -v3_struct_0(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3041 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3042 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B))))))))) # label(t53_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3043 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,k5_lattices(A),B))))) # label(t41_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3044 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3045 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_lattices(A) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3046 (all A (v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,B,k1_lattices(A,B,C)))))))) # label(t22_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3047 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v11_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)))))))))) # label(t31_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3048 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v13_lattices(A) & v14_lattices(A) -> -v3_struct_0(A) & v15_lattices(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3049 (all A (l2_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3050 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all D all E all F (g3_lattices(D,E,F) = g3_lattices(A,B,C) -> C = F & E = B & D = A)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3051 (all A (v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v7_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) -> r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D))))))))))) # label(t27_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3052 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3053 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B)) & m1_subset_1(B,u1_struct_0(A))))))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3054 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> -v3_struct_0(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3055 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3056 (all A (v11_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 5.04/5.10 3057 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> l1_lattices(g1_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3058 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3059 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3060 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k2_lattices(A,B,C),D))))))) <-> v7_lattices(A)))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3061 (exists A (l3_lattices(A) & v5_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3062 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3063 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3064 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3065 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,k6_lattices(A),B))))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3066 (exists A (-v3_struct_0(A) & v3_lattices(A) & v7_lattices(A) & v9_lattices(A) & v13_lattices(A) & v15_lattices(A) & v14_lattices(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3067 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3068 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3069 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3070 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3071 (all A (l2_lattices(A) -> (v2_lattices(A) -> g2_lattices(u1_struct_0(A),u2_lattices(A)) = A))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3072 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v4_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k1_lattices(A,C,B)))))))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3073 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3074 (all A (l3_lattices(A) -> (v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v8_lattices(A) & v9_lattices(A) & v12_lattices(A) & v10_lattices(A) & v7_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3075 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3076 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3077 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_lattices(A) = k4_lattices(A,k5_lattices(A),B))))) # label(t40_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3078 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k4_lattices(A,B,C)))))))) # label(t50_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3079 (exists A (-v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v13_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & l3_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3080 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3081 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)))))))) -> v11_lattices(A)))) # label(t29_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3082 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3083 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_lattices(A,B) = g1_lattices(C,D) -> D = B & C = A)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3084 (all A (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k4_lattices(A,B,C) = k4_lattices(A,B,D) & k3_lattices(A,B,D) = k3_lattices(A,B,C) -> D = C))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3085 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (k3_tarski(k4_orders_2(A,C)) = B -> m1_orders_2(D,A,B) | k3_tarski(k4_orders_2(A,C)) = D))))))))) # label(t88_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3086 (all A (v2_orders_2(A) & l1_orders_2(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)) -> (v5_orders_2(k2_struct_0(A,B,C),A) & m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) <-> r3_orders_2(A,C,B) | r3_orders_2(A,B,C)))))))) # label(t36_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3087 $T # label(t74_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3088 $T # label(d1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3089 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,B,B))) # label(irreflexivity_r2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3090 $T # label(t19_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3091 $T # label(t98_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3092 $T # label(t118_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3093 $T # label(t75_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3094 $T # label(t105_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3095 $T # label(t111_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3096 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r7_relat_2(u1_orders_2(A),B) <-> v5_orders_2(B,A)))))) # label(d11_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3097 $T # label(t106_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3098 $T # label(t101_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3099 $T # label(t122_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3100 $T # label(t131_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3101 $T # label(t104_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3102 $T # label(t141_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3103 $T # label(t147_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3104 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-(B = k1_xboole_0 & C = k1_xboole_0) & m1_orders_2(B,A,C) & m1_orders_2(C,A,B)))))))) # label(t69_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3105 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != B & m1_orders_2(B,A,B)) & -(-m1_orders_2(B,A,B) & B = k1_xboole_0))))) # label(t68_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3106 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,C,B))) <-> r7_orders_1(u1_orders_2(A),B)))))) # label(t158_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3107 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all C (m1_orders_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3108 $T # label(t144_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3109 $T # label(t23_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3110 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r2_hidden(B,k2_orders_2(A,k1_struct_0(A,B))))))) # label(t50_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3111 (all A (l1_orders_2(A) -> v1_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A),A) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc4_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3112 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_orders_2(A) -> m1_subset_1(k1_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3113 $T # label(t20_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3114 (exists A (l1_orders_2(A) & v2_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v1_orders_2(A) & -v3_struct_0(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3115 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(k1_struct_0(A,B),A))))) # label(t35_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3116 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> -((all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,D,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_orders_2(A,B,C) & m1_subset_1(C,u1_struct_0(A))))))))) # label(t162_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3117 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> k2_orders_2(A,k2_pre_topc(A)) = k1_xboole_0)) # label(t46_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3118 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> r2_hidden(k1_funct_1(B,u1_struct_0(A)),C))))))) # label(t79_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3119 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_orders_2(A,k1_pre_topc(A),B) = k1_xboole_0)))) # label(t60_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3120 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_orders_1(u1_orders_2(A),B) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t135_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3121 $T # label(t54_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3122 $T # label(t130_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3123 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) & r1_orders_2(A,C,B) -> C = B))))))) # label(t25_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3124 $T # label(t22_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3125 $T # label(t113_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3126 $T # label(t149_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3127 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r2_hidden(B,k1_orders_2(A,k1_struct_0(A,B))))))) # label(t48_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3128 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & v4_orders_2(A) & v3_orders_2(A) -> (exists C m2_orders_2(C,A,B)))) # label(existence_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3129 $T # label(t155_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3130 $T # label(t91_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3131 (all A all B (m1_relset_1(B,A,A) & -v1_xboole_0(A) -> -v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3132 (all A all B (m1_relset_1(B,A,A) -> (all C all D (g1_orders_2(C,D) = g1_orders_2(A,B) -> B = D & A = C)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3133 $T # label(t34_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3134 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_orders_2(A,B) = a_2_0_orders_2(A,B))))) # label(d12_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3135 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> u1_struct_0(A) = k2_orders_2(A,k1_pre_topc(A)))) # label(t45_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3136 $T # label(t140_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3137 $T # label(t41_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3138 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r6_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,B,C)))))))) # label(t159_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3139 $T # label(t8_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3140 (all A all B (m1_relset_1(B,A,A) -> v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3141 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_orders_2(A,B,C) & r2_orders_2(A,C,B)))))))) # label(t28_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3142 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -r2_hidden(B,k3_orders_2(A,C,B)))))))) # label(t62_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3143 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r3_orders_1(u1_orders_2(A),B))))) # label(t136_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3144 $T # label(t150_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3145 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) & m1_orders_2(C,A,D) -> k3_orders_2(A,D,B) = k3_orders_2(A,C,B)))))))))) # label(t71_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3146 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> v3_orders_1(k2_wellord1(u1_orders_2(A),B)))))) # label(t109_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3147 $T # label(t120_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3148 (all A (l1_orders_2(A) -> (v1_orders_2(A) -> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3149 $T # label(t16_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3150 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k2_orders_2(A,k1_struct_0(A,C))) <-> r2_orders_2(A,B,C)))))))) # label(t52_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3151 $T # label(t129_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3152 $T # label(t93_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3153 (all A (l1_orders_2(A) -> (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> v5_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t37_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3154 $T # label(t138_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3155 (all A all B (v4_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all C (m2_orders_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(C,A))))) # label(dt_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3156 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (k1_funct_1(C,u1_struct_0(A)) = B -> k1_xboole_0 = k3_orders_2(A,D,B)))))))))) # label(t81_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3157 $T # label(t4_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3158 $T # label(t115_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3159 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_orders_2(A,B,C) = k5_subset_1(u1_struct_0(A),k2_orders_2(A,k1_struct_0(A,C)),B))))))) # label(d14_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3160 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,D) -> r1_tarski(k3_orders_2(A,C,B),k3_orders_2(A,D,B))))))))))) # label(t65_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3161 $T # label(t132_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3162 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> k1_orders_2(A,k2_pre_topc(A)) = k1_xboole_0)) # label(t44_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3163 $T # label(t114_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3164 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> k1_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A))) # label(t43_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3165 $T # label(t21_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3166 $T # label(t154_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3167 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(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)) -> (r2_orders_2(A,C,D) & r1_orders_2(A,B,C) | r2_orders_2(A,B,C) & r1_orders_2(A,C,D) -> r2_orders_2(A,B,D)))))))))) # label(t32_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3168 (all A (l1_orders_2(A) -> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3169 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k1_orders_2(A,k1_struct_0(A,B))) <-> r2_orders_2(A,B,C)))))))) # label(t51_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3170 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) & B != C <-> r2_orders_2(A,B,C)))))))) # label(d10_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3171 $T # label(t102_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3172 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_orders_1(k2_wellord1(u1_orders_2(A),B)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t108_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3173 (exists A (v1_orders_2(A) & l1_orders_2(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3174 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 != B -> (m1_orders_2(C,A,B) <-> (exists D (m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & k3_orders_2(A,B,D) = C)))) & (k1_xboole_0 = B -> (m1_orders_2(C,A,B) <-> k1_xboole_0 = C)))))))) # label(d15_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3175 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(D,C) & r2_orders_2(A,D,E) & r2_hidden(E,B) -> r2_hidden(D,B)))))) & C != B & -m1_orders_2(B,A,C) & r2_wellord1(u1_orders_2(A),C)))))))) # label(t73_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3176 (all A all B (-v3_struct_0(A) & v4_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (exists C m1_orders_2(C,A,B)))) # label(existence_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3177 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> -r1_xboole_0(C,D))))))))) # label(t82_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3178 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> (C != D -> (-m1_orders_2(D,A,C) <-> m1_orders_2(C,A,D))))))))))) # label(t83_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3179 $T # label(t121_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.10 3180 $T # label(t92_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3181 (all A all B (v2_orders_2(A) & v4_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k4_orders_2(A,B)))) # label(fc5_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3182 $T # label(t90_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3183 $T # label(t95_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3184 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_orders_2(A,C,B) & r1_orders_2(A,B,C)))))))) # label(t30_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3185 $T # label(t151_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3186 $T # label(t139_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3187 (all A all B all C (-v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v3_orders_2(B) -> (r2_hidden(A,a_2_1_orders_2(B,C)) <-> (exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,D,E)))) & D = A & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3188 $T # label(t119_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3189 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(C,A) -> (k1_xboole_0 != C & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> D = k1_funct_1(B,k1_orders_2(A,k3_orders_2(A,C,D)))))) & r2_wellord1(u1_orders_2(A),C) <-> m2_orders_2(C,A,B)))))))) # label(d16_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3190 (all A (l1_orders_2(A) -> (r1_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v2_orders_2(A)))) # label(d4_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3191 (all A all B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> v1_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3192 $T # label(t33_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3193 $T # label(t148_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3194 $T # label(t146_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3195 $T # label(t15_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3196 $T # label(dt_k4_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3197 (all A all B all C (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v2_orders_2(A) -> (r1_orders_2(A,B,C) <-> r3_orders_2(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3198 $T # label(t86_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3199 $T # label(t58_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3200 $T # label(t100_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3201 $T # label(t12_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3202 $T # label(t14_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3203 (all A all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k2_orders_2(B,k1_struct_0(B,C))) & r2_hidden(A,D) <-> r2_hidden(A,k3_orders_2(B,D,C))))))))) # label(t56_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3204 $T # label(t153_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3205 $T # label(t17_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3206 $T # label(t134_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3207 $T # label(t127_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3208 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (B != C -> r2_orders_2(A,C,B)))) <-> r8_orders_1(u1_orders_2(A),B)))))) # label(t160_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3209 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k2_orders_2(A,C)) & r2_hidden(B,C)))))))) # label(t49_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3210 $T # label(t152_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3211 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((r2_orders_2(A,B,C) <-> -r1_orders_2(A,C,B)) <-> (exists D (r2_hidden(C,D) & r2_hidden(B,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(D,A)))))))))) # label(t39_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3212 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_1_orders_2(A,B) = k2_orders_2(A,B))))) # label(d13_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3213 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3214 $T # label(t94_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3215 $T # label(t63_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3216 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> (r2_xboole_0(C,D) <-> m1_orders_2(C,A,D)))))))))) # label(t84_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3217 $T # label(t13_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3218 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B))))) # label(t89_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3219 $T # label(t9_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3220 $T # label(d2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3221 $T # label(t125_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3222 $T # label(t53_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3223 $T # label(d8_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3224 $T # label(t5_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3225 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> k1_xboole_0 != k3_tarski(k4_orders_2(A,B)))))) # label(t87_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3226 $T # label(t42_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3227 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k1_orders_2(A,C)) & r2_hidden(B,C)))))))) # label(t47_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3228 (all A all B all C (-v3_struct_0(A) & v2_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> r3_orders_2(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3229 $T # label(t116_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3230 $T # label(t11_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3231 $T # label(t96_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3232 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(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)) -> (r2_orders_2(A,C,D) & r2_orders_2(A,B,C) -> r2_orders_2(A,B,D)))))))))) # label(t29_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3233 $T # label(t112_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3234 $T # label(t2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3235 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> m2_orders_2(k1_tarski(k1_funct_1(B,u1_struct_0(A))),A,B))))) # label(t78_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3236 $T # label(t117_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3237 $T # label(d7_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3238 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_orders_1(D,k1_orders_1(u1_struct_0(A))) -> (all E (m2_orders_2(E,A,D) -> (r2_hidden(B,E) & C = k1_funct_1(D,u1_struct_0(A)) -> r3_orders_2(A,C,B)))))))))))) # label(t80_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3239 $T # label(t6_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3240 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(k4_tarski(B,C),u1_orders_2(A)) <-> r1_orders_2(A,B,C)))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3241 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v4_orders_2(A) -> m1_subset_1(k2_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3242 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_orders_2(A,B,C) -> r1_tarski(k3_orders_2(A,D,B),k3_orders_2(A,D,C))))))))))) # label(t64_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3243 $T # label(t76_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3244 $T # label(d3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3245 $T # label(t85_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3246 $T # label(t99_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3247 $T # label(t110_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3248 (all A (l1_orders_2(A) -> (r4_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v4_orders_2(A)))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3249 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k3_relat_1(k2_wellord1(u1_orders_2(A),B)))))) # label(t107_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3250 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3251 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r9_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C != B -> r2_orders_2(A,B,C))))))))) # label(t161_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3252 $T # label(t103_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3253 $T # label(t137_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3254 (all A all B all C (l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> ((exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,E,D)))) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_orders_2(B,C))))) # label(fraenkel_a_2_0_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3255 $T # label(t126_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3256 (all A (v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((exists D (v5_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r2_hidden(C,D))) & -r1_orders_2(A,C,B) & -r1_orders_2(A,B,C)) & -((all D (v5_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r2_hidden(B,D)))) & (r1_orders_2(A,C,B) | r1_orders_2(A,B,C))))))))) # label(t38_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3257 $T # label(t55_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3258 $T # label(t145_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3259 $T # label(t124_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3260 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> -((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_orders_2(A,C,B) & m1_subset_1(C,u1_struct_0(A)))))) & (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,C,D)))) & m1_subset_1(C,u1_struct_0(A))))))))) # label(t163_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3261 $T # label(t27_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3262 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> v4_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(u1_orders_2(A)) & v1_relat_2(u1_orders_2(A)) & v1_relat_1(u1_orders_2(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3263 $T # label(t1_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3264 (all A (l1_orders_2(A) -> (v3_orders_2(A) <-> r8_relat_2(u1_orders_2(A),u1_struct_0(A))))) # label(d5_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3265 (all A (l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A))))) # label(rc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3266 (all A all B all C (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v2_orders_2(A) -> m1_subset_1(k3_orders_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3267 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_wellord1(u1_orders_2(A),B) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t40_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3268 (all A (v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r1_orders_2(A,B,C) -> r1_orders_2(A,B,D)))))))))) # label(t26_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3269 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_orders_2(C,A,B) -> r1_tarski(C,B))))))) # label(t67_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3270 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,E) & m1_orders_2(E,A,D) & r2_hidden(B,D) & r2_orders_2(A,B,C) -> r2_hidden(B,E)))))))))))) # label(t70_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3271 $T # label(t3_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3272 (all A (l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,B))))) # label(t24_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3273 $T # label(t97_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3274 $T # label(t59_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3275 $T # label(t133_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3276 $T # label(t128_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3277 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (C = k4_orders_2(A,B) <-> (all D (r2_hidden(D,C) <-> m2_orders_2(D,A,B))))))))) # label(d17_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3278 $T # label(t157_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3279 $T # label(t10_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3280 $T # label(t143_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3281 $T # label(t77_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3282 $T # label(t18_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3283 $T # label(t142_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3284 $T # label(t123_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3285 $T # label(t156_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3286 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_orders_2(A,C,B),C))))))) # label(t61_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3287 $T # label(t66_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3288 $T # label(t31_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3289 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k3_orders_2(A,D,C)) <-> r2_orders_2(A,B,C) & r2_hidden(B,D)))))))))) # label(t57_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3290 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_wellord1(u1_orders_2(A),C) & B != C & -m1_orders_2(B,A,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(E,B) & r2_orders_2(A,D,E) -> r2_hidden(D,B)))))) & r1_tarski(B,C)))))))) # label(t72_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3291 $T # label(t7_orders_2) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3292 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) -> k5_filter_0(A,B,C) = k6_filter_0(A,B,C))) # label(redefinition_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3293 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v10_lattices(A) & r2_hidden(k5_lattices(A),B) & l3_lattices(A) & v13_lattices(A) -> u1_struct_0(A) = B & k1_filter_0(A) = B))))) # label(t32_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3294 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,E),C) -> r3_lattices(A,E,D)))) & r3_lattices(A,k4_lattices(A,B,D),C) <-> k4_filter_0(A,B,C) = D)))))))))) # label(d8_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3295 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (u1_struct_0(A) != B & (all C (m1_filter_0(C,A) -> (r1_tarski(B,C) -> B = C | C = u1_struct_0(A)))) <-> v1_filter_0(B,A)))))) # label(d4_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3296 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,E) -> r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,E)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,E,C))))))))))))) # label(t4_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3297 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v14_lattices(A) -> k6_lattices(k8_filter_0(A,k2_filter_0(A,B))) = k6_lattices(A)))))) # label(t72_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3298 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v10_lattices(A) & l3_lattices(A) & (all C (m1_filter_0(C,A) -> -(r2_hidden(B,C) & v1_filter_0(C,A)))) & B != k5_lattices(A) & v13_lattices(A) & -v3_struct_0(A)))))) # label(t24_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3299 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k9_filter_0(A,C,D),B) <-> r1_filter_0(A,B,C,D)))))))))) # label(d13_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3300 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (C = k6_domain_1(u1_struct_0(A),B) -> k2_filter_0(A,B) = k3_filter_0(A,C)))))))) # label(t30_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3301 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_filter_0(k3_filter_0(A,B),A))) # label(dt_k3_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3302 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k7_filter_0(A,B,C) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t52_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3303 (exists A (l3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v3_filter_0(A) & v10_lattices(A) & v6_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3304 (all A all B (v3_filter_0(A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_partfun1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k11_filter_0(A,B)) & v3_relat_2(k11_filter_0(A,B)))) # label(dt_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3305 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> m1_filter_0(k6_domain_1(u1_struct_0(A),k6_lattices(A)),A)))) # label(t13_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3306 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,E) -> r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,E,C)) & r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,C,E))))))))))))) # label(t5_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3307 (all A (-v3_struct_0(A) & v3_lattices(A) & v10_lattices(A) & l3_lattices(A) -> A = k8_filter_0(A,k1_filter_0(A)))) # label(t62_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3308 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3309 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r2_hidden(k6_lattices(A),B)))))) # label(t12_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3310 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (exists B m1_filter_0(B,A)))) # label(existence_m1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3311 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = a_3_1_filter_0(A,B,C))))))) # label(t48_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3312 (all A all B all C (v10_lattices(A) & v17_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k7_filter_0(A,B,C),A))) # label(dt_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3313 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v10_lattices(A) & l3_lattices(A) & v13_lattices(A) & -v3_struct_0(A) -> k2_filter_0(A,k5_lattices(A)) = k1_filter_0(A)))) # label(t20_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3314 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) <-> u1_struct_0(A) != B & (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k7_lattices(A,C),B) | r2_hidden(C,B)))))))) # label(t57_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3315 $T # label(t21_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3316 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(k5_filter_0(A,B,C)))) # label(fc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3317 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> v8_relat_2(k10_filter_0(A,B)) & v1_partfun1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(k10_filter_0(A,B))))))) # label(t84_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3318 $T # label(t33_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3319 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,B,D) -> r3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t7_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3320 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(B,D) -> r2_hidden(k4_filter_0(A,C,B),D)))))))))) # label(t42_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3321 (all A all B all C (v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> (r2_hidden(A,a_2_0_filter_0(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & r3_lattices(B,C,D) & D = A))))) # label(fraenkel_a_2_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3322 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,k3_filter_0(A,C))) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) & k3_filter_0(A,k4_subset_1(u1_struct_0(A),k3_filter_0(A,B),C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t47_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3323 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B))) & v10_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v17_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t75_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3324 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m1_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,C,D) & r2_hidden(C,B) -> r2_hidden(D,B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_lattices(A,C,D),B))))))))))) # label(t9_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3325 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_filter_0(D,A) -> -((r2_hidden(B,D) & -r2_hidden(C,D) | -r2_hidden(B,D) & r2_hidden(C,D)) & v1_filter_0(D,A)))) & C != B))))))) # label(t60_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3326 (all A all B all C all D (m1_filter_0(D,B) & m1_filter_0(C,B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_filter_0(B,C,D)) <-> (exists E ((exists F ((exists G (m1_subset_1(G,u1_struct_0(B)) & r3_lattices(B,k4_lattices(B,F,G),E) & r2_hidden(G,D) & r2_hidden(F,C))) & m1_subset_1(F,u1_struct_0(B)))) & E = A & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3327 $T # label(t16_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3328 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (m1_filter_0(k6_domain_1(u1_struct_0(A),B),A) -> v14_lattices(A)))))) # label(t14_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3329 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m1_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k4_lattices(A,C,D),B) <-> r2_hidden(D,B) & r2_hidden(C,B))))))))))) # label(d1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3330 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_filter_0(B,A) -> -(u1_struct_0(A) != B & (all C (m1_filter_0(C,A) -> -(v1_filter_0(C,A) & r1_tarski(B,C)))))))))) # label(t22_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3331 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k4_lattices(A,D,B),C) & r3_lattices(A,k4_lattices(A,B,D),C)))))))))) # label(t2_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3332 $T # label(t17_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3333 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,E) & r2_hidden(B,D) -> r2_hidden(k4_lattices(A,B,C),k5_filter_0(A,D,E)) & r2_hidden(k4_lattices(A,C,B),k5_filter_0(A,D,E))))))))))))) # label(t44_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3334 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k10_filter_0(A,D)) <-> r1_filter_0(A,D,B,C)))))))))) # label(t87_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3335 $T # label(t61_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3336 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k1_filter_0(A),A))) # label(dt_k1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3337 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v11_lattices(A) -> v11_lattices(k8_filter_0(A,B))))))) # label(t68_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3338 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (all E (m1_subset_1(E,u1_struct_0(k8_filter_0(A,D))) -> (all F (m1_subset_1(F,u1_struct_0(k8_filter_0(A,D))) -> (E = B & C = F -> k3_lattices(A,B,C) = k3_lattices(k8_filter_0(A,D),E,F) & k4_lattices(A,B,C) = k4_lattices(k8_filter_0(A,D),E,F)))))))))))))) # label(t64_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3339 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k4_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3340 $T # label(t79_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3341 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B))))))) # label(t11_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3342 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) -> m1_filter_0(k2_filter_0(A,B),A))) # label(dt_k2_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3343 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,D,C)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,D)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,D,C)) & r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,C,D))))))))))) # label(t1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3344 $T # label(t25_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3345 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k6_filter_0(A,B,C))))))) # label(t51_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3346 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) & v17_lattices(A) -> v3_relat_2(k12_filter_0(A,B)) & v8_relat_2(k12_filter_0(A,B)) & v1_partfun1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k12_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3347 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k3_filter_0(A,k5_filter_0(A,B,C)))))))) # label(t50_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3348 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> k1_realset1(u1_lattices(A),B) = u1_lattices(k8_filter_0(A,B)) & k1_realset1(u2_lattices(A),B) = u2_lattices(k8_filter_0(A,B)) & u1_struct_0(k8_filter_0(A,B)) = B)))) # label(t63_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3349 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r1_filter_0(A,D,B,C) -> r1_filter_0(A,D,C,B)))))))))) # label(t89_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.11 3350 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,B,k3_lattices(A,D,C)) & r3_lattices(A,B,k3_lattices(A,C,D))))))))))) # label(t3_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3351 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(B,A) & v17_lattices(A) & v10_lattices(A) -> k12_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k12_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3352 (all A all B (l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,B)) & v4_lattices(k8_filter_0(A,B)) & v7_lattices(k8_filter_0(A,B)) & v8_lattices(k8_filter_0(A,B)) & v9_lattices(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)) & v6_lattices(k8_filter_0(A,B)) & v5_lattices(k8_filter_0(A,B)) & v3_lattices(k8_filter_0(A,B)))) # label(fc2_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3353 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t73_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3354 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_filter_0(C,A) -> ((all D (m1_filter_0(D,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) <-> C = k3_filter_0(A,B)))))))) # label(d5_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3355 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v2_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) | r2_hidden(C,B) <-> r2_hidden(k3_lattices(A,C,D),B))))))))))) # label(d6_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3356 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(B,D) -> r2_hidden(k3_lattices(A,C,B),D) & r2_hidden(k3_lattices(A,B,C),D)))))))))) # label(t10_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3357 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v3_filter_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r1_lattices(A,k2_lattices(A,B,D),C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_lattices(A,k2_lattices(A,B,E),C) -> r1_lattices(A,E,D))))))))))))) # label(d7_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3358 (all A all B all C (-v3_struct_0(A) & l3_lattices(A) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v10_lattices(A) -> m1_subset_1(k5_filter_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3359 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v13_lattices(A) & l3_lattices(A) & r2_hidden(k5_lattices(A),B) & v10_lattices(A) & -v3_struct_0(A) -> k3_filter_0(A,B) = k1_filter_0(A) & u1_struct_0(A) = k3_filter_0(A,B)))))) # label(t31_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3360 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> r1_tarski(C,k5_filter_0(A,B,C)) & r1_tarski(B,k5_filter_0(A,B,C)))))))) # label(t49_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3361 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k7_lattices(A,B),C) = k4_filter_0(A,B,C))))))) # label(t55_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3362 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(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_filter_0(D,A) -> (r2_hidden(B,D) & r2_hidden(k4_filter_0(A,B,C),D) -> r2_hidden(C,D)))))))))) # label(t41_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3363 $T # label(t86_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3364 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v11_lattices(A))) # label(t39_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3365 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_filter_0(A,B) = a_2_0_filter_0(A,B))))) # label(d3_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3366 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v14_lattices(A) -> v14_lattices(k8_filter_0(A,B))))))) # label(t66_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3367 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,C,B) = k9_filter_0(A,B,C))))))) # label(t77_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3368 $T # label(t43_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3369 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> v3_filter_0(k8_filter_0(A,B))))))) # label(t69_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3370 (all A all B (m1_filter_0(B,A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> k11_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3371 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v3_filter_0(A))) # label(t40_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3372 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E exists F (m1_subset_1(F,u1_struct_0(B)) & k4_lattices(B,E,F) = A & r2_hidden(F,D) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_filter_0(B,C,D))))) # label(fraenkel_a_3_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3373 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> (k8_filter_0(A,B) = C <-> (exists D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & (exists E (v1_funct_2(E,k2_zfmisc_1(B,B),B) & C = g3_lattices(B,D,E) & E = k1_realset1(u1_lattices(A),B) & D = k1_realset1(u2_lattices(A),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E))) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D)))))))))) # label(d10_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3374 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> r1_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t81_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3375 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k9_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k9_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3376 $T # label(t8_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3377 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,B,C) = k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,C,B)))))))) # label(d11_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3378 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k4_filter_0(A,C,D),E) & r2_hidden(k4_filter_0(A,B,C),E) -> r2_hidden(k4_filter_0(A,B,D),E)))))))))))) # label(t54_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3379 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (-v3_struct_0(C) & v10_lattices(C) & v3_filter_0(C) & l3_lattices(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> (all G (m1_filter_0(G,C) -> (all H (m1_subset_1(H,u1_struct_0(A)) -> (all I (m1_subset_1(I,u1_struct_0(A)) -> (all J (m1_subset_1(J,u1_struct_0(A)) -> (r1_filter_0(C,G,D,E) & r1_filter_0(C,G,E,F) -> r1_filter_0(C,G,D,F)) & (r1_filter_0(A,B,I,J) & r1_filter_0(A,B,H,I) -> r1_filter_0(A,B,H,J)))))))))))))))))))))) # label(t90_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3380 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_filter_0(A,B,B) = k6_lattices(A))))) # label(t38_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3381 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v12_lattices(A) -> v12_lattices(k8_filter_0(A,B))))))) # label(t67_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3382 $T # label(t36_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3383 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v13_lattices(k8_filter_0(A,k2_filter_0(A,B))))))) # label(t70_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3384 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,B,k3_lattices(A,k7_lattices(A,B),C)),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,D),C) -> r3_lattices(A,D,k3_lattices(A,k7_lattices(A,B),C)))))))))))) # label(t34_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3385 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) -> -v3_struct_0(A) & v5_lattices(A) & v8_lattices(A) & v10_lattices(A) & v11_lattices(A) & v12_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A)))) # label(cc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3386 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k5_lattices(k8_filter_0(A,k2_filter_0(A,B))))))) # label(t71_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3387 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k1_filter_0(A) = u1_struct_0(A))) # label(d2_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3388 (all A all B all C (v10_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> k7_filter_0(A,B,C) = k5_filter_0(A,B,C))) # label(redefinition_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3389 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r2_hidden(B,C) -> r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C))))))))) # label(t29_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3390 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> k5_filter_0(A,B,C) = a_3_0_filter_0(A,B,C))))))) # label(d9_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3391 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) <-> -r2_hidden(k7_lattices(A,C),B))))))))) # label(t59_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3392 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) -> v1_relat_1(k10_filter_0(A,B)))) # label(dt_k10_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3393 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> r3_relat_2(k10_filter_0(A,B),u1_struct_0(A)))))) # label(t82_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3394 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> k3_relat_1(k10_filter_0(A,B)) = u1_struct_0(A)))))) # label(t85_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3395 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,C) -> r3_lattices(A,k3_lattices(A,B,D),C)))))))))) # label(t6_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3396 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (all E (m1_subset_1(E,u1_struct_0(k8_filter_0(A,D))) -> (all F (m1_subset_1(F,u1_struct_0(k8_filter_0(A,D))) -> (E = B & F = C -> (r3_lattices(A,B,C) <-> r3_lattices(k8_filter_0(A,D),E,F))))))))))))))) # label(t65_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3397 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(k4_lattices(A,E,F) = B & r2_hidden(F,D) & r2_hidden(E,C)))))) & r2_hidden(B,k5_filter_0(A,C,D))))))))) # label(t45_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3398 $T # label(t76_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3399 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)))))) # label(t80_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3400 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> k3_filter_0(A,B) = B)))) # label(t26_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3401 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k3_filter_0(A,k4_subset_1(u1_struct_0(A),D,k6_domain_1(u1_struct_0(A),C)))) -> r2_hidden(k4_filter_0(A,C,B),k3_filter_0(A,D))))))))))) # label(t53_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3402 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) -> m1_filter_0(k6_filter_0(A,B,C),A))) # label(dt_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3403 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (-v3_struct_0(C) & l3_lattices(C) & v3_filter_0(C) & v10_lattices(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_filter_0(E,C) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> r1_filter_0(A,B,F,F) & r1_filter_0(C,E,D,D))))))))))))) # label(t88_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3404 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (v1_relat_1(C) -> (r1_tarski(k3_relat_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)) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E),C) <-> r2_hidden(k9_filter_0(A,D,E),B)))))) <-> C = k10_filter_0(A,B)))))))) # label(d12_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3405 (all A all B (v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,B)) & l3_lattices(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)))) # label(dt_k8_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3406 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(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)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k9_filter_0(A,C,D),E) & r2_hidden(k9_filter_0(A,B,C),E) -> r2_hidden(k9_filter_0(A,B,D),E)))))))))))) # label(t78_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3407 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) <-> v2_filter_0(B,A) & k1_filter_0(A) != B))))) # label(t58_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3408 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,C,B) <-> r2_hidden(B,k2_filter_0(A,C))))))))) # label(t18_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3409 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(-(all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = B)) & k2_filter_0(A,B) = u1_struct_0(A)))))) # label(t23_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3410 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> r8_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t83_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3411 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m1_filter_0(u1_struct_0(A),A))) # label(t15_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3412 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> k5_filter_0(A,C,B) = k5_filter_0(A,B,C))))))) # label(t46_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3413 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k3_filter_0(A,B),k3_filter_0(A,C))))))))) # label(t27_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3414 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_lattices(A) = k4_lattices(A,B,k7_lattices(A,C)) <-> r3_lattices(A,B,C)))))))) # label(t56_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3415 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v10_lattices(A) & v15_lattices(A) & v10_lattices(A) & l3_lattices(A) & v12_lattices(A) & -v3_struct_0(A) & l3_lattices(A) & v16_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B))) & v10_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v16_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t74_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3416 $T # label(t28_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3417 $T # label(t35_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3418 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> v14_lattices(A))) # label(t37_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3419 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(B,k2_filter_0(A,B)) & r2_hidden(k3_lattices(A,B,C),k2_filter_0(A,B)) & r2_hidden(k3_lattices(A,C,B),k2_filter_0(A,B)))))))) # label(t19_filter_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3420 (all A all B (-v3_struct_0(A) & l3_lattices(A) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & v10_lattices(A) -> r1_filter_1(A,A))) # label(reflexivity_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3421 (all A (-v1_xboole_0(A) -> (all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(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) -> (m2_filter_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & m2_relset_1(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) -> ((all E all F all G all H (r2_hidden(G,E) & r2_hidden(H,F) & r2_hidden(F,k8_eqrel_1(A,B)) & r2_hidden(E,k8_eqrel_1(A,B)) -> k1_binop_1(D,E,F) = k6_eqrel_1(A,B,k1_binop_1(C,G,H)))) <-> k4_filter_1(A,B,C) = D)))))))))) # label(d4_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3422 (all A all B all C (v1_partfun1(B,A,A) & m1_subset_1(C,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & -v1_xboole_0(A) -> m2_subset_1(k2_filter_1(A,B,C),k1_zfmisc_1(A),k8_eqrel_1(A,B)))) # label(dt_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3423 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_filter_1(A,B,k4_lattices(A,C,D)) = k4_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) & k6_filter_1(A,B,k3_lattices(A,C,D)) = k3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)))))))))) # label(t15_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3424 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v8_relat_2(B) & -v1_xboole_0(A) -> v1_funct_1(k3_filter_1(A,B,C)) & v1_funct_2(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & m2_relset_1(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)))) # label(dt_k3_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3425 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_filter_0(B,A) -> -v3_struct_0(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & v17_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)))))) # label(t21_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3426 (all A all B (v1_relat_1(B) & -v1_xboole_0(A) -> (all C (m2_filter_1(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(dt_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3427 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k10_filter_1(A,B,k3_lattices(A,C,D),k3_lattices(B,E,F)) = k3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) & k10_filter_1(A,B,k4_lattices(A,C,D),k4_lattices(B,E,F)) = k4_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)))))))))))))) # label(t36_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3428 (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_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) -> (r6_binop_1(B,E,F) & r6_binop_1(A,C,D) <-> r6_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t30_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3429 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,D,C)),k4_filter_0(A,k3_lattices(A,B,D),C)))))))))) # label(t57_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3430 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (m1_filter_1(C,A,B) -> (all D (m2_relset_1(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & v1_funct_2(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & v1_funct_1(D) -> (k3_filter_1(A,B,C) = D <-> (all E all F (r2_hidden(F,E) & r2_hidden(E,k8_eqrel_1(A,B)) -> k1_funct_1(D,E) = k6_eqrel_1(A,B,k1_funct_1(C,F)))))))))))))) # label(d3_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3431 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((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) -> (r2_hidden(k1_domain_1(A,A,D,E),B) & r2_hidden(k1_domain_1(A,A,F,G),B) -> r2_hidden(k1_domain_1(A,A,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,G)),B)))))))))) <-> m2_filter_1(C,A,B)))))))) # label(d2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3432 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> k8_filter_1(A,B) = g3_lattices(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u2_lattices(A),u2_lattices(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u1_lattices(A),u1_lattices(B))))))) # label(d7_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3433 (all A all B all C all D (l3_lattices(A) & v10_lattices(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & -v3_struct_0(B) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k10_filter_1(A,B,C,D),u1_struct_0(k8_filter_1(A,B))))) # label(dt_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3434 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (all C (m1_filter_1(C,A,B) -> m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C))))) # label(dt_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3435 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (exists C m2_filter_1(C,A,B)))) # label(existence_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3436 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_filter_1(C,A,B) -> (v2_binop_1(C,A) -> v2_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B))))))))) # label(t5_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3437 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) <-> r3_lattices(A,C,D) & r3_lattices(B,E,F)))))))))))))) # label(t37_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3438 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all D (m1_subset_1(D,u1_struct_0(k5_filter_1(A,B))) -> ((all E (v3_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) -> (E = k10_filter_0(A,B) -> D = k2_filter_1(u1_struct_0(A),E,C)))) <-> k6_filter_1(A,B,C) = D)))))))))) # label(d6_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3439 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k1_relat_1(k9_filter_1(A)) = u1_struct_0(A) & u1_struct_0(A) = k2_relat_1(k9_filter_1(A)) & k3_relat_1(k9_filter_1(A)) = u1_struct_0(A))) # label(t33_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3440 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v13_lattices(A) -> -v3_struct_0(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & k6_filter_1(A,B,k5_lattices(A)) = k5_lattices(k5_filter_1(A,B)) & v13_lattices(k5_filter_1(A,B))))))) # label(t18_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3441 (all A all B all C (v10_lattices(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & -v3_struct_0(A) -> k1_filter_1(A,C,B) = k1_filter_1(A,B,C))) # label(commutativity_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3442 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_filter_0(A,B) = k2_filter_0(A,C) -> C = B))))))) # label(t2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3443 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (v14_lattices(B) & v14_lattices(A) <-> v14_lattices(k8_filter_1(A,B))))))) # label(t41_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3444 (all A all B all C (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & v10_lattices(A) -> B = k1_filter_1(A,B,B))) # label(idempotence_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3445 (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_xboole_0(k7_eqrel_1(A,B)))) # label(fc1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3446 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> m2_filter_1(u1_lattices(A),u1_struct_0(A),k11_filter_0(A,B)))))) # label(t14_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3447 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k4_filter_0(A,C,D),B) <-> r3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D))))))))))) # label(t16_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3448 (all A all B (v10_lattices(A) & l3_lattices(A) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & -v3_struct_0(A) -> (r1_filter_1(A,B) -> r1_filter_1(B,A)))) # label(symmetry_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3449 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v10_lattices(A) & v11_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & v11_lattices(B) & l3_lattices(B) & l3_lattices(A) & -v3_struct_0(A) <-> v11_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B))))))) # label(t39_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3450 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & l3_lattices(B) & l3_lattices(A) -> v3_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3451 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v16_lattices(B) & v15_lattices(B) <-> v10_lattices(k8_filter_1(A,B)) & v15_lattices(k8_filter_1(A,B)) & v16_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B))))))) # label(t46_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3452 (all A all B all C (-v1_xboole_0(A) & v8_relat_2(B) & m1_subset_1(C,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k6_eqrel_1(A,B,C) = k2_filter_1(A,B,C))) # label(redefinition_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3453 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_filter_0(A,B,k4_filter_0(A,C,D)) = k4_filter_0(A,k4_lattices(A,B,C),D))))))))) # label(t17_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3454 (all A (m1_subset_1(A,f1_s1_filter_1) -> p1_s1_filter_1(k2_filter_1(f1_s1_filter_1,f2_s1_filter_1,A)))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s1_filter_1),k8_eqrel_1(f1_s1_filter_1,f2_s1_filter_1)) -> p1_s1_filter_1(A))) # label(s1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3455 (all A (-v1_xboole_0(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,A) -> (all D (m2_filter_1(D,A,B) -> (r3_binop_1(A,C,D) -> r3_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t8_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3456 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_filter_1(A,k8_filter_1(k5_filter_1(A,k2_filter_0(A,B)),k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t62_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3457 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (exists C m1_filter_1(C,A,B)))) # label(existence_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3458 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (-v3_struct_0(C) & v10_lattices(C) & l3_lattices(C) -> (r1_filter_1(B,C) & r1_filter_1(A,B) -> r1_filter_1(A,C)))))))) # label(t34_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3459 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,C,D))) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,B,D),C)) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,D,C))) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,D,B),C)))))))))) # label(t56_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3460 (all A (m1_subset_1(A,f1_s5_filter_1) -> (all B (m1_subset_1(B,f1_s5_filter_1) -> (all C (m1_subset_1(C,f2_s5_filter_1) -> (all D (m1_subset_1(D,f2_s5_filter_1) -> p1_s5_filter_1(k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,A,C),k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,B,D)))))))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1)) -> (all B (m1_subset_1(B,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1)) -> p1_s5_filter_1(A,B))))) # label(s5_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3461 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> r1_filter_1(k8_filter_1(A,B),k8_filter_1(B,A)))))) # label(t50_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3462 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r2_binop_1(B,D,F) & r2_binop_1(A,C,E) <-> r2_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F))))))))))))))) # label(t26_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3463 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> m2_relset_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v1_funct_2(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v1_funct_1(k7_filter_1(A,B,C,D)))) # label(dt_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3464 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (r3_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) <-> r3_binop_1(B,D,F) & r3_binop_1(A,C,E)))))))))))))) # label(t27_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3465 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r6_binop_1(A,C,D) -> r6_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t11_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3466 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (m2_filter_1(C,A,B) -> (v1_binop_1(C,A) -> v1_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B))))))))) # label(t4_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3467 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k9_filter_0(A,B,D) = k9_filter_0(A,B,C) -> D = C))))))))) # label(t53_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3468 (all A (m1_subset_1(A,f1_s3_filter_1) -> (all B (m1_subset_1(B,f1_s3_filter_1) -> (all C (m1_subset_1(C,f1_s3_filter_1) -> p1_s3_filter_1(k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,A),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,B),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,C)))))))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> (all B (m2_subset_1(B,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> (all C (m2_subset_1(C,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> p1_s3_filter_1(A,B,C))))))) # label(s3_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3469 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) -> (v1_binop_1(C,A) & v1_binop_1(D,B) <-> v1_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B))))))))))) # label(t23_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3470 (all A (m1_subset_1(A,f1_s6_filter_1) -> (all B (m1_subset_1(B,f1_s6_filter_1) -> (all C (m1_subset_1(C,f1_s6_filter_1) -> (all D (m1_subset_1(D,f2_s6_filter_1) -> (all E (m1_subset_1(E,f2_s6_filter_1) -> (all F (m1_subset_1(F,f2_s6_filter_1) -> p1_s6_filter_1(k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,A,D),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,B,E),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,C,F)))))))))))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> (all B (m1_subset_1(B,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> (all C (m1_subset_1(C,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> p1_s6_filter_1(A,B,C))))))) # label(s6_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3471 (all A (m1_subset_1(A,f1_s4_filter_1) -> (all B (m1_subset_1(B,f2_s4_filter_1) -> p1_s4_filter_1(k1_domain_1(f1_s4_filter_1,f2_s4_filter_1,A,B)))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s4_filter_1,f2_s4_filter_1)) -> p1_s4_filter_1(A))) # label(s4_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.12 3472 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & v10_lattices(A) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v13_lattices(A) -> k5_lattices(k8_filter_1(A,B)) = k10_filter_1(A,B,k5_lattices(A),k5_lattices(B))))))) # label(t43_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3473 (all A all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> ((exists C exists D (m1_subset_1(D,u1_struct_0(B)) & r3_lattices(B,C,D) & k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,D) = A & m1_subset_1(C,u1_struct_0(B)))) <-> r2_hidden(A,a_1_0_filter_1(B))))) # label(fraenkel_a_1_0_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3474 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r2_binop_1(A,C,D) -> r2_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t7_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3475 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> v10_lattices(k5_filter_1(A,B)) & k6_lattices(k5_filter_1(A,B)) = k6_filter_1(A,B,k6_lattices(A)) & l3_lattices(k5_filter_1(A,B)) & v14_lattices(k5_filter_1(A,B)) & -v3_struct_0(k5_filter_1(A,B)))))) # label(t19_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3476 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (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) & m2_relset_1(G,k2_zfmisc_1(A,A),A) & v1_funct_2(G,k2_zfmisc_1(A,A),A) -> (all H (m2_relset_1(H,k2_zfmisc_1(B,B),B) & v1_funct_2(H,k2_zfmisc_1(B,B),B) & v1_funct_1(H) -> k2_binop_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k7_filter_1(A,B,G,H),k1_domain_1(A,B,C,E),k1_domain_1(A,B,D,F)) = k1_domain_1(A,B,k2_binop_1(A,A,A,G,C,D),k2_binop_1(B,B,B,H,E,F)))))))))))))))))) # label(t22_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3477 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r1_binop_1(B,D,F) & r1_binop_1(A,C,E) <-> r1_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F))))))))))))))) # label(t25_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3478 (all A (m1_subset_1(A,f1_s2_filter_1) -> (all B (m1_subset_1(B,f1_s2_filter_1) -> p1_s2_filter_1(k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,A),k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,B)))))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1)) -> (all B (m2_subset_1(B,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1)) -> p1_s2_filter_1(A,B))))) # label(s2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3479 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k9_filter_0(A,B,k9_filter_0(A,B,C)))))))) # label(t54_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3480 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (v13_lattices(B) & v13_lattices(A) <-> v13_lattices(k8_filter_1(A,B))))))) # label(t40_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3481 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) -> (r4_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) <-> r4_binop_1(B,E,F) & r4_binop_1(A,C,D)))))))))))))) # label(t28_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3482 (all A all B (v10_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) & -v3_struct_0(A) -> -v3_struct_0(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & v3_lattices(k5_filter_1(A,B)))) # label(dt_k5_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3483 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (v3_filter_0(k8_filter_1(A,B)) <-> v3_filter_0(A) & v3_filter_0(B)))))) # label(t48_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3484 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(C,A) & v2_binop_1(D,B) <-> v2_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B))))))))))) # label(t24_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3485 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,B,C) = k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C))))))))) # label(t51_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3486 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> k3_funct_4(C,D) = k7_filter_1(A,B,C,D))) # label(redefinition_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3487 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v12_lattices(A) & v12_lattices(B) <-> v12_lattices(k8_filter_1(A,B))))))) # label(t38_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3488 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all C (v10_lattices(C) & l3_lattices(C) & v3_lattices(C) & -v3_struct_0(C) -> (k5_filter_1(A,B) = C <-> (all D (v3_relat_2(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(D,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(D) -> (k10_filter_0(A,B) = D -> C = g3_lattices(k8_eqrel_1(u1_struct_0(A),D),k4_filter_1(u1_struct_0(A),D,u2_lattices(A)),k4_filter_1(u1_struct_0(A),D,u1_lattices(A)))))))))))))) # label(d5_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3489 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k3_lattices(A,B,k9_filter_0(A,B,C)),k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B)) -> r3_lattices(A,D,k3_lattices(A,B,k9_filter_0(A,B,C)))))))))))) # label(t61_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3490 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) -> m1_filter_0(k1_filter_1(A,B,C),A))) # label(dt_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3491 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,D)),k4_filter_0(A,B,k4_lattices(A,C,D))))))))))) # label(t58_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3492 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k9_filter_1(A)) <-> r3_lattices(A,B,C)))))))) # label(t32_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3493 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(B) & v14_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) -> k10_filter_1(A,B,k6_lattices(A),k6_lattices(B)) = k6_lattices(k8_filter_1(A,B))))))) # label(t44_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3494 (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_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (r5_binop_1(A,C,D) & r5_binop_1(B,E,F) <-> r5_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t29_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3495 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (m1_filter_1(C,A,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(k1_domain_1(A,A,D,E),B) -> r2_hidden(k1_domain_1(A,A,k8_funct_2(A,A,C,D),k8_funct_2(A,A,C,E)),B))))))))))))) # label(d1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3496 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,k7_lattices(A,C)) = k7_lattices(A,k4_filter_0(A,B,C)) & k7_lattices(A,k9_filter_0(A,B,C)) = k3_lattices(A,k4_lattices(A,B,k7_lattices(A,C)),k4_lattices(A,k7_lattices(A,B),C)) & k7_lattices(A,k9_filter_0(A,B,C)) = k9_filter_0(A,k7_lattices(A,B),C) & k9_filter_0(A,B,k7_lattices(A,C)) = k7_lattices(A,k9_filter_0(A,B,C)))))))) # label(t52_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3497 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> v3_filter_0(k5_filter_1(A,B)))))) # label(t20_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3498 (all A all B all C all D (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & v10_lattices(B) & v10_lattices(A) -> k10_filter_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3499 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m2_filter_1(E,A,B) -> k2_filter_1(A,B,k2_binop_1(A,A,A,E,C,D)) = k2_binop_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B),k8_eqrel_1(A,B),k4_filter_1(A,B,E),k2_filter_1(A,B,C),k2_filter_1(A,B,D)))))))))))) # label(t3_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3500 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r5_binop_1(A,C,D) -> r5_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t10_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3501 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r4_binop_1(A,C,D) -> r4_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t9_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3502 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r1_lattice2(A,C,D) -> r1_lattice2(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t12_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3503 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) -> -v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v10_lattices(A)))))) # label(t35_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3504 (all A all B (-v3_struct_0(A) & l3_lattices(A) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & v10_lattices(A) -> v8_lattices(k8_filter_1(A,B)) & v9_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & v7_lattices(k8_filter_1(A,B)) & v6_lattices(k8_filter_1(A,B)) & v5_lattices(k8_filter_1(A,B)) & v4_lattices(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B)))) # label(fc3_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3505 (all A all B (l3_lattices(A) & l3_lattices(B) & -v3_struct_0(B) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)))) # label(fc2_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3506 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (r4_wellord1(k9_filter_1(A),k9_filter_1(B)) <-> r1_filter_1(A,B)))))) # label(d9_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3507 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> a_1_0_filter_1(A) = k9_filter_1(A))) # label(d8_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3508 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k6_filter_1(A,B,C),u1_struct_0(k5_filter_1(A,B))))) # label(dt_k6_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3509 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (-v3_struct_0(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v17_lattices(k8_filter_1(A,B)) <-> -v3_struct_0(A) & l3_lattices(A) & l3_lattices(B) & v17_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & v17_lattices(A) & v10_lattices(A)))))) # label(t47_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3510 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(E,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) & r2_hidden(C,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) -> r2_hidden(k4_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) & r2_hidden(k3_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D))))))))))))) # label(t60_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3511 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> m2_filter_1(u2_lattices(A),u1_struct_0(A),k11_filter_0(A,B)))))) # label(t13_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3512 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (r2_hidden(k9_filter_0(A,E,F),B) & r2_hidden(k9_filter_0(A,C,D),B) -> r2_hidden(k9_filter_0(A,k4_lattices(A,C,E),k4_lattices(A,D,F)),B) & r2_hidden(k9_filter_0(A,k3_lattices(A,C,E),k3_lattices(A,D,F)),B)))))))))))))) # label(t59_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3513 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (-v3_struct_0(A) & v15_lattices(A) & v10_lattices(B) & v15_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) -> (r2_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) <-> r2_lattices(B,E,F) & r2_lattices(A,C,D))))))))))))))) # label(t45_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3514 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v1_relat_1(k9_filter_1(A)))) # label(dt_k9_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3515 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (r1_lattice2(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) <-> r1_lattice2(B,E,F) & r1_lattice2(A,C,D)))))))))))))) # label(t31_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3516 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_filter_0(A,C,B) = k4_filter_0(A,k3_lattices(A,B,C),B) & k4_filter_0(A,B,C) = k4_filter_0(A,B,k4_lattices(A,B,C)))))))) # label(t55_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3517 (all A (-v1_xboole_0(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,A) -> (all D (m2_filter_1(D,A,B) -> (r1_binop_1(A,C,D) -> r1_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t6_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3518 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> m1_filter_0(k5_subset_1(u1_struct_0(A),B,C),A))))))) # label(t1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3519 (all A all B all C (v10_lattices(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & -v3_struct_0(A) -> k3_xboole_0(B,C) = k1_filter_1(A,B,C))) # label(redefinition_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3520 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (v15_lattices(k8_filter_1(A,B)) <-> v15_lattices(A) & v15_lattices(B)))))) # label(t42_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3521 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> k1_lattice2(k8_filter_1(A,B)) = k8_filter_1(k1_lattice2(A),k1_lattice2(B)))))) # label(t49_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3522 (all A all B all C (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v1_funct_2(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & m2_relset_1(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & v1_funct_1(k4_filter_1(A,B,C)))) # label(dt_k4_filter_1) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3523 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,B,C) = k11_lattice3(A,C,B))))))) # label(t15_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3524 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v3_lattice3(A) -> v1_lattice3(A) & v2_lattice3(A)))) # label(t12_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3525 r1_tarski(f2_s2_lattice3,k1_relat_1(f4_s2_lattice3)) -> a_0_2_lattice3 = k9_relat_1(f4_s2_lattice3,a_0_1_lattice3) # label(s2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3526 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (v6_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k16_lattice3(A,a_3_5_lattice3(A,B,C)),k3_lattices(A,C,k16_lattice3(A,B)))))))) # label(t36_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3527 (all A (A = k6_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)))) # label(t4_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3528 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> k15_lattice3(A,a_3_6_lattice3(A,B,C)) = k4_filter_0(A,B,C)))))))) # label(t52_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3529 (all A v4_lattice3(k1_lattice3(A))) # label(t25_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3530 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice3(A))) -> (r1_lattices(k1_lattice3(A),B,C) <-> r1_tarski(B,C)))))) # label(t2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3531 (all A (l1_orders_2(A) -> (v2_lattice3(k7_lattice3(A)) <-> v1_lattice3(A)))) # label(t10_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3532 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattice3(A,B))))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3533 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v1_lattice3(A) & v4_orders_2(A) -> m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3534 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r1_orders_2(A,D,C))))))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3535 (all A ((exists B (k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B)) = A & p1_s2_lattice3(B) & m1_subset_1(B,f1_s2_lattice3))) <-> r2_hidden(A,a_0_2_lattice3))) # label(fraenkel_a_0_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3536 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C r3_lattices(A,k3_lattices(A,B,k16_lattice3(A,C)),k16_lattice3(A,a_3_4_lattice3(A,B,C)))))))) # label(t35_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3537 (all A all B all C (v2_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v4_orders_2(A) -> k11_lattice3(A,B,C) = k12_lattice3(A,B,C))) # label(redefinition_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3538 (all A (v3_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3539 (all A all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v6_lattice3(B) & v4_lattice3(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_lattices(B,C,k16_lattice3(B,A)) = k16_lattice3(B,a_3_9_lattice3(A,B,C)) & k3_lattices(B,k16_lattice3(B,A),C) = k16_lattice3(B,a_3_10_lattice3(A,B,C)))))) # label(t55_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3540 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> v10_lattices(A) & k6_lattices(A) = k15_lattice3(A,u1_struct_0(A)) & l3_lattices(A) & v14_lattices(A) & -v3_struct_0(A))) # label(t51_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3541 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,B,k13_lattice3(A,B,C)) = B)))))) # label(t18_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3542 (all A (l1_orders_2(A) -> k7_lattice3(A) = g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))))) # label(d5_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3543 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & r1_orders_2(A,D,B) & m1_subset_1(D,u1_struct_0(A)))))))) <-> v2_lattice3(A)))) # label(d11_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3544 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k15_lattice3(A,a_2_3_lattice3(A,B)) & k16_lattice3(A,a_2_4_lattice3(A,B)) = B)))) # label(t45_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3545 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k7_lattice3(A))) -> k9_lattice3(A,B) = B)))) # label(d7_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3546 (all A (r2_hidden(A,a_0_0_lattice3) <-> (exists B (m1_subset_1(B,f2_s1_lattice3) & p1_s1_lattice3(B) & f1_s1_lattice3 = A)))) # label(fraenkel_a_0_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3547 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k16_lattice3(A,k1_struct_0(A,B)) & k15_lattice3(A,k1_struct_0(A,B)) = B)))) # label(t43_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3548 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) -> ((exists E (r2_hidden(E,D) & k3_lattices(B,C,E) = A & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_4_lattice3(B,C,D))))) # label(fraenkel_a_3_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3549 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> m1_subset_1(k5_lattice3(A,B),u1_struct_0(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3550 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) -> r3_lattices(A,B,k15_lattice3(A,C)) & r3_lattices(A,k16_lattice3(A,C),B))))))) # label(t38_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3551 (all A all B all C all D (-v3_struct_0(C) & v4_lattice3(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v6_lattice3(C) & v10_lattices(C) -> (r2_hidden(A,a_3_9_lattice3(B,C,D)) <-> (exists E (r2_hidden(E,B) & k3_lattices(C,D,E) = A & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_9_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3552 (all A all B all C all D (-v3_struct_0(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & k1_lattices(B,D,E) = A & r2_hidden(E,C))) <-> r2_hidden(A,a_3_1_lattice3(B,C,D))))) # label(fraenkel_a_3_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3553 (all A (l1_orders_2(A) -> (v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,B,D) & r1_orders_2(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,C,E) & r1_orders_2(A,B,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) & r1_orders_2(A,B,D) <-> D = k10_lattice3(A,B,C)))))))))))) # label(d13_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3554 (all A (l1_orders_2(A) -> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k7_lattice3(k7_lattice3(A)))) # label(t8_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3555 (all A all B (v4_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> B = k6_lattice3(A,k6_lattice3(A,B)))) # label(involutiveness_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3556 (all A (v13_lattices(k1_lattice3(A)) & k1_xboole_0 = k5_lattices(k1_lattice3(A)))) # label(t3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3557 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B k16_lattice3(A,a_2_2_lattice3(A,B)) = k15_lattice3(A,B)))) # label(t37_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3558 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v5_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r4_lattice3(A,C,B) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,B) -> r1_lattices(A,C,F)))) & r4_lattice3(A,E,a_3_0_lattice3(A,B,D)) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,a_3_0_lattice3(A,B,D)) -> r1_lattices(A,E,F)))) -> r1_lattices(A,k2_lattices(A,D,C),E))))))))))) # label(d19_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3559 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3560 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r1_orders_2(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3561 (all A (l3_lattices(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k15_lattice3(A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r4_lattice3(A,D,B) -> r1_lattices(A,C,D)))) & r4_lattice3(A,C,B))))))) # label(d21_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3562 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3563 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)))) # label(t11_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3564 (all A all B all C (v4_lattice3(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_2_lattice3(B,C)) <-> (exists D (r4_lattice3(B,D,C) & A = D & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3565 (all A (l1_orders_2(A) -> (v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,B))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k11_lattice3(A,B,C) <-> r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D))))))))))))))) # label(d14_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3566 (all A (v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3567 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_lattice3(A,B) = B)))) # label(d6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3568 (all A all B all C all D (v4_lattice3(C) & v6_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> ((exists E (r2_hidden(E,B) & k3_lattices(C,E,D) = A & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_10_lattice3(B,C,D))))) # label(fraenkel_a_3_10_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3569 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C (r1_tarski(B,C) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)) & r3_lattices(A,k16_lattice3(A,C),k16_lattice3(A,B)))))) # label(t46_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3570 $T # label(t39_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3571 (all A (v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k10_lattice3(A,C,B) = k10_lattice3(A,B,C))))))) # label(t13_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3572 (all A all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_lattice3(B))) -> (r2_lattice3(k3_lattice3(B),A,C) <-> r4_lattice3(B,k5_lattice3(B,C),A)))))) # label(t31_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3573 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)))) # label(fc5_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3574 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice3(A))) -> k3_xboole_0(B,C) = k2_lattices(k1_lattice3(A),B,C) & k2_xboole_0(B,C) = k1_lattices(k1_lattice3(A),B,C))))) # label(t1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3575 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k3_lattice3(k1_lattice2(A)) = k7_lattice3(k3_lattice3(A)) & k6_lattice3(u1_struct_0(A),k2_lattice3(A)) = k2_lattice3(k1_lattice2(A)))) # label(t20_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3576 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> -(r2_hidden(E,C) & r3_lattices(A,D,E)))) & r2_hidden(D,B)))) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)))))) # label(t48_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3577 (all A (v3_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v11_lattices(k1_lattice3(A)) & v12_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A)) & v16_lattices(k1_lattice3(A)) & v15_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3578 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> k5_lattice3(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3579 (exists A (l3_lattices(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v4_lattice3(A) & v6_lattice3(A) & v5_lattice3(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A))) # label(rc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3580 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) -> (r2_hidden(A,a_3_5_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k3_lattices(B,D,E) = A & r2_hidden(E,C)))))) # label(fraenkel_a_3_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3581 (all A (l1_orders_2(A) -> (v2_lattice3(A) -> -v3_struct_0(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3582 (all A (l1_orders_2(A) -> v3_lattices(k14_lattice3(A)) & l3_lattices(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)) & -v3_struct_0(k14_lattice3(A)))) # label(dt_k14_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.13 3583 (exists A (m1_subset_1(A,f2_s1_lattice3) & p1_s1_lattice3(A))) -> k1_tarski(f1_s1_lattice3) = a_0_0_lattice3 # label(s1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3584 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k10_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3585 (all A all B all C (v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_orders_2(A) -> k13_lattice3(A,C,B) = k13_lattice3(A,B,C))) # label(commutativity_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3586 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v17_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r3_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) <-> r4_lattice3(B,C,A)))))) # label(t23_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3587 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) & r3_lattice3(A,B,C) -> B = k16_lattice3(A,C))))))) # label(t42_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3588 (all A all B (l3_lattices(B) & v3_lattices(B) -> (B = k1_lattice3(A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> k5_subset_1(A,C,D) = k1_binop_1(u1_lattices(B),C,D) & k1_binop_1(u2_lattices(B),C,D) = k4_subset_1(A,C,D))))) & u1_struct_0(B) = k1_zfmisc_1(A)))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3589 (exists A (l1_orders_2(A) & -v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_lattice3(A) & v1_lattice3(A) & v1_orders_2(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3590 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> k13_lattice3(A,B,C) = k10_lattice3(A,B,C))) # label(redefinition_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3591 (all A (l1_orders_2(A) -> v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) # label(dt_k7_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3592 (all A all B all C all D (-v3_struct_0(C) & v4_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v5_lattice3(C) & v10_lattices(C) -> (r2_hidden(A,a_3_8_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(C)) & A = k4_lattices(C,E,D) & r2_hidden(E,B)))))) # label(fraenkel_a_3_8_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3593 (exists A (l1_orders_2(A) & -v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v3_lattice3(A) & v4_orders_2(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3594 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v4_lattice3(B) -> (r2_hidden(A,a_2_5_lattice3(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & r3_lattices(B,D,E))) & D = A))))) # label(fraenkel_a_2_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3595 (all A ((exists B (m1_subset_1(B,f1_s2_lattice3) & f3_s2_lattice3(B) = A & p1_s2_lattice3(B))) <-> r2_hidden(A,a_0_1_lattice3))) # label(fraenkel_a_0_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3596 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k15_lattice3(A,k2_struct_0(A,B,C)) & k16_lattice3(A,k2_struct_0(A,B,C)) = k4_lattices(A,B,C))))))) # label(t44_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3597 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v4_lattice3(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & k15_lattice3(B,D) = A & r2_hidden(D,C))) <-> r2_hidden(A,a_2_7_lattice3(B,C))))) # label(fraenkel_a_2_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3598 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v5_lattice3(B) & v4_lattice3(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k4_lattices(B,C,k15_lattice3(B,A)) = k15_lattice3(B,a_3_7_lattice3(A,B,C)) & k15_lattice3(B,a_3_8_lattice3(A,B,C)) = k4_lattices(B,k15_lattice3(B,A),C))))) # label(t54_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3599 (all A all B all C all D (-v3_struct_0(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) -> (r2_hidden(A,a_3_6_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k4_lattices(B,C,E),D)))))) # label(fraenkel_a_3_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3600 (all A all B all C (l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_1_lattice3(B,C)) <-> (exists D (D = A & r3_lattice3(B,D,C) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3601 (all A all B (v10_lattices(B) & l3_lattices(B) & v17_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) <-> r3_lattice3(B,C,A)))))) # label(t24_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3602 (all A (-v3_struct_0(A) & l1_orders_2(A) -> v1_orders_2(k7_lattice3(A)) & -v3_struct_0(k7_lattice3(A)))) # label(fc6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3603 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B k15_lattice3(A,a_2_1_lattice3(A,B)) = k16_lattice3(A,B)))) # label(d22_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3604 (all A all B (v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v4_relat_2(k6_lattice3(A,B)) & m2_relset_1(k6_lattice3(A,B),A,A) & v1_partfun1(k6_lattice3(A,B),A,A) & v8_relat_2(k6_lattice3(A,B)) & v1_relat_2(k6_lattice3(A,B)))) # label(dt_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3605 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r4_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,D,B)))))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3606 (all A all B (l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)))) # label(dt_k16_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3607 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) -> r3_lattices(A,B,k16_lattice3(A,C)))))))) # label(t40_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3608 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) -> (r2_hidden(A,a_2_3_lattice3(B,C)) <-> (exists D (A = D & r3_lattices(B,D,C) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3609 (all A all B all C (v10_lattices(C) & v17_lattices(C) & l3_lattices(C) & -v3_struct_0(C) -> (r2_hidden(A,a_2_0_lattice3(B,C)) <-> (exists D (r2_hidden(D,B) & k7_lattices(C,D) = A & m1_subset_1(D,u1_struct_0(C))))))) # label(fraenkel_a_2_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3610 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k1_zfmisc_1(A),A) & m2_relset_1(B,k1_zfmisc_1(A),A) & v1_funct_1(B) -> -((all C (m1_subset_1(C,A) -> C = k8_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)))) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k8_funct_2(k1_zfmisc_1(A),A,B,k10_relset_1(k1_zfmisc_1(A),A,B,C)) = k1_funct_1(B,k3_tarski(C)))) & (all C (v3_lattices(C) & v10_lattices(C) & v4_lattice3(C) & l3_lattices(C) & -v3_struct_0(C) -> -(A = u1_struct_0(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k1_funct_1(B,D) = k15_lattice3(C,D))))))))))) # label(t56_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3611 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))))) # label(dt_k8_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3612 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,C,E) & r1_orders_2(A,B,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) & r1_orders_2(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))) <-> v1_lattice3(A)))) # label(d10_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3613 (all A all B all C all D (-v3_struct_0(C) & v10_lattices(C) & v5_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v4_lattice3(C) -> (r2_hidden(A,a_3_7_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(C)) & A = k4_lattices(C,D,E) & r2_hidden(E,B)))))) # label(fraenkel_a_3_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3614 (all A all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_lattice3(B))) -> (r3_lattice3(B,k5_lattice3(B,C),A) <-> r1_lattice3(k3_lattice3(B),A,C)))))) # label(t29_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3615 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) -> ((exists E (k4_lattices(B,C,E) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_2_lattice3(B,C,D))))) # label(fraenkel_a_3_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3616 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,D,C) -> r3_lattices(A,D,B)))) <-> B = k16_lattice3(A,C))))))) # label(t34_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3617 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3618 (all A all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,C,A) <-> r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C))))))) # label(t30_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3619 (all A all B (v4_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> k4_relat_1(B) = k6_lattice3(A,B))) # label(redefinition_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3620 (all A v6_lattice3(k1_lattice3(A))) # label(t27_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3621 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v2_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3622 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (k3_lattice3(B) = k3_lattice3(A) -> g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))))) # label(t6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3623 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (r1_tarski(B,k1_zfmisc_1(u1_struct_0(A))) -> k15_lattice3(A,a_2_7_lattice3(A,B)) = k15_lattice3(A,k3_tarski(B)))))) # label(t49_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3624 (all A (l1_orders_2(A) -> (v1_lattice3(A) -> -v3_struct_0(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3625 (all A all B all C all D (m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_3_lattice3(B,C,D)) <-> (exists E (r2_hidden(E,C) & A = k4_lattices(B,D,E) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3626 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v5_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,C,k15_lattice3(A,B)),k15_lattice3(A,a_3_3_lattice3(A,B,C)))))))) # label(t33_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3627 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C r3_lattices(A,k15_lattice3(A,a_3_2_lattice3(A,B,C)),k4_lattices(A,B,k15_lattice3(A,C)))))))) # label(t32_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3628 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (exists B (-v3_struct_0(B) & v3_lattices(B) & k3_lattice3(B) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) & l3_lattices(B) & v10_lattices(B))))) # label(t19_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3629 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) <-> r3_lattices(A,B,C)))))))) # label(t7_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3630 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k9_filter_1(A) = k2_lattice3(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3631 (all A all B (-v3_struct_0(A) & l3_lattices(A) -> m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3632 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(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)) -> (v3_orders_2(A) -> k11_lattice3(A,k11_lattice3(A,B,C),D) = k11_lattice3(A,B,k11_lattice3(A,C,D))))))))))) # label(t16_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3633 (all A (v2_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)) & v5_lattices(k14_lattice3(A)) & v6_lattices(k14_lattice3(A)) & v8_lattices(k14_lattice3(A)) & v9_lattices(k14_lattice3(A)) & v4_lattice3(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)) & v7_lattices(k14_lattice3(A)) & v4_lattices(k14_lattice3(A)))) # label(fc7_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3634 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) -> m1_subset_1(k4_lattice3(A,B),u1_struct_0(k3_lattice3(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3635 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & v10_lattices(B) -> (r2_hidden(A,a_2_6_lattice3(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & (exists E (r3_lattices(B,E,D) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) & D = A))))) # label(fraenkel_a_2_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3636 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> k4_xboole_0(A,B) = k7_lattices(k1_lattice3(A),B))) # label(t5_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3637 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k11_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3638 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(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)) -> (v3_orders_2(A) -> k10_lattice3(A,B,k10_lattice3(A,C,D)) = k10_lattice3(A,k10_lattice3(A,B,C),D)))))))))) # label(t14_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3639 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(k7_lattice3(A))) -> m1_subset_1(k9_lattice3(A,B),u1_struct_0(A)))) # label(dt_k9_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3640 (all A all B all C (v4_orders_2(A) & v2_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) -> k12_lattice3(A,C,B) = k12_lattice3(A,B,C))) # label(commutativity_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3641 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (k15_lattice3(A,a_2_5_lattice3(A,B)) = k15_lattice3(A,B) & k16_lattice3(A,a_2_6_lattice3(A,B)) = k16_lattice3(A,B))))) # label(t47_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3642 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,B,D)))))))))) # label(d16_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3643 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v3_lattices(B) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) <-> k14_lattice3(A) = B)))))) # label(d15_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3644 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,k4_lattices(A,C,D)) <-> r3_lattice3(A,B,k2_struct_0(A,C,D))))))))))) # label(t21_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3645 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) & r4_lattice3(A,B,C) -> B = k15_lattice3(A,C))))))) # label(t41_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3646 (all A (l1_orders_2(A) -> ((all B exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & r2_lattice3(A,B,C) & m1_subset_1(C,u1_struct_0(A)))) <-> v3_lattice3(A)))) # label(d12_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3647 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> l3_lattices(A) & k5_lattices(A) = k15_lattice3(A,k1_xboole_0) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A))) # label(t50_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3648 (all A v5_lattice3(k1_lattice3(A))) # label(t26_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3649 (all A (v2_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k13_lattice3(A,k12_lattice3(A,B,C),C))))))) # label(t17_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3650 (all A (v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3651 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattice3(A,C,B) & r3_lattice3(A,E,a_3_1_lattice3(A,B,D)) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,a_3_1_lattice3(A,B,D)) -> r1_lattices(A,F,E)))) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,B) -> r1_lattices(A,F,C)))) -> r1_lattices(A,E,k1_lattices(A,D,C))))))))) <-> v6_lattice3(A)))) # label(d20_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3652 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k3_lattices(A,C,D),B) <-> r4_lattice3(A,B,k2_struct_0(A,C,D))))))))))) # label(t22_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3653 (all A all B all C all D (-v3_struct_0(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(A,a_3_0_lattice3(B,C,D)) <-> (exists E (r2_hidden(E,C) & k2_lattices(B,D,E) = A & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3654 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) <-> r3_lattice3(B,C,A)))))) # label(t28_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3655 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k2_lattice3(A)) & v4_relat_2(k2_lattice3(A)) & v1_relat_2(k2_lattice3(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3656 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> r1_orders_2(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B))))))))) # label(t9_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3657 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> v5_lattice3(A)))) # label(t53_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3658 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r4_lattice3(A,D,B) -> r1_lattices(A,C,D)))) & r4_lattice3(A,C,B) & m1_subset_1(C,u1_struct_0(A)))) <-> v4_lattice3(A)))) # label(d18_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3659 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v10_lattices(B) -> (r2_hidden(A,a_2_4_lattice3(B,C)) <-> (exists D (D = A & r3_lattices(B,C,D) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3660 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B all C (r1_yellow_0(A,C) & r1_yellow_0(A,k2_xboole_0(B,C)) & r1_yellow_0(A,B) -> k10_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k2_xboole_0(B,C)))))) # label(t36_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3661 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,B,D) -> r1_yellow_0(A,k2_tarski(B,C)) & k10_lattice3(A,B,C) = D) & (k10_lattice3(A,B,C) = D & r1_yellow_0(A,k2_tarski(B,C)) -> r1_orders_2(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D)))))))))) # label(t18_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3662 (all A all B (l1_orders_2(A) -> m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)))) # label(dt_k1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3663 (exists A (-v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_realset2(A) & v3_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & v1_orders_2(A) & l1_orders_2(A))) # label(rc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3664 (all A (l1_orders_2(A) -> (all B all C all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) & r2_lattice3(A,C,D) -> r2_lattice3(A,k2_xboole_0(B,C),D)) & (r1_lattice3(A,B,D) & r1_lattice3(A,C,D) -> r1_lattice3(A,k2_xboole_0(B,C),D)))))) # label(t10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3665 (all A (l1_orders_2(A) & v3_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r2_lattice3(A,B,C) -> r2_lattice3(A,B,D)))))))) # label(t11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3666 (all A (-v3_struct_0(A) & v3_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (k2_yellow_0(A,B) = k16_lattice3(k14_lattice3(A),B) & k1_yellow_0(A,B) = k15_lattice3(k14_lattice3(A),B))))) # label(t28_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3667 (all A (l1_orders_2(A) -> m1_subset_1(k4_yellow_0(A),u1_struct_0(A)))) # label(dt_k4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3668 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> (r2_lattice3(B,C,E) -> r2_lattice3(A,C,D)) & (r1_lattice3(B,C,E) -> r1_lattice3(A,C,D))))))))))))) # label(t63_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3669 (all A (l1_orders_2(A) -> (all B all C (r1_tarski(B,C) & r2_yellow_0(A,B) & r2_yellow_0(A,C) -> r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)))))) # label(t35_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3670 (all A (l1_orders_2(A) -> (exists B m1_yellow_0(B,A)))) # label(existence_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3671 (all A (l1_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3672 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (m1_yellow_0(B,A) <-> r1_tarski(u1_struct_0(B),u1_struct_0(A)) & r1_tarski(u1_orders_2(B),u1_orders_2(A))))))) # label(d13_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3673 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_lattice3(A,k1_xboole_0,B) & r1_lattice3(A,k1_xboole_0,B))))) # label(t6_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3674 (all A (l1_orders_2(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & r2_lattice3(A,u1_struct_0(A),B))) <-> v2_yellow_0(A)))) # label(d5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3675 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v8_yellow_0(B,A) -> v6_yellow_0(B,A)))))) # label(cc10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3676 (all A all B (m2_relset_1(B,A,A) -> k1_toler_1(B,A) = B)) # label(t56_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3677 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k12_lattice3(A,B,C) <-> r3_orders_2(A,B,C)))))))) # label(t25_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3678 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_lattice3(A) -> v1_lattice3(A) & v2_lattice3(A) & -v3_struct_0(A)))) # label(cc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3679 (all A (l1_orders_2(A) -> (all B ((exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_lattice3(A,B,E) -> r1_orders_2(A,D,E)))) -> D = C))) & r2_lattice3(A,B,C) & m1_subset_1(C,u1_struct_0(A)))) <-> r1_yellow_0(A,B))))) # label(d7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3680 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A) & v4_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A))))) # label(t57_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3681 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r1_orders_2(B,E,F) & F = D & E = C -> r1_orders_2(A,C,D)))))))))))))) # label(t60_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3682 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,C,B) -> r2_lattice3(A,k1_tarski(C),B)) & (r2_lattice3(A,k1_tarski(C),B) -> r1_orders_2(A,C,B)) & (r1_orders_2(A,B,C) -> r1_lattice3(A,k1_tarski(C),B)) & (r1_lattice3(A,k1_tarski(C),B) -> r1_orders_2(A,B,C)))))))) # label(t7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3683 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) & r1_orders_2(A,C,D) -> r1_orders_2(A,B,D)))))))) <-> v3_orders_2(A)))) # label(d2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3684 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r1_orders_2(A,C,D) & r2_hidden(E,u1_struct_0(B)) & r2_hidden(F,u1_struct_0(B)) & D = F & E = C -> r1_orders_2(B,E,F)))))))))))))) # label(t61_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3685 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (-v3_struct_0(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) -> v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) & -v3_struct_0(B)))))) # label(cc11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3686 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v7_yellow_0(B,A) -> v5_yellow_0(B,A)))))) # label(cc9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3687 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) <-> u1_orders_2(B) = k1_toler_1(u1_orders_2(A),u1_struct_0(B))))))) # label(d14_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3688 (all A (v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k1_yellow_0(A,C) = B <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r1_orders_2(A,B,D)))) & r2_lattice3(A,C,B))))))) # label(t32_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3689 (all A (l1_orders_2(A) & v2_yellow_0(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,k4_yellow_0(A)))))) # label(t45_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3690 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B all C (r2_yellow_0(A,B) & r2_yellow_0(A,C) & r2_yellow_0(A,k2_xboole_0(B,C)) -> k11_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) = k2_yellow_0(A,k2_xboole_0(B,C)))))) # label(t37_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3691 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (r2_yellow_0(A,C) -> k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t27_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3692 (all A (l1_orders_2(A) -> (all B (r2_yellow_0(A,B) <-> (exists C (r1_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_lattice3(A,B,E) -> r1_orders_2(A,E,D)))) -> D = C))) & m1_subset_1(C,u1_struct_0(A)))))))) # label(d8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3693 (all A (l1_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (m1_yellow_0(C,A) & v4_yellow_0(C,A) -> (u1_struct_0(B) = u1_struct_0(C) -> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))))))))) # label(t58_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3694 (all A (l1_orders_2(A) -> k4_yellow_0(A) = k2_yellow_0(A,k1_xboole_0))) # label(d12_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3695 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (D = E -> (r1_lattice3(A,C,D) -> r1_lattice3(B,C,E)) & (r2_lattice3(A,C,D) -> r2_lattice3(B,C,E))))))))))) # label(t62_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3696 (all A (v2_yellow_0(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> r1_yellow_0(A,u1_struct_0(A)) & r2_yellow_0(A,k1_xboole_0))) # label(t43_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3697 (all A (v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) -> v2_orders_2(B) & v4_yellow_0(B,A)))))) # label(cc6_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3698 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (r1_yellow_0(A,B) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & r2_lattice3(A,B,C))))))) # label(t15_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3699 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B ((r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) -> r2_yellow_0(A,B)) & (r2_yellow_0(A,B) -> r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))) & (r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) -> r1_yellow_0(A,B)) & (r1_yellow_0(A,B) -> r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))))))) # label(t50_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3700 (all A (l1_orders_2(A) & v3_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,C) & r1_lattice3(A,B,C) -> r1_lattice3(A,B,D)))))))) # label(t12_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3701 (all A (l1_orders_2(A) -> (all B all C (r1_tarski(B,C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_lattice3(A,B,D)) & (r2_lattice3(A,C,D) -> r2_lattice3(A,B,D)))))))) # label(t9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3702 (all A (l1_orders_2(A) -> m1_subset_1(k3_yellow_0(A),u1_struct_0(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3703 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) -> (v2_yellow_0(A) -> v2_yellow_0(B)) & (v1_yellow_0(A) -> v1_yellow_0(B))))))) # label(t13_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3704 (all A (l1_orders_2(A) -> k1_yellow_0(A,k1_xboole_0) = k3_yellow_0(A))) # label(d11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3705 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((r1_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_orders_2(A,D,B)))) -> r2_yellow_0(A,C) & B = k2_yellow_0(A,C)) & (r2_yellow_0(A,C) & k2_yellow_0(A,C) = B -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_orders_2(A,D,B)))) & r1_lattice3(A,C,B)))))))) # label(t31_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3706 (all A all B (l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_yellow_0(k5_yellow_0(A,B),A) & v4_yellow_0(k5_yellow_0(A,B),A) & v1_orders_2(k5_yellow_0(A,B)))) # label(dt_k5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3707 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) <-> r1_lattice3(A,B,D)))) & r2_yellow_0(A,B) -> r2_yellow_0(A,C))))) # label(t48_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3708 (all A (l1_orders_2(A) -> (v2_yellow_0(A) & v1_yellow_0(A) <-> v3_yellow_0(A)))) # label(d6_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3709 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> ((all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> r1_yellow_0(A,B))) <-> v1_lattice3(A)))) # label(t54_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3710 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v2_orders_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,B)))))) # label(d1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3711 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (m1_yellow_0(B,A) & -v3_struct_0(B) & v4_yellow_0(B,A) & v1_orders_2(B))))) # label(rc4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3712 (all A (v2_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,B,C) = k2_yellow_0(A,k2_struct_0(A,B,C)))))))) # label(t40_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3713 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(k2_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) & r2_yellow_0(A,k2_struct_0(B,C,D)) -> k2_yellow_0(B,k2_struct_0(B,C,D)) = k2_yellow_0(A,k2_struct_0(B,C,D)) & r2_yellow_0(B,k2_struct_0(B,C,D))))))))))) # label(t66_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3714 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B ((exists C (m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))))) <-> r2_yellow_0(A,B))))) # label(t16_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3715 (all A all B (m1_relset_1(B,k1_tarski(A),k1_tarski(A)) -> v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) & -v3_struct_0(g1_orders_2(k1_tarski(A),B)))) # label(fc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3716 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,k2_tarski(C,D),B) -> r1_orders_2(A,B,C) & r1_orders_2(A,B,D)) & (r1_orders_2(A,B,C) & r1_orders_2(A,B,D) -> r1_lattice3(A,k2_tarski(C,D),B)) & (r1_orders_2(A,D,B) & r1_orders_2(A,C,B) -> r2_lattice3(A,k2_tarski(C,D),B)) & (r2_lattice3(A,k2_tarski(C,D),B) -> r1_orders_2(A,C,B) & r1_orders_2(A,D,B)))))))))) # label(t8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3717 (all A (l1_orders_2(A) -> (all B all C (r1_tarski(B,C) & r1_yellow_0(A,B) & r1_yellow_0(A,C) -> r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)))))) # label(t34_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3718 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_yellow_0(A,B) -> (C = k2_yellow_0(A,B) <-> r1_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))))))))) # label(d10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3719 (all A (v2_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v5_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (D = F & C = E -> k12_lattice3(B,C,D) = k12_lattice3(A,E,F)))))))))))))) # label(t70_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3720 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> (r1_lattice3(A,C,D) -> r1_lattice3(B,C,E)) & (r2_lattice3(A,C,D) -> r2_lattice3(B,C,E)))))))))))) # label(t2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3721 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B all C (r1_yellow_0(A,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) <-> r2_lattice3(A,B,D)))) -> k1_yellow_0(A,B) = k1_yellow_0(A,C))))) # label(t47_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.14 3722 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) & r2_yellow_0(A,C) -> r2_yellow_0(B,C) & k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t64_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3723 (all A (l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> (all D ((r1_lattice3(A,D,C) -> r1_lattice3(A,D,B)) & (r2_lattice3(A,D,B) -> r2_lattice3(A,D,C))))))))))) # label(t4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3724 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) -> r2_lattice3(A,B,C)) & (r1_lattice3(A,B,C) -> r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)) & (r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) -> r1_lattice3(A,B,C)) & (r2_lattice3(A,B,C) -> r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)))))) # label(t5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3725 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v1_yellow_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,k3_yellow_0(A),B))))) # label(t44_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3726 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k13_lattice3(A,B,C) = k1_yellow_0(A,k2_struct_0(A,B,C)))))))) # label(t41_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3727 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_yellow_0(A,B))) -> v3_lattice3(A)))) # label(t53_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3728 (all A all B (l1_orders_2(A) -> m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)))) # label(dt_k2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3729 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v1_yellow_0(A) -> r2_yellow_0(A,u1_struct_0(A)) & r1_yellow_0(A,k1_xboole_0))) # label(t42_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3730 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) -> v4_orders_2(B) & v4_yellow_0(B,A)))))) # label(cc8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3731 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) -> k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t68_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3732 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t59_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3733 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_lattice3(A) -> -v3_struct_0(A) & v3_yellow_0(A)))) # label(cc3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3734 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(k1_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) & r1_yellow_0(A,k2_struct_0(B,C,D)) -> r1_yellow_0(B,k2_struct_0(B,C,D)) & k1_yellow_0(B,k2_struct_0(B,C,D)) = k1_yellow_0(A,k2_struct_0(B,C,D))))))))))) # label(t67_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3735 (all A (l1_orders_2(A) -> (exists B (v1_orders_2(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A))))) # label(rc3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3736 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) -> k1_yellow_0(B,C) = k1_yellow_0(A,C)))))))) # label(t69_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3737 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_realset2(A) & v2_orders_2(A) -> v4_orders_2(A) & v3_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3738 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B all C (r1_yellow_0(A,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) <-> r2_lattice3(A,C,D)))) -> r1_yellow_0(A,C))))) # label(t46_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3739 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,u1_struct_0(B)) & r2_hidden(D,u1_struct_0(B)) & r1_yellow_0(A,k2_struct_0(A,C,D)) -> r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B))))))) <-> v6_yellow_0(B,A)))))) # label(d17_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3740 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_yellow_0(A,B) -> (k1_yellow_0(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & r2_lattice3(A,B,C))))))) # label(d9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3741 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & v3_lattice3(A) -> v3_lattice3(B)))))) # label(t3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3742 (all A (v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v6_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (E = C & F = D -> k13_lattice3(B,C,D) = k13_lattice3(A,E,F)))))))))))))) # label(t71_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3743 (all A (l1_orders_2(A) -> (v4_orders_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,C,B) & r1_orders_2(A,B,C) -> C = B)))))))) # label(d3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3744 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v8_yellow_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r1_yellow_0(A,C) -> r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)))))))))) # label(d19_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3745 (all A (v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (r2_yellow_0(A,B) & r1_yellow_0(A,B))))) # label(t17_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3746 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (m1_yellow_0(B,A) & v5_yellow_0(B,A) & v8_yellow_0(B,A) & v7_yellow_0(B,A) & v6_yellow_0(B,A) & v4_yellow_0(B,A) & v1_orders_2(B) & -v3_struct_0(B))))) # label(rc5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3747 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) & r1_yellow_0(A,C) -> r1_yellow_0(B,C) & k1_yellow_0(B,C) = k1_yellow_0(A,C)))))))) # label(t65_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3748 (all A (l1_orders_2(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & r1_lattice3(A,u1_struct_0(A),B))) <-> v1_yellow_0(A)))) # label(d4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3749 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_yellow_0(A,C) -> r2_hidden(k2_yellow_0(A,C),u1_struct_0(B))))) <-> v7_yellow_0(B,A)))))) # label(d18_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3750 (all A (l1_orders_2(A) -> (v1_yellow_0(A) & v2_yellow_0(A) -> v3_yellow_0(A)))) # label(cc5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3751 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) -> (all C ((r1_yellow_0(A,C) -> r1_yellow_0(B,C)) & (r2_yellow_0(A,C) -> r2_yellow_0(B,C))))))))) # label(t14_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3752 (all A (v3_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (-v3_struct_0(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) -> -v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v6_yellow_0(B,A) & v4_yellow_0(B,A)))))) # label(cc12_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3753 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (r1_yellow_0(A,B) | r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) -> k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))))))) # label(t51_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3754 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_yellow_0(A,k1_struct_0(A,B)) & r1_yellow_0(A,k1_struct_0(A,B)))))) # label(t38_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3755 (all A (v4_orders_2(A) & l1_orders_2(A) -> (v1_lattice3(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_yellow_0(A,k2_tarski(B,C))))))))) # label(t20_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3756 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_orders_2(C) & m1_yellow_0(C,A) & v4_yellow_0(C,A) -> (k5_yellow_0(A,B) = C <-> u1_struct_0(C) = B))))))) # label(d15_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3757 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & r1_orders_2(A,D,B) -> r2_yellow_0(A,k2_tarski(B,C)) & k11_lattice3(A,B,C) = D) & (k11_lattice3(A,B,C) = D & r2_yellow_0(A,k2_tarski(B,C)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & r1_orders_2(A,D,B)))))))))) # label(t19_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3758 (exists A (-v3_struct_0(A) & v1_orders_2(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> p1_s1_yellow_0(B,C)))))) & f1_s1_yellow_0 = u1_struct_0(A) & l1_orders_2(A))) # label(s1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3759 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (r2_yellow_0(A,B) | r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) -> k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) = k2_yellow_0(A,B))))) # label(t52_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3760 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(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)) -> (k12_lattice3(A,B,C) = D <-> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & r1_orders_2(A,D,B)))))))))) # label(t23_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3761 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (E = C & D = F -> (r1_orders_2(A,C,D) -> r1_orders_2(B,E,F)) & (r2_orders_2(A,C,D) -> r2_orders_2(B,E,F)))))))))))))))) # label(t1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3762 (all A (l1_orders_2(A) -> (v3_yellow_0(A) -> v2_yellow_0(A) & v1_yellow_0(A)))) # label(cc4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3763 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((r1_yellow_0(A,C) & k1_yellow_0(A,C) = B -> r2_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r1_orders_2(A,B,D))))) & ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r1_orders_2(A,B,D)))) & r2_lattice3(A,C,B) -> B = k1_yellow_0(A,C) & r1_yellow_0(A,C)))))))) # label(t30_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3764 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) <-> r1_lattice3(A,C,D)))) & r2_yellow_0(A,B) -> k2_yellow_0(A,B) = k2_yellow_0(A,C))))) # label(t49_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3765 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k13_lattice3(A,B,C) <-> r1_orders_2(A,B,D) & r1_orders_2(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E))))))))))))) # label(t22_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3766 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> l1_orders_2(B))))) # label(dt_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3767 (exists A (v3_orders_2(A) & v2_lattice3(A) & v3_lattice3(A) & v2_yellow_0(A) & v3_yellow_0(A) & v1_yellow_0(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3768 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (k1_yellow_0(k3_lattice3(A),B) = k15_lattice3(A,B) & k2_yellow_0(k3_lattice3(A),B) = k16_lattice3(A,B))))) # label(t29_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3769 (all A (v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) -> v3_orders_2(B) & v4_yellow_0(B,A)))))) # label(cc7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3770 (all A (v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_orders_2(A,D,B)))) & r1_lattice3(A,C,B) <-> B = k2_yellow_0(A,C))))))) # label(t33_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3771 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k13_lattice3(A,B,C) = B <-> r1_orders_2(A,C,B)))))))) # label(t24_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3772 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_yellow_0(A,k1_struct_0(A,B)) = B & B = k2_yellow_0(A,k1_struct_0(A,B)))))) # label(t39_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3773 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (r1_yellow_0(A,C) -> k1_yellow_0(B,C) = k1_yellow_0(A,C)))))))) # label(t26_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3774 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,u1_struct_0(B)) & r2_hidden(D,u1_struct_0(B)) & r2_yellow_0(A,k2_struct_0(A,C,D)) -> r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B))))))) <-> v5_yellow_0(B,A)))))) # label(d16_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3775 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (v2_lattice3(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> r2_yellow_0(A,B)))))) # label(t55_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3776 (all A (l1_orders_2(A) & v4_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_yellow_0(A,k2_tarski(B,C)))))) <-> v2_lattice3(A)))) # label(t21_yellow_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3777 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (v5_waybel_0(k2_waybel_0(A,B),B,A) <-> v9_waybel_0(B,A)))))) # label(d10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3778 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,C) & r2_hidden(C,B) -> r2_hidden(D,B)))))) <-> v12_waybel_0(B,A)))))) # label(d19_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3779 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v1_waybel_0(D,A) -> v1_xboole_0(D) | r4_waybel_0(A,B,C,D)))) <-> v22_waybel_0(C,A,B)))))))) # label(d37_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3780 (all A (v2_yellow_0(A) & l1_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)) & v1_waybel_0(k2_pre_topc(A),A))) # label(fc3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3781 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) & v4_waybel_0(B,A) -> (all C (v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r1_yellow_0(A,C) -> k1_yellow_0(A,C) = k1_yellow_0(B,C) & r1_yellow_0(B,C) | k1_xboole_0 = C))))))) # label(t7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3782 (all A (l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & v1_waybel_0(B,A) & -v1_xboole_0(B) -> ((exists C (B = k6_waybel_0(A,C) & m1_subset_1(C,u1_struct_0(A)))) <-> v14_waybel_0(B,A)))))) # label(t48_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3783 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (exists B (v13_waybel_0(B,A) & v12_waybel_0(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3784 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v13_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r2_hidden(C,B) -> r2_hidden(D,B))))))))))) # label(d20_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3785 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (D != k1_xboole_0 -> r1_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(D = k1_yellow_0(A,E) & r1_yellow_0(A,E))))))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_hidden(k1_yellow_0(A,D),C)))) -> v1_waybel_0(C,A)))))))) # label(t51_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3786 (all A (l1_orders_2(A) -> v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A),A) & v1_finset_1(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v2_waybel_0(k1_pre_topc(A),A) & v1_waybel_0(k1_pre_topc(A),A) & v5_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))) # label(fc1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3787 $T # label(dt_k8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3788 $T # label(dt_k11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3789 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) -> (all B (v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k12_lattice3(A,C,D),B))))))))))) # label(t41_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3790 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (v8_waybel_0(B,A) <-> v5_orders_3(k2_waybel_0(A,B),B,A)))))) # label(d9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3791 (all A all B (v4_orders_2(A) & v2_lattice3(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v2_waybel_0(k13_waybel_0(A,B),A))) # label(fc23_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3792 (all A (-v3_struct_0(A) & l1_orders_2(A) -> -v1_xboole_0(k2_pre_topc(A)) & v12_waybel_0(k2_pre_topc(A),A) & v13_waybel_0(k2_pre_topc(A),A))) # label(fc15_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3793 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) -> m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3794 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r4_waybel_0(A,B,C,D))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(D,A) & -v1_xboole_0(D) -> r4_waybel_0(A,B,C,D))) -> v18_waybel_0(C,A,B)))))))) # label(t74_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3795 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(D,A) -> r3_waybel_0(A,B,C,D) | v1_xboole_0(D)))) <-> v21_waybel_0(C,A,B)))))))) # label(d36_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3796 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_tarski(k6_waybel_0(A,B),k6_waybel_0(A,C))))))))) # label(t21_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3797 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C all D (r1_tarski(C,D) -> (r1_waybel_0(A,B,C) -> r1_waybel_0(A,B,D)) & (r2_waybel_0(A,B,C) -> r2_waybel_0(A,B,D)))))))) # label(t8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3798 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (v2_waybel_0(D,A) & v13_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> r3_waybel_0(A,B,C,D))) -> v21_waybel_0(C,A,B)))))))) # label(t70_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3799 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v23_waybel_0(C,A,B) <-> k2_relat_1(C) = u1_struct_0(B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) <-> r1_orders_2(A,D,E)))))) & v2_funct_1(C)))))))) # label(t66_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3800 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(k13_waybel_0(A,B)))) # label(fc21_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3801 (all A (l1_orders_2(A) & v1_lattice3(A) -> v1_waybel_0(k2_pre_topc(A),A) & -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3802 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_waybel_0(A,B) = k6_waybel_0(A,C) -> B = C))))))) # label(t19_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3803 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_waybel_0(k4_waybel_0(A,B),A) <-> v1_waybel_0(B,A)))))) # label(t30_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3804 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,k4_waybel_0(A,B),C) <-> r2_lattice3(A,B,C)))))))) # label(t31_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3805 (all A all B (v2_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & -v3_struct_0(A) -> v1_waybel_0(k6_waybel_0(A,B),A) & -v1_xboole_0(k6_waybel_0(A,B)))) # label(fc9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3806 (exists A (-v3_struct_0(A) & v3_orders_2(A) & v16_waybel_0(A) & v4_orders_2(A) & v2_orders_2(A) & l1_orders_2(A))) # label(rc12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3807 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(B)) -> r1_waybel_0(A,B,a_3_1_waybel_0(A,B,C)))) <-> v11_waybel_0(B,A)))))) # label(d14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3808 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A))))) # label(rc10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3809 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(D,A) & -v1_xboole_0(D) -> r3_waybel_0(A,B,C,D))) -> v17_waybel_0(C,A,B)))))))) # label(t71_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3810 (all A all B (-v3_struct_0(B) & l1_waybel_0(B,A) & l1_struct_0(A) & -v3_struct_0(A) -> v1_funct_2(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(k2_waybel_0(A,B)))) # label(dt_k2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3811 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> (all C (-r2_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) <-> r1_waybel_0(A,B,C))))))) # label(t9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3812 (all A all B all C (l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists D (A = k1_yellow_0(B,D) & r1_yellow_0(B,D) & m1_subset_1(D,k1_zfmisc_1(C)) & v1_finset_1(D))) <-> r2_hidden(A,a_2_2_waybel_0(B,C))))) # label(fraenkel_a_2_2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3813 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3814 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) & v1_waybel_0(B,A) <-> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r2_lattice3(A,C,D) & r2_hidden(D,B)))))))))) # label(t1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3815 (all A (v2_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & v12_waybel_0(B,A) & v2_waybel_0(B,A) & v1_waybel_0(B,A) & -v1_xboole_0(B))))) # label(rc11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3816 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k7_waybel_0(A,B)) <-> r1_orders_2(A,B,C)))))))) # label(t18_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3817 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,C,B) | r1_orders_2(A,B,C))))) <-> v16_waybel_0(A)))) # label(d29_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3818 (all A (l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(r2_yellow_0(A,E) & D = k2_yellow_0(A,E)))) & r2_hidden(D,C)))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (D != k1_xboole_0 -> r2_hidden(k2_yellow_0(A,D),C)))) & r2_yellow_0(A,B) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) -> k2_yellow_0(A,B) = k2_yellow_0(A,C)))))))) # label(t59_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3819 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k12_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3820 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v13_waybel_0(C,A) & v13_waybel_0(B,A) -> v13_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & v13_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3821 (all A (l1_orders_2(A) -> (exists B (v1_waybel_0(B,A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3822 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(B,A) <-> r1_tarski(k4_waybel_0(A,B),B)))))) # label(t23_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3823 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k5_waybel_0(A,k13_waybel_0(A,B))) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(C,A) & v2_waybel_0(C,A) & -v1_xboole_0(C) -> (r1_tarski(B,C) -> r1_tarski(k5_waybel_0(A,k13_waybel_0(A,B)),C)))))))) # label(t62_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3824 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) -> (r2_hidden(A,a_2_0_waybel_0(B,C)) <-> (exists D (D = A & (exists E (r1_orders_2(B,D,E) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3825 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_waybel_0(C,A) & C = D -> v2_waybel_0(D,B))))))))))) # label(t4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.15 3826 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & v2_orders_2(A) -> v2_waybel_0(k7_waybel_0(A,B),A) & -v1_xboole_0(k7_waybel_0(A,B)))) # label(fc10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3827 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v13_waybel_0(B,A) <-> r1_tarski(k5_waybel_0(A,B),B)))))) # label(t24_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3828 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,B) <-> r2_yellow_0(A,k5_waybel_0(A,B))))))) # label(t37_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3829 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) -> (r2_hidden(A,a_2_3_waybel_0(B,C)) <-> (exists D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & k2_yellow_0(B,D) = A & r2_yellow_0(B,D)))))) # label(fraenkel_a_2_3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3830 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(D,A) & -v1_xboole_0(D) -> r4_waybel_0(A,B,C,D))) -> v5_orders_3(C,A,B)))))))) # label(t72_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3831 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (m1_yellow_0(B,A) & v1_orders_2(B) & v8_yellow_0(B,A) & v3_waybel_0(B,A) & v4_waybel_0(B,A) & v7_yellow_0(B,A) & v6_yellow_0(B,A) & v5_yellow_0(B,A) & v4_yellow_0(B,A) & -v3_struct_0(B))))) # label(rc3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3832 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,B) -> k2_yellow_0(A,k5_waybel_0(A,B)) = k2_yellow_0(A,B)))))) # label(t38_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3833 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(D = k2_yellow_0(A,E) & r2_yellow_0(A,E)))) & r2_hidden(D,C)))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_hidden(k2_yellow_0(A,D),C)))) -> v2_waybel_0(C,A)))))))) # label(t56_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3834 (all A all B (l1_orders_2(B) & -v3_struct_0(B) & l1_orders_2(A) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B)))))) # label(cc6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3835 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v1_lattice3(A) & v24_waybel_0(A) -> -v3_struct_0(A) & v1_lattice3(A) & v2_yellow_0(A) & v2_orders_2(A)))) # label(cc9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3836 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r3_waybel_0(A,B,C,D) <-> (r2_yellow_0(A,D) -> r2_yellow_0(B,k4_pre_topc(A,B,C,D)) & k2_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k2_yellow_0(A,D)))))))))))) # label(d30_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3837 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(B)) -> r1_waybel_0(A,B,a_3_0_waybel_0(A,B,C)))) <-> v10_waybel_0(B,A)))))) # label(d13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3838 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(k2_yellow_0(A,E) = D & r2_yellow_0(A,E)))) & r2_hidden(D,C)))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k2_yellow_0(A,D),C)))) -> (r2_yellow_0(A,B) <-> r2_yellow_0(A,C))))))))) # label(t58_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3839 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_orders_2(A) & v2_lattice3(A) & v2_orders_2(A)))) # label(cc13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3840 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v16_waybel_0(A) & v4_orders_2(A) -> v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)) & v16_waybel_0(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)) & -v3_struct_0(k7_lattice3(A)))) # label(fc24_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3841 (all A all B (l1_waybel_0(B,A) & l1_struct_0(A) -> (v6_waybel_0(B,A) -> g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) = B))) # label(abstractness_v6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3842 (all A (l1_struct_0(A) -> (exists B l1_waybel_0(B,A)))) # label(existence_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3843 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(r2_yellow_0(A,E) & k2_yellow_0(A,E) = D))) & r2_hidden(D,C)))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k2_yellow_0(A,D),C)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) <-> r1_lattice3(A,B,D))))))))))) # label(t57_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3844 $T # label(dt_k10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3845 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,B) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(E,B) & r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E)))) & r2_hidden(C,B)))))) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v2_waybel_0(C,A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k5_setfam_1(u1_struct_0(A),B) -> v2_waybel_0(C,A))))))))) # label(t47_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3846 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C ((all D (m1_subset_1(D,u1_struct_0(B)) -> (exists E (r2_hidden(k3_waybel_0(A,B,E),C) & r1_orders_2(B,D,E) & m1_subset_1(E,u1_struct_0(B)))))) <-> r2_waybel_0(A,B,C))))))) # label(d12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3847 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -v1_xboole_0(k4_waybel_0(A,B)))) # label(fc7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3848 (all A all B (v2_orders_2(A) & v4_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> v1_waybel_0(k12_waybel_0(A,B),A))) # label(fc22_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.11/5.16 3849 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k13_waybel_0(A,B) = a_2_3_waybel_0(A,B))))) # label(d28_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3850 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k5_waybel_0(B,D) = k5_waybel_0(A,C) & k4_waybel_0(B,D) = k4_waybel_0(A,C))))))))))) # label(t13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3851 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k13_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3852 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (-v1_xboole_0(D) & v2_waybel_0(D,A) & v13_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) -> v5_orders_3(C,A,B)))))))) # label(t69_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3853 (all A all B all C all D (l1_struct_0(A) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) & m1_relset_1(C,B,B) -> v6_waybel_0(g1_waybel_0(A,B,C,D),A) & l1_waybel_0(g1_waybel_0(A,B,C,D),A))) # label(dt_g1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3854 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v3_orders_2(A) -> v13_waybel_0(k7_waybel_0(A,B),A))) # label(fc14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3855 (all A (l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (v2_lattice3(A) | v1_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(B,A) & v1_waybel_0(B,A) & v1_waybel_0(C,A) & v12_waybel_0(C,A) -> v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t44_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3856 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(B)) -> (exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_orders_2(B,D,E) -> r1_orders_2(A,k3_waybel_0(A,B,E),k3_waybel_0(A,B,C))))) & m1_subset_1(D,u1_struct_0(B)))))) <-> v11_waybel_0(B,A)))))) # label(t12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3857 (all A (l1_orders_2(A) & v1_yellow_0(A) & -v3_struct_0(A) -> v2_waybel_0(k2_pre_topc(A),A) & -v1_xboole_0(k2_pre_topc(A)))) # label(fc5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3858 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_yellow_0(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> v2_lattice3(A) & v3_yellow_0(A) & v2_yellow_0(A) & v1_yellow_0(A) & v3_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3859 (all A (v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) -> (v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & -v1_xboole_0(B) <-> v5_yellow_0(k5_yellow_0(A,B),A)))))) # label(t63_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3860 (all A (l1_orders_2(A) -> (v7_waybel_0(A) <-> v1_waybel_0(k2_pre_topc(A),A)))) # label(d6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.16 3861 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r1_orders_2(A,E,C) & r1_orders_2(A,E,D) & r2_hidden(E,B)))) & r2_hidden(D,B)))))) <-> v2_waybel_0(B,A)))))) # label(d2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3862 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> ((all C (v2_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_yellow_0(A,C) -> C = k1_xboole_0 | r2_hidden(k2_yellow_0(A,C),u1_struct_0(B))))) <-> v3_waybel_0(B,A)))))) # label(d3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3863 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> (v10_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(B)) -> (exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_orders_2(B,D,E) -> r1_orders_2(A,k3_waybel_0(A,B,C),k3_waybel_0(A,B,E))))) & m1_subset_1(D,u1_struct_0(B))))))))))) # label(t11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3864 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(B,A) <-> v2_waybel_0(k5_waybel_0(A,B),A)))))) # label(t35_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3865 (all A all B (-v3_struct_0(A) & l1_orders_2(B) & -v3_struct_0(B) & l1_orders_2(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) & v1_funct_1(C) -> v5_orders_3(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_funct_1(C) & v1_funct_1(C)))))) # label(cc8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3866 (all A (l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(D = k1_yellow_0(A,E) & r1_yellow_0(A,E)))) & r2_hidden(D,C)))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (D != k1_xboole_0 -> r2_hidden(k1_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r1_yellow_0(A,D)))) -> (r1_yellow_0(A,B) <-> r1_yellow_0(A,C))))))))) # label(t53_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3867 (all A (l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> k2_xboole_0(k8_waybel_0(A),k1_tarski(k1_xboole_0)) = k10_waybel_0(A))) # label(d25_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3868 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v12_waybel_0(C,A)))) -> v12_waybel_0(k5_setfam_1(u1_struct_0(A),B),A) & m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t26_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3869 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_1_waybel_0(A,B) = k5_waybel_0(A,B))))) # label(t15_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3870 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_waybel_0(A,k1_struct_0(A,B)) = k6_waybel_0(A,B))))) # label(d17_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3871 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) -> k1_yellow_0(A,B) = k1_yellow_0(A,k4_waybel_0(A,B))))))) # label(t33_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3872 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v13_waybel_0(C,A)))) -> m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t28_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3873 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v23_waybel_0(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (D = k2_funct_1(C) -> v23_waybel_0(D,B,A))))))))))) # label(t68_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3874 (all A all B all C all D (-v3_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) & l1_struct_0(B) & -v3_struct_0(B) & l1_struct_0(A) -> k1_waybel_0(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3875 (all A (l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k5_waybel_0(A,B)) & r1_tarski(B,k4_waybel_0(A,B)))))) # label(t16_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3876 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_orders_2(A) & v4_orders_2(A) -> -v1_xboole_0(k12_waybel_0(A,B)))) # label(fc20_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3877 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> ((all B (v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r3_orders_2(A,C,D)))) & r2_lattice3(A,B,C) & m1_subset_1(C,u1_struct_0(A)))))) <-> v24_waybel_0(A)))) # label(d39_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3878 (all A all B (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> v12_waybel_0(k4_waybel_0(A,B),A) & v1_waybel_0(k4_waybel_0(A,B),A))) # label(fc16_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3879 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k7_waybel_0(A,C) = k7_waybel_0(A,B) -> C = B))))))) # label(t20_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3880 (exists A (m1_subset_1(A,u1_struct_0(f2_s1_waybel_0)) & (all B (m1_subset_1(B,u1_struct_0(f2_s1_waybel_0)) -> (r1_orders_2(f2_s1_waybel_0,A,B) -> p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B))))))) <-> r1_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,a_0_0_waybel_0) # label(s1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3881 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v23_waybel_0(C,A,B) -> v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) & k2_relat_1(k2_funct_1(C)) = u1_struct_0(A) & m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(k2_funct_1(C))))))))) # label(t67_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3882 (all A (v2_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v1_waybel_0(k1_struct_0(A,B),A) & v2_waybel_0(k1_struct_0(A,B),A))))) # label(t5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3883 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_orders_2(C) -> (all D (-v3_struct_0(D) & l1_orders_2(D) -> (g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) -> (all E (m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) -> (E = F -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) -> (all H (m1_subset_1(H,k1_zfmisc_1(u1_struct_0(C))) -> (H = G -> (r4_waybel_0(A,B,E,G) -> r4_waybel_0(C,D,F,H)) & (r3_waybel_0(A,B,E,G) -> r3_waybel_0(C,D,F,H))))))))))))))))))))) # label(t65_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3884 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v13_waybel_0(k5_waybel_0(A,B),A))) # label(fc12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3885 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v19_waybel_0(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> r3_waybel_0(A,B,C,k2_struct_0(A,D,E))))))))))))) # label(d34_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3886 $T # label(dt_k9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3887 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_waybel_0(A,B)) <-> r1_orders_2(A,C,B)))))))) # label(t17_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3888 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) -> (v8_yellow_0(B,A) -> v4_waybel_0(B,A)))))) # label(cc2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3889 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & v1_waybel_0(B,A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3890 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r4_waybel_0(A,B,C,D))) <-> v18_waybel_0(C,A,B)))))))) # label(d33_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3891 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> a_1_1_waybel_0(A) = k9_waybel_0(A))) # label(d24_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3892 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) -> (-v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) <-> v6_yellow_0(k5_yellow_0(A,B),A)))))) # label(t64_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3893 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k6_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3894 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> ((all B (-v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_yellow_0(A,B))) <-> v24_waybel_0(A)))) # label(t75_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3895 (all A all B (v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_yellow_0(A) & -v3_struct_0(A) -> -v1_xboole_0(k12_waybel_0(A,B)))) # label(fc18_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3896 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r1_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(k1_yellow_0(A,E) = D & r1_yellow_0(A,E))))))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k1_yellow_0(A,D),C)))) & r1_yellow_0(A,B) -> k1_yellow_0(A,C) = k1_yellow_0(A,B)))))))) # label(t54_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3897 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (-(-v3_struct_0(B) & -v3_struct_0(A)) -> (v3_struct_0(A) & v3_struct_0(B) <-> v23_waybel_0(C,A,B))) & -(-v3_struct_0(A) & -(v23_waybel_0(C,A,B) <-> v2_funct_1(C) & (exists D (v1_funct_1(D) & v5_orders_3(D,B,A) & k2_funct_1(C) = D & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)))) & v5_orders_3(C,A,B)) & -v3_struct_0(B)))))))) # label(d38_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3898 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> (exists B (v6_waybel_0(B,A) & v8_waybel_0(B,A) & v9_waybel_0(B,A) & v11_waybel_0(B,A) & v10_waybel_0(B,A) & v7_waybel_0(B) & -v3_struct_0(B) & l1_waybel_0(B,A))))) # label(rc6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3899 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_lattice3(A) & v2_orders_2(A) -> v2_orders_2(A) & v25_waybel_0(A) & v24_waybel_0(A) & -v3_struct_0(A)))) # label(cc10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3900 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> k2_xboole_0(k9_waybel_0(A),k1_tarski(k1_xboole_0)) = k11_waybel_0(A))) # label(d26_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3901 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k12_waybel_0(A,B) = a_2_2_waybel_0(A,B))))) # label(d27_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3902 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_realset2(A) & v2_orders_2(A) -> v16_waybel_0(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3903 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) -> (v7_yellow_0(B,A) -> v3_waybel_0(B,A)))))) # label(cc1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3904 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> (v12_waybel_0(C,A) -> v12_waybel_0(D,B)) & (v13_waybel_0(C,A) -> v13_waybel_0(D,B)))))))))))) # label(t25_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3905 (all A (l1_orders_2(A) -> (v4_orders_2(A) & v25_waybel_0(A) & v2_yellow_0(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) & v2_orders_2(A)))) # label(cc14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3906 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (-v1_xboole_0(D) & v12_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(D,A) -> r4_waybel_0(A,B,C,D))) -> v22_waybel_0(C,A,B)))))))) # label(t73_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3907 (all A (l1_orders_2(A) -> (exists B (v12_waybel_0(B,A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3908 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r4_waybel_0(A,B,C,D) <-> (r1_yellow_0(A,D) -> k1_waybel_0(A,B,C,k1_yellow_0(A,D)) = k1_yellow_0(B,k4_pre_topc(A,B,C,D)) & r1_yellow_0(B,k4_pre_topc(A,B,C,D)))))))))))) # label(d31_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.17 3909 (all A all B (l1_orders_2(A) & l1_orders_2(B) & -v3_struct_0(B) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v18_waybel_0(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) & v1_funct_1(C)))))) # label(cc7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3910 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & v3_orders_2(A) -> v12_waybel_0(k6_waybel_0(A,B),A))) # label(fc13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3911 (all A all B all C all D (l1_orders_2(B) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) & -v3_struct_0(C) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & A = k3_waybel_0(B,C,E) & r1_orders_2(B,k3_waybel_0(B,C,D),k3_waybel_0(B,C,E)))) <-> r2_hidden(A,a_3_0_waybel_0(B,C,D))))) # label(fraenkel_a_3_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3912 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,B) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E) & r2_hidden(E,B)))) & r2_hidden(C,B)))))) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v1_waybel_0(C,A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k5_setfam_1(u1_struct_0(A),B) -> v1_waybel_0(C,A))))))))) # label(t46_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3913 (all A all B all C (-v3_struct_0(A) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) & l1_struct_0(A) -> m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)))) # label(dt_k3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3914 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) -> (-v3_struct_0(B) & v9_waybel_0(B,A) & v7_waybel_0(B) -> -v3_struct_0(B) & v11_waybel_0(B,A) & v7_waybel_0(B)))))) # label(cc4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3915 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & -v1_xboole_0(B) -> ((all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (k1_xboole_0 != C -> r2_hidden(k2_yellow_0(A,C),B)))) <-> v2_waybel_0(B,A)))))) # label(t43_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3916 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (D != k1_xboole_0 -> r1_yellow_0(A,D)))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_hidden(k1_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(k1_yellow_0(A,E) = D & r1_yellow_0(A,E)))) & r2_hidden(D,C)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) <-> r2_lattice3(A,C,D))))))))))) # label(t52_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3917 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v2_yellow_0(A) & v4_orders_2(A) -> -v1_xboole_0(k13_waybel_0(A,B)))) # label(fc19_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3918 (all A all B all C (l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists D ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & r1_orders_2(B,E,D))) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_1_waybel_0(B,C))))) # label(fraenkel_a_2_1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3919 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,k4_waybel_0(A,B)) <-> r1_yellow_0(A,B)))))) # label(t32_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3920 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) -> (-v3_struct_0(B) & v8_waybel_0(B,A) & v7_waybel_0(B) -> -v3_struct_0(B) & v10_waybel_0(B,A) & v7_waybel_0(B)))))) # label(cc3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3921 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> a_1_0_waybel_0(A) = k8_waybel_0(A))) # label(d23_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3922 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(B,A) & v12_waybel_0(C,A) -> v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & v12_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t27_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3923 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) -> m1_subset_1(k4_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3924 (all A all B (v2_orders_2(A) & l1_orders_2(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_orders_2(A) & -v3_struct_0(A) -> v2_waybel_0(k5_waybel_0(A,B),A) & v13_waybel_0(k5_waybel_0(A,B),A))) # label(fc17_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3925 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v3_waybel_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v2_waybel_0(C,B) -> (r2_yellow_0(A,C) -> C = k1_xboole_0 | r2_yellow_0(B,C) & k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3926 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice3(A,B,C) <-> r1_lattice3(A,k5_waybel_0(A,B),C)))))))) # label(t36_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3927 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) -> (v1_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k13_lattice3(A,C,D),B))))))))))) # label(t40_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3928 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_lattice3(A) | r2_yellow_0(A,B) -> k2_yellow_0(A,k13_waybel_0(A,B)) = k2_yellow_0(A,B)))))) # label(t60_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3929 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> -(r2_hidden(E,B) & r1_orders_2(A,D,E) & r1_orders_2(A,C,E)))) & r2_hidden(D,B) & r2_hidden(C,B)))))) <-> v1_waybel_0(B,A)))))) # label(d1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3930 (all A all B all C all D (-v3_struct_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) & l1_orders_2(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_waybel_0(B,C,D)) <-> (exists E (r1_orders_2(B,k3_waybel_0(B,C,E),k3_waybel_0(B,C,D)) & k3_waybel_0(B,C,E) = A & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3931 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_yellow_0(A,k6_waybel_0(A,B)) & B = k1_yellow_0(A,k6_waybel_0(A,B)))))) # label(t34_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3932 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C ((exists D (m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_orders_2(B,D,E) -> r2_hidden(k3_waybel_0(A,B,E),C)))))) <-> r1_waybel_0(A,B,C))))))) # label(d11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3933 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v5_waybel_0(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,D,E) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (k1_funct_1(C,D) = F & G = k1_funct_1(C,E) -> r1_orders_2(B,G,F)))))))))))))))))) # label(d5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3934 (all A all B all C all D (l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) & -v1_xboole_0(B) -> -v3_struct_0(g1_waybel_0(A,B,C,D)) & v6_waybel_0(g1_waybel_0(A,B,C,D),A))) # label(fc6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3935 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> ((all C (v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r1_yellow_0(A,C) -> C = k1_xboole_0 | r2_hidden(k1_yellow_0(A,C),u1_struct_0(B))))) <-> v4_waybel_0(B,A)))))) # label(d4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3936 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -v1_xboole_0(k5_waybel_0(A,B)))) # label(fc8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3937 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & v2_waybel_0(B,A) & -v1_xboole_0(B) -> ((exists C (m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & r2_hidden(C,B))) <-> v15_waybel_0(B,A)))))) # label(d22_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3938 (all A (l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k13_waybel_0(A,B)) & r1_tarski(B,k12_waybel_0(A,B)))))) # label(t50_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3939 (all A all B (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) -> ((exists C (-v1_xboole_0(C) & v12_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v1_waybel_0(C,B))) <-> r2_hidden(A,a_1_0_waybel_0(B))))) # label(fraenkel_a_1_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3940 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3941 (all A (l1_struct_0(A) -> (exists B (l1_waybel_0(B,A) & v6_waybel_0(B,A))))) # label(rc4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3942 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C (r2_waybel_0(A,B,C) <-> -r1_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)))))))) # label(t10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3943 (all A (l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_waybel_0(B,A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> ((exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & r2_hidden(C,B))) <-> v14_waybel_0(B,A)))))) # label(d21_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3944 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v1_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) -> (v15_waybel_0(B,A) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & k7_waybel_0(A,C) = B))))))) # label(t49_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3945 (all A (v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & r1_lattice3(A,C,D))))) <-> v2_waybel_0(B,A) & -v1_xboole_0(B)))))) # label(t2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3946 (all A (v2_lattice3(A) & l1_orders_2(A) -> -v1_xboole_0(k2_pre_topc(A)) & v2_waybel_0(k2_pre_topc(A),A))) # label(fc4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3947 (all A all B (-v3_struct_0(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (r2_hidden(A,a_1_1_waybel_0(B)) <-> (exists C (-v1_xboole_0(C) & v2_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & C = A & v13_waybel_0(C,B)))))) # label(fraenkel_a_1_1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3948 (all A all B (l1_waybel_0(B,A) & l1_struct_0(A) -> v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)))) # label(dt_u1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3949 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_waybel_0(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) <-> (exists E (r1_orders_2(A,D,E) & r2_hidden(E,B) & m1_subset_1(E,u1_struct_0(A)))))))))))))) # label(d15_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3950 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (-v1_xboole_0(B) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_waybel_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(C) -> (C != k1_xboole_0 -> r2_hidden(k1_yellow_0(A,C),B))))))))) # label(t42_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3951 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_lattice3(A) | r1_yellow_0(A,B) -> k1_yellow_0(A,B) = k1_yellow_0(A,k12_waybel_0(A,B))))))) # label(t55_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3952 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> k2_waybel_0(A,B) = u1_waybel_0(A,B))))) # label(d7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3953 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_waybel_0(C,A) & C = D -> v1_waybel_0(D,B))))))))))) # label(t3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3954 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v25_waybel_0(A) & -v3_struct_0(A) -> v1_yellow_0(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3955 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_waybel_0(A,B) = a_2_0_waybel_0(A,B))))) # label(t14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3956 (all A (l1_struct_0(A) -> (exists B (v2_orders_2(B) & v3_orders_2(B) & v7_waybel_0(B) & v6_waybel_0(B,A) & v4_orders_2(B) & -v3_struct_0(B) & l1_waybel_0(B,A))))) # label(rc5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3957 (all A (v2_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (v25_waybel_0(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))) & r1_lattice3(A,B,C) & m1_subset_1(C,u1_struct_0(A))))))))) # label(d40_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3958 (exists A (v1_orders_2(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v25_waybel_0(A) & v24_waybel_0(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3959 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_tarski(k7_waybel_0(A,C),k7_waybel_0(A,B))))))))) # label(t22_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3960 (all A all B (v3_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & -v3_struct_0(A) -> v12_waybel_0(k4_waybel_0(A,B),A))) # label(fc11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3961 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) -> (v2_lattice3(A) | v1_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(C,A) & v13_waybel_0(C,A) & v2_waybel_0(B,A) & v13_waybel_0(B,A) -> v2_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t45_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3962 (all A (l1_struct_0(A) -> (all B (l1_waybel_0(B,A) -> l1_orders_2(B))))) # label(dt_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3963 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> ((all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_yellow_0(A,B))) <-> v25_waybel_0(A)))) # label(t76_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3964 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_waybel_0(B,A,u1_waybel_0(A,B),C) = k3_waybel_0(A,B,C))))))) # label(d8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3965 (all A all B all C all D (l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & m1_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) -> (all E all F all G all H (g1_waybel_0(E,F,G,H) = g1_waybel_0(A,B,C,D) -> E = A & B = F & D = H & C = G)))) # label(free_g1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3966 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) <-> v17_waybel_0(C,A,B)))))))) # label(d32_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3967 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_yellow_0(A,k7_waybel_0(A,B)) = B & r2_yellow_0(A,k7_waybel_0(A,B)))))) # label(t39_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3968 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_waybel_0(A,B) = k5_waybel_0(A,k1_struct_0(A,B)))))) # label(d18_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3969 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_0(A,B,C,k2_struct_0(A,D,E)))))) <-> v20_waybel_0(C,A,B)))))))) # label(d35_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3970 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_waybel_0(C,A) & v12_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r1_tarski(B,C) -> r1_tarski(k4_waybel_0(A,k12_waybel_0(A,B)),C)))) & r1_tarski(B,k4_waybel_0(A,k12_waybel_0(A,B))))))) # label(t61_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3971 (all A all B all C all D (l1_struct_0(A) & -v3_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) & -v3_struct_0(A) -> m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)))) # label(dt_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3972 (all A ((exists B (m1_subset_1(B,u1_struct_0(f2_s1_waybel_0)) & k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B) = A & p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B)))) <-> r2_hidden(A,a_0_0_waybel_0))) # label(fraenkel_a_0_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3973 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> ((exists E (r1_orders_2(A,E,D) & r2_hidden(E,B) & m1_subset_1(E,u1_struct_0(A)))) <-> r2_hidden(D,C)))) <-> k5_waybel_0(A,B) = C))))))) # label(d16_waybel_0) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3974 (all A k3_yellow_1(A) = k2_yellow_1(k1_zfmisc_1(A))) # label(t4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3975 (all A all B (l1_orders_2(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc10_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3976 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_orders_2(k3_lattice3(A)) & v2_yellow_0(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v3_lattice3(k3_lattice3(A)) & v3_yellow_0(k3_lattice3(A)) & v1_yellow_0(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3977 (all A all B (m1_pboole(B,A) & v1_yellow_1(B) -> (all C (l1_orders_2(C) & v1_orders_2(C) -> ((all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (r2_hidden(D,k4_card_3(k12_pralg_1(A,B))) -> ((exists F (v1_funct_1(F) & (exists G (v1_relat_1(G) & D = F & (all H -(r2_hidden(H,A) & (all I (l1_orders_2(I) -> (all J (m1_subset_1(J,u1_struct_0(I)) -> (all K (m1_subset_1(K,u1_struct_0(I)) -> -(I = k1_funct_1(B,H) & k1_funct_1(G,H) = K & r1_orders_2(I,J,K) & J = k1_funct_1(F,H)))))))))) & G = E & v1_funct_1(G))) & v1_relat_1(F))) <-> r1_orders_2(C,D,E))))))) & u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B)) <-> k5_yellow_1(A,B) = C))))) # label(d4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3978 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) -> k3_tarski(B) = k1_yellow_0(k3_yellow_1(A),B))) # label(t21_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3979 (all A all B (l1_orders_2(B) & l1_orders_2(A) -> v1_orders_2(k7_yellow_1(A,B)) & m1_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) & v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)))) # label(dt_k7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3980 (all A all B (-v3_struct_0(B) & l1_orders_2(B) & v2_orders_2(B) -> -v3_struct_0(k6_yellow_1(A,B)) & v2_orders_2(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)))) # label(fc12_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3981 (all A (v1_orders_2(k2_yellow_1(A)) & l1_orders_2(k2_yellow_1(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3982 (all A all B (v4_orders_2(B) & l1_orders_2(B) & v1_lattice3(B) & -v3_struct_0(B) & -v1_xboole_0(A) -> v1_orders_2(k6_yellow_1(A,B)) & v1_lattice3(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & -v3_struct_0(k6_yellow_1(A,B)))) # label(fc18_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3983 (all A (v1_relat_2(k1_yellow_1(A)) & m2_relset_1(k1_yellow_1(A),A,A) & v1_partfun1(k1_yellow_1(A),A,A) & v8_relat_2(k1_yellow_1(A)) & v4_relat_2(k1_yellow_1(A)))) # label(dt_k1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3984 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v2_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_yellow_0(k2_yellow_1(u1_pre_topc(A))) & -v3_realset2(k2_yellow_1(u1_pre_topc(A))) & v3_lattice3(k2_yellow_1(u1_pre_topc(A))) & v2_lattice3(k2_yellow_1(u1_pre_topc(A))) & v1_lattice3(k2_yellow_1(u1_pre_topc(A))) & v2_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v1_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v4_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_orders_2(k2_yellow_1(u1_pre_topc(A))) & v1_orders_2(k2_yellow_1(u1_pre_topc(A))) & -v3_struct_0(k2_yellow_1(u1_pre_topc(A))))) # label(fc9_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3985 (all A all B (l1_orders_2(B) -> k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)))) # label(d5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3986 (all A g1_orders_2(A,k1_yellow_1(A)) = k2_yellow_1(A)) # label(d1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3987 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_yellow_1(B) & m1_pboole(B,A))) # label(rc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3988 (all A all B (l1_orders_2(B) -> v1_orders_2(k6_yellow_1(A,B)) & l1_orders_2(k6_yellow_1(A,B)))) # label(dt_k6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3989 (all A k3_yellow_0(k3_yellow_1(A)) = k1_xboole_0) # label(t18_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3990 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> r1_tarski(B,C)))))) -> k1_yellow_1(u1_struct_0(A)) = u1_orders_2(A)))) # label(t10_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3991 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3992 (all A all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) -> -v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)))) # label(fc16_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3993 (all A all B (l1_orders_2(B) -> u1_struct_0(k6_yellow_1(A,B)) = k1_funct_2(A,u1_struct_0(B)))) # label(t28_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3994 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> (r2_hidden(k2_xboole_0(B,C),A) -> k10_lattice3(k2_yellow_1(A),B,C) = k2_xboole_0(B,C)))))))) # label(t8_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3995 (all A k4_yellow_0(k3_yellow_1(A)) = A) # label(t19_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3996 (all A (-v1_xboole_0(A) -> v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & -v3_struct_0(k2_yellow_1(A)))) # label(fc6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3997 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> k4_yellow_0(k2_yellow_1(u1_pre_topc(A))) = u1_struct_0(A))) # label(t24_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3998 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) <-> v1_tops_2(B,A)))))) # label(t25_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 3999 (all A (l1_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)))) # label(fc13_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4000 (all A (-v1_xboole_0(A) -> (v2_yellow_0(k2_yellow_1(A)) -> r2_hidden(k3_tarski(A),A)))) # label(t15_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4001 (all A (v1_relat_1(A) & v1_yellow_1(A) & v1_funct_1(A) -> v1_funct_1(A) & v2_pralg_1(A) & v1_relat_1(A))) # label(cc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4002 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> k1_xboole_0 = k3_yellow_0(k2_yellow_1(u1_pre_topc(A))))) # label(t23_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4003 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) -> k3_tarski(B) = k1_yellow_0(k2_yellow_1(u1_pre_topc(A)),B))))) # label(t22_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4004 (all A (l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v2_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_orders_2(k6_yellow_1(k1_xboole_0,A)) & v4_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) & v2_lattice3(k6_yellow_1(k1_xboole_0,A)) & v2_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)))) # label(fc14_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4005 (all A all B (-v1_xboole_0(A) & -v3_struct_0(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) -> v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v2_lattice3(k6_yellow_1(A,B)) & -v3_struct_0(k6_yellow_1(A,B)))) # label(fc17_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4006 (all A all B (m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_yellow_1(A))) -> (r3_orders_2(k3_yellow_1(A),B,C) <-> r1_tarski(B,C)))))) # label(t2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4007 (all A k3_yellow_1(A) = k3_lattice3(k1_lattice3(A))) # label(d2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4008 (all A (-v1_xboole_0(A) -> (r2_hidden(k3_tarski(A),A) -> k4_yellow_0(k2_yellow_1(A)) = k3_tarski(A)))) # label(t14_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4009 (all A (v10_lattices(A) & v14_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_yellow_0(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)))) # label(fc2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4010 (all A all B all C (-v1_xboole_0(A) & v1_yellow_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) -> k1_funct_1(B,C) = k4_yellow_1(A,B,C))) # label(redefinition_k4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4011 (all A (-v1_xboole_0(A) -> (r2_hidden(k1_xboole_0,A) -> k3_yellow_0(k2_yellow_1(A)) = k1_xboole_0))) # label(t13_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4012 (all A (-v3_struct_0(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)))) # label(fc8_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4013 (all A (-v1_xboole_0(A) -> ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k3_xboole_0(B,C),A))) -> v2_lattice3(k2_yellow_1(A))))) # label(t12_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4014 (all A (-v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)))) # label(fc7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4015 (all A all B all C (v1_yellow_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> l1_orders_2(k4_yellow_1(A,B,C)))) # label(dt_k4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4016 (all A (-v1_xboole_0(A) -> (v1_yellow_0(k2_yellow_1(A)) -> r2_hidden(k1_setfam_1(A),A)))) # label(t16_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.18 4017 (all A (-v1_xboole_0(A) -> ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_xboole_0(B,C),A))) -> v1_lattice3(k2_yellow_1(A))))) # label(t11_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4018 (all A all B (m1_pboole(B,A) & v1_yellow_1(B) -> v1_orders_2(k5_yellow_1(A,B)) & l1_orders_2(k5_yellow_1(A,B)))) # label(dt_k5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4019 (all A (v1_yellow_1(A) & m1_pboole(A,k1_xboole_0) -> g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) = k5_yellow_1(k1_xboole_0,A))) # label(t26_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4020 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) -> k2_yellow_0(k3_yellow_1(A),B) = k1_setfam_1(B))) # label(t20_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4021 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_yellow_0(k2_yellow_1(B),k3_yellow_1(A)) & v4_yellow_0(k2_yellow_1(B),k3_yellow_1(A)))) # label(t5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4022 (all A (v1_orders_2(k3_yellow_1(A)) & l1_orders_2(k3_yellow_1(A)))) # label(dt_k3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4023 (all A (-v1_xboole_0(A) -> (v2_lattice3(k2_yellow_1(A)) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> r1_tarski(k11_lattice3(k2_yellow_1(A),B,C),k3_xboole_0(B,C))))))))) # label(t7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4024 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> (r1_tarski(B,C) <-> r3_orders_2(k2_yellow_1(A),B,C)))))))) # label(t3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4025 (all A all B (v3_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) -> -v3_struct_0(k6_yellow_1(A,B)) & v3_orders_2(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)))) # label(fc15_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4026 (all A (-v1_xboole_0(A) -> (v1_lattice3(k2_yellow_1(A)) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> r1_tarski(k2_xboole_0(B,C),k10_lattice3(k2_yellow_1(A),B,C))))))))) # label(t6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4027 (all A (v4_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)))) # label(fc5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4028 (all A all B (m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_yellow_1(A))) -> k3_xboole_0(B,C) = k12_lattice3(k3_yellow_1(A),B,C) & k2_xboole_0(B,C) = k13_lattice3(k3_yellow_1(A),B,C))))) # label(t17_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4029 (all A (k1_yellow_1(A) = u1_orders_2(k2_yellow_1(A)) & A = u1_struct_0(k2_yellow_1(A)))) # label(t1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4030 (all A k1_yellow_1(A) = k1_wellord2(A)) # label(redefinition_k1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4031 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> v1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v1_yellow_0(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4032 (all A (l1_orders_2(A) -> k6_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))))) # label(t27_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4033 (all A all B (l1_orders_2(B) & -v3_struct_0(B) -> -v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)))) # label(fc11_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4034 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> (r2_hidden(k3_xboole_0(B,C),A) -> k11_lattice3(k2_yellow_1(A),B,C) = k3_xboole_0(B,C)))))))) # label(t9_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4035 (all A (v1_relat_1(A) -> ((all B (r2_hidden(B,k2_relat_1(A)) -> l1_orders_2(B))) <-> v1_yellow_1(A)))) # label(d3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4036 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v1_orders_2(C) & v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) -> (k7_yellow_1(A,B) = C <-> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (r2_hidden(D,u1_struct_0(C)) <-> r2_hidden(D,k1_funct_2(u1_struct_0(A),u1_struct_0(B))) & v5_orders_3(D,A,B))))))))))) # label(d6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4037 (all A (v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v22_waybel_0(B,A,A) & v11_quantal1(B) -> v4_waybel_0(k2_yellow_2(A,A,B),A) & v2_orders_2(k2_yellow_2(A,A,B)) & v4_orders_2(k2_yellow_2(A,A,B)) & v2_lattice3(k2_yellow_2(A,A,B)) & l1_orders_2(k2_yellow_2(A,A,B)) & v3_lattice3(k2_yellow_2(A,A,B)) & v1_lattice3(k2_yellow_2(A,A,B)) & v3_orders_2(k2_yellow_2(A,A,B))))))) # label(t37_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4038 (all A (v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v18_waybel_0(C,A,B) -> v8_yellow_0(k2_yellow_2(A,B,C),B)))))))) # label(t34_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4039 (all A (l1_orders_2(A) & -v3_struct_0(A) -> v11_quantal1(k7_grcat_1(A)))) # label(t23_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4040 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_lattice3(A,D,E) & v5_orders_3(C,A,B) -> r2_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E))))))))))))) # label(t16_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4041 (all A all B all C (-v3_struct_0(B) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> (r2_hidden(A,a_2_0_yellow_2(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & k1_waybel_0(B,B,C,D) = D))))) # label(fraenkel_a_2_0_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4042 (all A (v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B all C (r1_yellow_0(A,C) & r1_yellow_0(A,B) -> k1_yellow_0(A,k2_xboole_0(B,C)) = k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) & r1_yellow_0(A,k2_xboole_0(B,C)))))) # label(t3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4043 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> r1_orders_2(B,k1_waybel_0(A,B,C,E),k1_waybel_0(A,B,D,E)))) <-> r1_yellow_2(u1_struct_0(A),B,C,D)))))))))) # label(t10_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4044 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B r2_yellow_0(A,B)) -> v3_lattice3(A)))) # label(t27_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4045 (all A all B all C all D (-v1_xboole_0(A) & l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) & v1_funct_2(C,A,u1_struct_0(B)) & -v3_struct_0(B) -> k7_yellow_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4046 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v13_waybel_0(C,A)))) -> m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t39_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4047 (all A (v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> -v3_struct_0(k2_yellow_1(k8_waybel_0(A))) & v1_orders_2(k2_yellow_1(k8_waybel_0(A))) & v2_orders_2(k2_yellow_1(k8_waybel_0(A))) & v4_orders_2(k2_yellow_1(k8_waybel_0(A))) & v1_lattice3(k2_yellow_1(k8_waybel_0(A))) & v3_orders_2(k2_yellow_1(k8_waybel_0(A))))) # label(fc5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4048 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v1_funct_1(k4_yellow_2(A)) & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & m2_relset_1(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) # label(dt_k4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4049 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_lattice3(A,C,B) <-> r1_tarski(C,k6_waybel_0(A,B))))))))) # label(t1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4050 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & v1_funct_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k6_waybel_0(A,C) = k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C))) <-> k4_yellow_2(A) = B))))) # label(d4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4051 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v5_orders_3(C,A,B) -> v1_waybel_0(k4_pre_topc(A,B,C,D),B)))))))))) # label(t17_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4052 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> k8_waybel_0(A) = k1_relat_1(k3_yellow_2(A)) & m1_subset_1(k1_yellow_2(k2_yellow_1(k8_waybel_0(A)),A,k3_yellow_2(A)),k1_zfmisc_1(u1_struct_0(A))))) # label(t51_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4053 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> k5_yellow_0(B,k1_yellow_2(A,B,C)) = k2_yellow_2(A,B,C))))))) # label(d2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4054 (all A all B (l1_orders_2(A) & v1_relat_1(B) & -v3_struct_0(A) -> m1_subset_1(k5_yellow_2(A,B),u1_struct_0(A)))) # label(dt_k5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4055 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (v1_relat_1(B) -> k2_yellow_0(A,k2_relat_1(B)) = k6_yellow_2(A,B))))) # label(d6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4056 (all A all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) -> (v1_waybel_0(A,B) & v12_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(A) <-> r2_hidden(A,k1_relat_1(k3_yellow_2(B)))))) # label(t52_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4057 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & v8_yellow_0(B,A) & -v3_struct_0(B) -> v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v3_lattice3(B))))) # label(t33_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4058 (all A all B (-v3_struct_0(A) & v1_relat_1(B) & l1_orders_2(A) -> m1_subset_1(k6_yellow_2(A,B),u1_struct_0(A)))) # label(dt_k6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4059 (all A (l1_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (v4_yellow_0(C,A) & m1_yellow_0(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> r1_tarski(u1_orders_2(B),u1_orders_2(C))))))))) # label(t6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4060 $T # label(t9_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4061 (all A (v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v12_waybel_0(C,A) & v1_waybel_0(C,A)))) -> v1_waybel_0(k6_setfam_1(u1_struct_0(A),B),A) & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t40_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4062 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_yellow_0(A,B))) -> (all B (k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) = k2_yellow_0(A,B) & r2_yellow_0(A,B)))))) # label(t28_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4063 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_orders_2(A) & -v3_struct_0(A) -> v4_yellow_0(k5_yellow_0(A,B),A) & v1_orders_2(k5_yellow_0(A,B)) & -v3_struct_0(k5_yellow_0(A,B)))) # label(fc1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4064 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v21_waybel_0(B,A,A) -> v5_orders_3(B,A,A)))))) # label(t19_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4065 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v24_waybel_0(A) & v3_orders_2(A) -> v1_funct_1(k3_yellow_2(A)) & v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & v1_relat_1(k3_yellow_2(A)))) # label(fc7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4066 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B r1_yellow_0(A,B)) -> v3_lattice3(A)))) # label(t26_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4067 (all A all B (-v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (m1_subset_1(A,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) <-> m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) & v12_waybel_0(A,B) & v1_waybel_0(A,B) & -v1_xboole_0(A)))) # label(t43_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4068 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v1_xboole_0(B) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(C,A) & v1_waybel_0(C,A) & -v1_xboole_0(C) -> m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & -v1_xboole_0(k5_subset_1(u1_struct_0(A),B,C)))))))) # label(t42_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4069 (all A all B all C all D (v3_orders_2(B) & m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) & m1_subset_1(D,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) & l1_orders_2(B) & v1_lattice3(B) & v4_orders_2(B) & v2_orders_2(B) -> (r2_hidden(A,a_3_0_yellow_2(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & E = A & -(-r2_hidden(E,C) & (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> -(k13_lattice3(B,F,G) = E & r2_hidden(G,D) & r2_hidden(F,C)))))) & -r2_hidden(E,D))))))) # label(fraenkel_a_3_0_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4070 (all A (v2_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v17_waybel_0(C,A,B) -> v7_yellow_0(k2_yellow_2(A,B,C),B)))))))) # label(t35_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4071 (all A (v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (v1_funct_2(D,B,u1_struct_0(A)) & m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_1(D) -> r3_orders_2(A,k7_yellow_2(B,A,D,C),k5_yellow_2(A,D)) & r3_orders_2(A,k6_yellow_2(A,D),k7_yellow_2(B,A,D,C)))))))))) # label(t55_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4072 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u1_struct_0(k2_yellow_2(A,B,C))) -> (exists E (m1_subset_1(E,u1_struct_0(A)) & k1_waybel_0(A,B,C,E) = D)))))))))) # label(t12_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4073 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v11_quantal1(B) -> a_2_0_yellow_2(A,B) = k1_yellow_2(A,A,B)))))) # label(t21_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4074 (all A all B all C (-v3_struct_0(B) & l1_struct_0(B) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & v1_funct_1(C) -> m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4075 (all A all B all C (-v3_struct_0(A) & l1_orders_2(A) & -v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> v4_yellow_0(k2_yellow_2(A,B,C),B) & v1_orders_2(k2_yellow_2(A,B,C)) & -v3_struct_0(k2_yellow_2(A,B,C)))) # label(fc2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4076 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) -> (E = D -> (v2_waybel_0(D,B) -> v2_waybel_0(E,C)) & (v1_waybel_0(D,B) -> v1_waybel_0(E,C)))))))))))))) # label(t8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4077 (all A (-v3_struct_0(A) & l1_orders_2(A) -> v5_orders_3(k7_grcat_1(A),A,A))) # label(t13_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4078 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> (exists D (r1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k2_struct_0(k2_yellow_1(k8_waybel_0(A)),B,C)) & k4_waybel_0(A,D) = k10_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) & a_3_0_yellow_2(A,B,C) = D & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))))))) # label(t46_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4079 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v11_quantal1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_waybel_0(A,A,B,C) = k1_waybel_0(A,A,B,k1_waybel_0(A,A,B,C))))))))) # label(t20_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4080 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_yellow_0(A,B))) -> v3_lattice3(A)))) # label(t30_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4081 (all A all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (-v3_struct_0(C) & m1_yellow_0(C,B) -> (v1_waybel_0(A,C) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) -> v1_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B)))) & (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) & v2_waybel_0(A,C) -> v2_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B)))))))) # label(t7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4082 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,C,u1_struct_0(A)) & v1_funct_2(D,C,u1_struct_0(A)) -> ((all E (m1_subset_1(E,C) -> r3_orders_2(A,B,k7_yellow_2(C,A,D,E)))) -> r3_orders_2(A,B,k6_yellow_2(A,D))))))))))) # label(t57_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4083 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_relat_1(B) -> k1_yellow_0(A,k2_relat_1(B)) = k5_yellow_2(A,B))))) # label(d5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4084 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))))) # label(t54_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4085 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) & v4_orders_2(A) -> v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A))) # label(t53_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4086 (all A all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_1(C) -> (r1_tarski(A,k1_yellow_2(B,B,C)) & v11_quantal1(C) -> A = k4_pre_topc(B,B,C,A)))))) # label(t22_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4087 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) -> v3_lattice3(k2_yellow_1(k8_waybel_0(A))))) # label(t50_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4088 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (-v3_struct_0(C) & l1_orders_2(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (v5_orders_3(D,A,B) & v5_orders_3(E,B,C) -> v5_orders_3(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t14_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4089 (all A all B all C (l1_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(A) -> m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4090 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_yellow_0(A,B))) -> (all B (r1_yellow_0(A,B) & k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) = k1_yellow_0(A,B)))))) # label(t29_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4091 (all A all B (l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,u1_struct_0(B)) & v1_funct_2(C,A,u1_struct_0(B)) -> (all D (m2_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) & v1_funct_1(D) -> (r1_yellow_2(A,B,C,D) <-> (all E -(r2_hidden(E,A) & (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> -(G = k1_funct_1(D,E) & r1_orders_2(B,F,G) & F = k1_funct_1(C,E))))))))))))))) # label(d1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4092 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_lattice3(A,C,B) <-> r1_tarski(C,k7_waybel_0(A,B))))))))) # label(t2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4093 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,C,u1_struct_0(A)) & m2_relset_1(D,C,u1_struct_0(A)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,C) -> r3_orders_2(A,k7_yellow_2(C,A,D,E),B))) -> r3_orders_2(A,k5_yellow_2(A,D),B)))))))))) # label(t56_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4094 (all A (v2_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v7_yellow_0(B,A) & m1_yellow_0(B,A) & v4_yellow_0(B,A) & -v3_struct_0(B) -> v2_orders_2(B) & v4_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & v2_lattice3(B) & v1_lattice3(B) & v3_orders_2(B))))) # label(t32_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4095 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v1_yellow_0(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k8_waybel_0(A))) -> -v1_xboole_0(k1_setfam_1(B)) & v1_waybel_0(k1_setfam_1(B),A) & m1_subset_1(k1_setfam_1(B),k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(k1_setfam_1(B),A))))) # label(t47_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4096 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & v3_lattice3(B) & v1_lattice3(B) & v4_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v17_waybel_0(C,A,B) | v18_waybel_0(C,A,B) -> v2_orders_2(k2_yellow_2(A,B,C)) & v4_orders_2(k2_yellow_2(A,B,C)) & v1_lattice3(k2_yellow_2(A,B,C)) & v2_lattice3(k2_yellow_2(A,B,C)) & l1_orders_2(k2_yellow_2(A,B,C)) & v3_lattice3(k2_yellow_2(A,B,C)) & v3_orders_2(k2_yellow_2(A,B,C))))))))) # label(t36_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4097 (all A all B (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & v1_lattice3(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(C,A) -> r3_orders_2(B,C,k1_yellow_0(B,A)) & r3_orders_2(B,k2_yellow_0(B,A),C)))))) # label(t24_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4098 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B r1_yellow_0(A,B)) <-> (all B r2_yellow_0(A,B))))) # label(t25_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4099 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> k11_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k3_xboole_0(B,C))))))) # label(t45_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4100 (all A all B all C (-v3_struct_0(A) & -v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(A) -> m1_yellow_0(k2_yellow_2(A,B,C),B) & v4_yellow_0(k2_yellow_2(A,B,C),B) & v1_orders_2(k2_yellow_2(A,B,C)))) # label(dt_k2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4101 (all A all B all C (l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> k2_relat_1(C) = k1_yellow_2(A,B,C))) # label(redefinition_k1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4102 (all A all B all C (-v3_struct_0(B) & l1_struct_0(B) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & v1_funct_1(C) -> k2_relat_1(C) = k8_yellow_2(A,B,C))) # label(redefinition_k8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4103 (all A (v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v22_waybel_0(B,A,A) -> v5_orders_3(B,A,A)))))) # label(t18_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4104 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> -v3_struct_0(k2_yellow_1(k8_waybel_0(A))) & v2_lattice3(k2_yellow_1(k8_waybel_0(A))) & v4_orders_2(k2_yellow_1(k8_waybel_0(A))) & v3_orders_2(k2_yellow_1(k8_waybel_0(A))) & v2_orders_2(k2_yellow_1(k8_waybel_0(A))) & v1_orders_2(k2_yellow_1(k8_waybel_0(A))))) # label(fc4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4105 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v25_waybel_0(A) & v24_waybel_0(A) & v2_yellow_0(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v25_waybel_0(A) & v2_yellow_0(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4106 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(B,C) -> r1_tarski(k2_wellord1(A,B),k2_wellord1(A,C)))))) # label(t5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4107 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_lattice3(A,D,E) & v5_orders_3(C,A,B) -> r1_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E))))))))))))) # label(t15_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4108 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0) = k2_pre_topc(A) & r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0))) # label(t49_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4109 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v13_waybel_0(C,A) & v2_waybel_0(C,A)))) -> m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t41_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4110 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v5_orders_3(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = a_2_1_yellow_2(A,B) -> v2_orders_2(k5_yellow_0(A,C)) & v3_orders_2(k5_yellow_0(A,C)) & v1_lattice3(k5_yellow_0(A,C)) & l1_orders_2(k5_yellow_0(A,C)) & v3_lattice3(k5_yellow_0(A,C)) & v2_lattice3(k5_yellow_0(A,C)) & v4_orders_2(k5_yellow_0(A,C)))))))))) # label(t31_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4111 (all A all B (-v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) -> (r2_hidden(A,C) -> m1_subset_1(A,u1_struct_0(B))))))) # label(t44_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4112 (all A all B all C (v3_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v4_orders_2(B) & v2_orders_2(B) -> ((exists D (k1_waybel_0(B,B,C,D) = D & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_1_yellow_2(B,C))))) # label(fraenkel_a_2_1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4113 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> v1_relat_1(k4_yellow_2(A)) & v1_funct_1(k4_yellow_2(A)) & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))))) # label(fc8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4114 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> v1_funct_1(k3_yellow_2(A)) & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & m2_relset_1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)))) # label(dt_k3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4115 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & v1_funct_1(B) -> (B = k3_yellow_2(A) <-> (all C (v1_waybel_0(C,A) & v12_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> k1_yellow_0(A,C) = k1_funct_1(B,C)))))))) # label(d3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4116 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v12_waybel_0(C,A)))) -> m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t38_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4117 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v3_orders_2(A) -> (all B all C (r2_yellow_0(A,C) & r2_yellow_0(A,B) -> k12_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) = k2_yellow_0(A,k2_xboole_0(B,C)) & r2_yellow_0(A,k2_xboole_0(B,C)))))) # label(t4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4118 (all A (l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k8_waybel_0(A)))) # label(fc3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4119 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> u1_struct_0(k2_yellow_2(A,B,C)) = k1_yellow_2(A,B,C))))))) # label(t11_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4120 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v1_yellow_0(A) & v3_orders_2(A) & v2_orders_2(A) -> v2_orders_2(k2_yellow_1(k8_waybel_0(A))) & v3_orders_2(k2_yellow_1(k8_waybel_0(A))) & v4_orders_2(k2_yellow_1(k8_waybel_0(A))) & v2_yellow_0(k2_yellow_1(k8_waybel_0(A))) & v3_yellow_0(k2_yellow_1(k8_waybel_0(A))) & v2_lattice3(k2_yellow_1(k8_waybel_0(A))) & v3_lattice3(k2_yellow_1(k8_waybel_0(A))) & v1_lattice3(k2_yellow_1(k8_waybel_0(A))) & v25_waybel_0(k2_yellow_1(k8_waybel_0(A))) & v24_waybel_0(k2_yellow_1(k8_waybel_0(A))) & v1_yellow_0(k2_yellow_1(k8_waybel_0(A))) & v1_orders_2(k2_yellow_1(k8_waybel_0(A))) & -v3_struct_0(k2_yellow_1(k8_waybel_0(A))))) # label(fc6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4121 (all A all B all C all D (l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_subset_1(D,A) & m1_relset_1(C,A,u1_struct_0(B)) & -v3_struct_0(B) & -v1_xboole_0(A) -> m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)))) # label(dt_k7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4122 (all A (v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v1_yellow_0(A) & v3_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) -> k1_setfam_1(B) = k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) & r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B))))) # label(t48_yellow_2) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4123 (all A (v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A))) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_3_waybel_1(A,B,C)))))))))) # label(t66_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4124 (all A all B all C (v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v3_orders_2(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_1_waybel_1(B,C)) <-> (exists D (r3_orders_2(B,k7_yellow_2(u1_struct_0(B),B,C,D),D) & D = A & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4125 (all A (v1_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & -v3_struct_0(k3_yellow_1(A)))) # label(fc1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4126 (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_orders_2(A) -> m1_subset_1(k6_waybel_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4127 (all A all B all C (l1_orders_2(A) & -v3_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_orders_2(B) & -v3_struct_0(A) -> v1_funct_1(k3_waybel_1(A,B,C)) & m2_relset_1(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & v1_funct_2(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)))) # label(dt_k3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4128 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v1_funct_1(B) & v7_waybel_1(B,A) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> v1_funct_1(B) & -v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A)))))) # label(cc3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4129 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v7_waybel_1(k7_grcat_1(A),A) & v8_waybel_1(k7_grcat_1(A),A) & v6_waybel_1(k7_grcat_1(A),A) & v23_waybel_0(k7_grcat_1(A),A,A) & v5_orders_3(k7_grcat_1(A),A,A) & -v1_xboole_0(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)))) # label(fc5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4130 (all A (l1_orders_2(A) & v1_yellow_0(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) = k7_waybel_1(A,k10_lattice3(A,B,C))))))))) # label(t87_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4131 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) -> r5_waybel_1(k2_yellow_2(k2_yellow_1(k8_waybel_0(A)),k2_yellow_1(k8_waybel_0(A)),k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),k3_yellow_2(A),k4_yellow_2(A))),A) & v7_waybel_1(k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),k3_yellow_2(A),k4_yellow_2(A)),k2_yellow_1(k8_waybel_0(A))))) # label(t61_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.19 4132 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_funct_1(k5_waybel_1(A,B)) & v1_funct_2(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4133 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v9_waybel_1(A) -> -v3_struct_0(A) & v2_yellow_0(A)))) # label(cc7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4134 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (v5_orders_3(C,A,B) & (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k7_waybel_0(B,E))))) <-> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(t11_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4135 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_waybel_1(A,B,C) <-> B = k2_yellow_0(A,C) & r2_hidden(k2_yellow_0(A,C),C) & r2_yellow_0(A,C))))))) # label(d6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4136 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)) = D & C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) -> v11_quantal1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)) & v11_quantal1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C))))))))))) # label(t22_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4137 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v5_orders_3(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_1_waybel_1(A,B) = C -> v7_yellow_0(k5_yellow_0(A,C),A))))))))) # label(t53_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4138 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> -((all C (v2_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) & v3_orders_2(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) -> (all E (m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_1(E) -> -(v5_orders_3(D,A,C) & v2_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v5_orders_3(E,C,A) & k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),E,D) = k7_grcat_1(C) & k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) = B & v2_funct_1(E)))))))) & v6_waybel_1(B,A)))))) # label(t37_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4139 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v7_waybel_1(B,A) -> v18_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,C) & r1_tarski(C,u1_struct_0(k2_yellow_2(A,A,B))) -> k7_yellow_2(u1_struct_0(A),A,B,k1_yellow_0(A,C)) = k1_yellow_0(k2_yellow_2(A,A,B),C) & r1_yellow_0(k2_yellow_2(A,A,B),C))))))))) # label(t58_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4140 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,B,C) = k11_lattice3(A,B,k6_waybel_1(A,B,C))))))))) # label(t80_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4141 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = a_2_0_waybel_1(A,B) -> (v17_waybel_0(B,A,A) -> v7_yellow_0(k5_yellow_0(A,C),A) & v7_yellow_0(k2_yellow_2(A,A,B),A)) & (v21_waybel_0(B,A,A) -> v3_waybel_0(k2_yellow_2(A,A,B),A) & v3_waybel_0(k5_yellow_0(A,C),A)))))))))) # label(t54_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4142 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,u1_struct_0(B)) & l1_orders_2(B) -> ((exists E (r2_hidden(E,D) & k11_lattice3(B,C,E) = A & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_1_waybel_1(B,C,D))))) # label(fraenkel_a_3_1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4143 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) -> (k4_waybel_1(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> k11_lattice3(A,B,D) = k7_yellow_2(u1_struct_0(A),A,C,D)))))))))) # label(d18_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4144 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v5_orders_3(B,A,A) -> v7_waybel_1(B,A) | (all C (-v3_struct_0(C) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) -> (all E (m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(E) -> -(B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),E,D) & v3_waybel_1(k1_waybel_1(C,A,D,E),C,A))))))))))))) # label(t41_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4145 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_yellow_0(A) = k6_waybel_1(A,B,k4_yellow_0(A))))))) # label(t76_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4146 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) & v4_orders_2(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_waybel_1(C,B,A) -> v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4147 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r4_waybel_1(A,B,C) <-> r1_yellow_0(A,C) & k1_yellow_0(A,C) = B & r2_hidden(k1_yellow_0(A,C),C))))))) # label(d7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4148 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k4_yellow_0(A) = k6_waybel_1(A,B,C) & k4_yellow_0(A) = k6_waybel_1(A,C,B) -> B = C)))))))) # label(t74_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4149 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r6_waybel_1(A,B,C) & m1_subset_1(C,u1_struct_0(A)))))) <-> v10_waybel_1(A)))) # label(d24_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4150 (all A (v2_orders_2(A) & v3_orders_2(A) & v3_yellow_0(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k7_waybel_1(A,k7_waybel_1(A,B)) = B)) & v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r6_waybel_1(A,B,k7_waybel_1(A,B))))))) # label(t89_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4151 (all A (v2_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> v3_lattice3(k2_yellow_2(A,A,B))))))) # label(t57_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4152 (all A all B (v3_orders_2(A) & v2_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> v1_funct_1(k4_waybel_1(A,B)) & -v1_xboole_0(k4_waybel_1(A,B)) & v5_orders_3(k4_waybel_1(A,B),A,A) & v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(k4_waybel_1(A,B)))) # label(fc8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4153 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_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_waybel_1(A,k10_lattice3(A,B,C),D) = k11_lattice3(A,k6_waybel_1(A,B,D),k6_waybel_1(A,C,D))))))))))) # label(t81_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4154 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v8_waybel_1(B,A) -> v17_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,C) & r1_tarski(C,u1_struct_0(k2_yellow_2(A,A,B))) -> k2_yellow_0(k2_yellow_2(A,A,B),C) = k7_yellow_2(u1_struct_0(A),A,B,k2_yellow_0(A,C)) & r2_yellow_0(k2_yellow_2(A,A,B),C))))))))) # label(t59_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4155 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (r1_yellow_0(A,B) & r2_hidden(k1_yellow_0(A,B),B) <-> r2_waybel_1(A,B))))) # label(d5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4156 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v2_waybel_1(A) & v10_waybel_1(A) & v3_yellow_0(A) & v1_lattice3(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_1(A) & v11_waybel_1(A) & v10_waybel_1(A) & v3_yellow_0(A) & v2_yellow_0(A) & v1_yellow_0(A) & v4_orders_2(A) & v2_orders_2(A)))) # label(cc9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4157 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,C,k6_waybel_1(A,B,C))))))))) # label(t75_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4158 (all A all B all C (l1_orders_2(A) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(B) & -v3_struct_0(B) & -v3_struct_0(A) -> -v1_xboole_0(k2_waybel_1(A,B,C)) & v2_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v1_partfun1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v1_funct_1(k2_waybel_1(A,B,C)) & v1_relat_1(k2_waybel_1(A,B,C)))) # label(fc6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4159 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_orders_3(k4_waybel_1(A,B),A,A))))) # label(t63_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4160 (all A all B all C (-v3_struct_0(A) & -v3_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & l1_struct_0(A) -> (v1_waybel_1(C,A,B) <-> v2_funct_1(C)))) # label(redefinition_v1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4161 $T # label(t1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4162 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> m1_subset_1(a_2_0_waybel_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(a_2_1_waybel_1(A,B)) & m1_subset_1(a_2_1_waybel_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(a_2_0_waybel_1(A,B))))))) # label(t46_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4163 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_yellow_0(A,a_3_5_waybel_1(A,B,C)) = k12_lattice3(A,C,k1_yellow_0(A,B))))))) -> v2_waybel_1(A)))) # label(t68_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4164 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> -(v18_waybel_0(C,B,A) & (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) -> -(v3_waybel_1(k1_waybel_1(A,B,D,C),A,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,D,E),k5_pre_topc(B,A,C,k6_waybel_0(A,E)))))))) & v3_lattice3(B)))))))) # label(t16_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4165 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k2_waybel_1(A,B,C) = C)))))) # label(t32_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4166 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v7_waybel_1(B,A) <-> v6_waybel_1(B,A) & r1_yellow_2(u1_struct_0(A),A,k7_grcat_1(A),B)))))) # label(d14_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4167 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v9_waybel_1(A) -> v2_waybel_1(A) & -v3_struct_0(A)))) # label(cc6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4168 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (r5_waybel_1(A,B) <-> (exists C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B)))))))) # label(d8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4169 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_pre_topc(A,A,k4_waybel_1(A,B),C) = a_3_1_waybel_1(A,B,C))))))) # label(t64_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4170 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> k4_yellow_0(A) = k6_waybel_1(A,B,C))))))))) # label(t72_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4171 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> -(v8_waybel_1(B,A) & (all C (-v3_struct_0(C) & v2_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) & v3_orders_2(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) -> -(v3_waybel_1(k1_waybel_1(A,C,D,E),A,C) & k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) = B)))))))))))) # label(t43_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4172 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (exists B (v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(B) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4173 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) -> k8_yellow_2(u1_struct_0(A),A,B) = k3_xboole_0(a_2_0_waybel_1(A,B),a_2_1_waybel_1(A,B))))))) # label(t45_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4174 (all A (l1_orders_2(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)) -> a_3_0_waybel_1(A,B,C) = k5_pre_topc(A,A,k4_waybel_1(A,B),k6_waybel_0(A,C)))))))) # label(t62_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4175 (all A all B all C all D (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & v3_lattice3(B) & v4_orders_2(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & A = k12_lattice3(B,D,E))) <-> r2_hidden(A,a_3_4_waybel_1(B,C,D))))) # label(fraenkel_a_3_4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4176 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> m2_relset_1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k4_waybel_1(A,B)))) # label(dt_k4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4177 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) <-> v4_orders_2(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A))) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) & v2_orders_2(A)))) # label(d19_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4178 (all A (v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D))))))))))) # label(t3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4179 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k6_waybel_1(A,C,D),k6_waybel_1(A,B,D)))))))))))) # label(t78_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4180 (all A (-v3_struct_0(A) & v3_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_4_waybel_1(A,B,C)))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A)))))) # label(t67_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4181 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,C) & r1_tarski(C,k8_yellow_2(u1_struct_0(A),A,B)) & v7_waybel_1(B,A) -> k7_yellow_2(u1_struct_0(A),A,B,k2_yellow_0(A,C)) = k2_yellow_0(A,C)))))))) # label(t30_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4182 (all A (l1_orders_2(A) -> (v11_waybel_1(A) & -v3_struct_0(A) -> v4_orders_2(A) & v2_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v2_yellow_0(A) & v1_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc10_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4183 (all A (v4_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v1_lattice3(A) -> k10_lattice3(A,k4_yellow_0(A),B) = k4_yellow_0(A)) & (v2_lattice3(A) & v2_orders_2(A) & v3_orders_2(A) -> k11_lattice3(A,k4_yellow_0(A),B) = B))))) # label(t5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4184 (all A all B all C all D (l1_orders_2(A) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) & l1_orders_2(B) -> k4_tarski(C,D) = k1_waybel_1(A,B,C,D))) # label(redefinition_k1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4185 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (C = a_2_1_waybel_1(A,B) -> v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C)) & v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))))))))))) # label(t49_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4186 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (v5_waybel_1(C,A,B) -> v18_waybel_0(C,B,A)))))))) # label(t14_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4187 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) & v23_waybel_0(k7_grcat_1(A),A,A) & v5_orders_3(k7_grcat_1(A),A,A) & -v1_xboole_0(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_relat_1(k7_grcat_1(A)))) # label(fc4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4188 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A)) & r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & v5_orders_3(D,B,A) & v5_orders_3(C,A,B) -> D = k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)) & k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) = C))))))))) # label(t21_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4189 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_0_waybel_1(A,B) = C -> (all D (v1_funct_2(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & m2_relset_1(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_1(D) -> (k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C) = D -> v7_waybel_1(D,k5_yellow_0(A,C))))))))))))) # label(t50_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4190 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) -> r1_orders_2(A,k6_waybel_1(A,B,C),k6_waybel_1(A,B,D)))))))))))) # label(t79_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4191 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> v2_waybel_1(A)))) # label(t69_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4192 (all A (-v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)))) # label(fc9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4193 (all A (l1_orders_2(A) -> (v9_waybel_1(A) & -v3_struct_0(A) -> v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) & -v3_struct_0(A)))) # label(cc5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4194 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k8_relat_1(u1_struct_0(k2_yellow_2(A,B,C)),C) = k2_waybel_1(A,B,C))))))) # label(d16_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4195 (all A all B (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) & l1_orders_2(A) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v4_waybel_1(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> -v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B) & v17_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C)))))) # label(cc1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4196 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (l1_orders_2(C) -> (r5_waybel_1(A,B) & r5_waybel_1(B,C) -> r5_waybel_1(A,C)))))))) # label(t8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4197 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k7_waybel_1(A,B),u1_struct_0(A)))) # label(dt_k7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4198 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> (v5_waybel_1(C,A,B) <-> (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v3_waybel_1(k1_waybel_1(A,B,D,C),A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))))))))))) # label(d12_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4199 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_0_waybel_1(A,B) = C -> v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C)))))))))))) # label(t48_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4200 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v11_waybel_1(A) -> v3_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) & v2_yellow_0(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4201 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> v2_yellow_0(A)))) # label(t71_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4202 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v8_waybel_1(B,A) -> v8_yellow_0(k2_yellow_2(A,A,B),A)) & (v7_waybel_1(B,A) -> v7_yellow_0(k2_yellow_2(A,A,B),A)))))) # label(t56_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4203 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v1_yellow_0(A) & v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r4_waybel_1(A,k7_waybel_1(A,B),a_2_2_waybel_1(A,B))))))) # label(t82_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4204 (all A all B all C all D (l1_orders_2(A) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(B) -> m1_waybel_1(k1_waybel_1(A,B,C,D),A,B))) # label(dt_k1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4205 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k1_struct_0(A,E))))) -> k7_grcat_1(A) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)))))))))) # label(t28_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4206 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k1_struct_0(B,E)))))))))))))) # label(t23_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4207 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (m1_waybel_1(C,A,B) <-> (exists D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & (exists E (C = k4_tarski(D,E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(E))) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)))))))))) # label(d9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4208 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> (v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) <-> v2_funct_1(D))))))))))) # label(t26_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4209 (all A (l1_orders_2(A) -> v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A),A,A))) # label(fc2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4210 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v2_waybel_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)) -> k10_lattice3(A,k11_lattice3(A,B,C),k11_lattice3(A,B,D)) = k11_lattice3(A,B,k10_lattice3(A,C,D))))))))))) # label(d3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4211 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> -((all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> -((all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k7_waybel_0(B,E))))) & v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))) & v17_waybel_0(C,A,B) & v3_lattice3(A)))))))) # label(t15_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4212 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m1_waybel_1(C,A,B) -> (v3_waybel_1(C,A,B) <-> (exists D ((exists E (v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v5_orders_3(D,A,B) & v5_orders_3(E,B,A) & (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(A)) -> (r1_orders_2(B,F,k7_yellow_2(u1_struct_0(A),B,D,G)) <-> r1_orders_2(A,k7_yellow_2(u1_struct_0(B),A,E,F),G)))))) & C = k1_waybel_1(A,B,D,E) & v1_funct_1(E))) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D)))))))))) # label(d10_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4213 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) <-> v11_quantal1(B) & v5_orders_3(B,A,A)))))) # label(d13_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4214 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v5_orders_3(C,A,B) -> v5_orders_3(k2_waybel_1(A,B,C),A,k2_yellow_2(A,B,C))))))))) # label(t33_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4215 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (C = a_2_1_waybel_1(A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_2(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) -> (D = k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C) -> v8_waybel_1(D,k5_yellow_0(A,C))))))))))))) # label(t51_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4216 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_yellow_0(A) = k6_waybel_1(A,B,B)))))) # label(t73_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4217 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v8_waybel_1(B,A) & r1_yellow_0(A,C) & r1_tarski(C,k8_yellow_2(u1_struct_0(A),A,B)) -> k7_yellow_2(u1_struct_0(A),A,B,k1_yellow_0(A,C)) = k1_yellow_0(A,C)))))))) # label(t31_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4218 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v7_waybel_1(B,A) -> v3_waybel_1(k1_waybel_1(k2_yellow_2(A,A,B),A,k3_waybel_1(A,A,B),k2_waybel_1(A,A,B)),k2_yellow_2(A,A,B),A)))))) # label(t39_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4219 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k6_waybel_0(A,E))))) & v5_orders_3(D,B,A) <-> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(t12_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4220 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & l1_orders_2(B) -> ((exists E (r1_orders_2(B,k11_lattice3(B,C,E),D) & A = E & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_waybel_1(B,C,D))))) # label(fraenkel_a_3_0_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4221 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A)) & r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C))))))))))) # label(t19_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4222 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k1_struct_0(A,E)))))))))))))) # label(t27_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4223 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> ((exists C (-v3_struct_0(C) & v2_orders_2(C) & v3_orders_2(C) & l1_orders_2(C) & (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & (exists E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & v5_orders_3(D,A,C) & k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) = B & k7_grcat_1(C) = k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),E,D) & v5_orders_3(E,C,A) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)))) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)))) & v4_orders_2(C))) -> v6_waybel_1(B,A)))))) # label(t38_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4224 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_waybel_1(A,B,C) = k7_yellow_2(u1_struct_0(A),A,k5_waybel_1(A,B),C))))))) # label(d21_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4225 (all A (-v3_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,C,k7_waybel_1(A,B)) <-> k11_lattice3(A,B,C) = k3_yellow_0(A))))))))) # label(t85_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4226 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A) -> v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v2_funct_1(C)))))))))) # label(t25_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4227 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v11_quantal1(B) -> k7_grcat_1(k2_yellow_2(A,A,B)) = k7_funct_2(u1_struct_0(k2_yellow_2(A,A,B)),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,A,B)),k3_waybel_1(A,A,B),k2_waybel_1(A,A,B))))))) # label(t36_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4228 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v8_waybel_1(B,A) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> -v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & v1_funct_1(B)))))) # label(cc4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4229 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> (v3_lattice3(B) -> (v18_waybel_0(C,B,A) <-> v5_waybel_1(C,A,B) & v5_orders_3(C,B,A))))))))) # label(t18_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4230 (all A (l1_orders_2(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)) -> (r6_waybel_1(A,B,C) <-> k4_yellow_0(A) = k10_lattice3(A,B,C) & k3_yellow_0(A) = k11_lattice3(A,B,C)))))))) # label(d23_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4231 (all A all B all C (v2_orders_2(B) & l1_orders_2(B) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_1(C) & v4_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & r3_orders_2(B,D,k7_yellow_2(u1_struct_0(B),B,C,D)) & D = A)) <-> r2_hidden(A,a_2_0_waybel_1(B,C))))) # label(fraenkel_a_2_0_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4232 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k1_struct_0(B,E))))) -> k7_grcat_1(B) = k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)))))))))) # label(t24_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.20 4233 (all A all B all C all D (v2_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & l1_orders_2(B) & v2_lattice3(B) & v4_orders_2(B) & v3_orders_2(B) -> (r2_hidden(A,a_3_3_waybel_1(B,C,D)) <-> (exists E (A = k12_lattice3(B,D,E) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4234 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k7_yellow_2(u1_struct_0(A),B,C,E) = k7_yellow_2(u1_struct_0(A),B,C,D) -> E = D)))))))))))) # label(d1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4235 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k7_grcat_1(k2_yellow_2(A,B,C)) = k3_waybel_1(A,B,C))))))) # label(d17_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4236 (all A all B all C all D (v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B)) & v2_lattice3(B) & v2_orders_2(B) -> (r2_hidden(A,a_3_2_waybel_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r3_orders_2(B,k12_lattice3(B,C,E),D) & A = E))))) # label(fraenkel_a_3_2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4237 (all A all B all C (l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> ((exists D (k11_lattice3(B,C,D) = k3_yellow_0(B) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_2_waybel_1(B,C))))) # label(fraenkel_a_2_2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4238 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D))))))))))) # label(t2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4239 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v4_waybel_1(C,A,B) <-> (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(d11_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4240 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_waybel_1(A,B,k3_yellow_0(A)) = k7_waybel_1(A,B))))) # label(d22_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4241 (all A (v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v2_lattice3(A) -> k11_lattice3(A,k3_yellow_0(A),B) = k3_yellow_0(A)) & (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) -> k10_lattice3(A,k3_yellow_0(A),B) = B))))) # label(t4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4242 (all A all B all C (-v3_struct_0(A) & l1_orders_2(A) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(B) & -v3_struct_0(B) -> v1_relat_1(k3_waybel_1(A,B,C)) & v2_funct_1(k3_waybel_1(A,B,C)) & -v1_xboole_0(k3_waybel_1(A,B,C)) & v1_partfun1(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & v5_orders_3(k3_waybel_1(A,B,C),k2_yellow_2(A,B,C),B) & v1_funct_2(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & v1_funct_1(k3_waybel_1(A,B,C)))) # label(fc7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4243 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v9_waybel_1(A) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(C) -> (v3_waybel_1(k1_waybel_1(A,A,C,k4_waybel_1(A,B)),A,A) <-> C = k5_waybel_1(A,B))))))))) # label(d20_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4244 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> -(v7_waybel_1(B,A) & (all C (v2_orders_2(C) & l1_orders_2(C) & v4_orders_2(C) & v3_orders_2(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) -> -(v3_waybel_1(k1_waybel_1(C,A,D,E),C,A) & B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),E,D))))))))))))) # label(t40_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4245 (all A all B all C (-v3_struct_0(A) & l1_orders_2(A) & -v3_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(B) -> v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & m2_relset_1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v1_funct_1(k2_waybel_1(A,B,C)))) # label(dt_k2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4246 (all A (v2_orders_2(A) & v2_lattice3(A) & v3_yellow_0(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (v9_waybel_1(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_waybel_1(A,k7_waybel_1(A,B)) = B)) -> v10_waybel_1(A) & v2_waybel_1(A)) & (v10_waybel_1(A) & v2_waybel_1(A) -> v9_waybel_1(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_waybel_1(A,k7_waybel_1(A,B)) = B))))) # label(t90_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4247 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> (v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) <-> v2_funct_1(C))))))))))) # label(t29_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4248 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,k11_lattice3(A,C,D),B) <-> r1_orders_2(A,D,k6_waybel_1(A,C,B)))))))))))) # label(t70_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4249 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> v4_waybel_1(C,A,B) & v5_waybel_1(D,A,B)))))))))) # label(t10_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4250 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v3_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_waybel_1(A,a_3_2_waybel_1(A,B,C)))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A)))))) # label(t65_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4251 (all A (v1_yellow_0(A) & l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B)))))))))) # label(t86_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4252 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) & v1_yellow_0(A) -> k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) & k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A)))) # label(t83_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4253 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> k2_relat_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,a_2_1_waybel_1(A,B))) = k8_yellow_2(u1_struct_0(A),A,B) & k2_relat_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,a_2_0_waybel_1(A,B))) = k8_yellow_2(u1_struct_0(A),A,B)))))) # label(t47_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4254 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(k2_yellow_2(A,B,C))) -> k7_yellow_2(u1_struct_0(k2_yellow_2(A,B,C)),B,k3_waybel_1(A,B,C),D) = D)))))))) # label(t34_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4255 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v8_waybel_1(B,A) -> v3_waybel_1(k1_waybel_1(A,k2_yellow_2(A,A,B),k2_waybel_1(A,A,B),k3_waybel_1(A,A,B)),A,k2_yellow_2(A,A,B))))))) # label(t42_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4256 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(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)) -> k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D)) = k13_lattice3(A,B,k12_lattice3(A,C,D)))))))) <-> v2_waybel_1(A)))) # label(t6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4257 (exists A (l1_orders_2(A) & -v3_struct_0(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) & v9_waybel_1(A) & v2_waybel_1(A) & v2_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) & v1_orders_2(A))) # label(rc5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4258 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> (exists B (v1_relat_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v8_waybel_1(B,A) & v6_waybel_1(B,A) & -v1_xboole_0(B) & v1_funct_1(B) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4259 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v5_orders_3(B,A,A) -> (all C (-v3_struct_0(C) & v2_orders_2(C) & v3_orders_2(C) & l1_orders_2(C) & v4_orders_2(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_1(E) -> -(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) = B & v3_waybel_1(k1_waybel_1(A,C,D,E),A,C)))))))) | v8_waybel_1(B,A)))))) # label(t44_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4260 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> (exists C m1_waybel_1(C,A,B)))) # label(existence_m1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4261 (all A (v2_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (exists B (v1_relat_1(B) & v1_funct_1(B) & -v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & v7_waybel_1(B,A) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4262 $T # label(dt_m1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4263 (all A (v2_orders_2(A) & v3_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> v3_waybel_1(k1_waybel_1(A,k2_yellow_1(k8_waybel_0(A)),k4_yellow_2(A),k3_yellow_2(A)),A,k2_yellow_1(k8_waybel_0(A))) & v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A))) # label(t60_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4264 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v5_orders_3(C,A,B) & r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A)) & v5_orders_3(D,B,A) -> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(t20_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4265 (all A (l1_orders_2(A) & v1_yellow_0(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,C,k7_waybel_1(A,B)) <-> r1_orders_2(A,B,k7_waybel_1(A,C)))))))))) # label(t84_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4266 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v4_waybel_1(C,A,B) -> v17_waybel_0(C,A,B)))))))) # label(t13_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4267 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v5_orders_3(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_0_waybel_1(A,B) = C -> v8_yellow_0(k5_yellow_0(A,C),A))))))))) # label(t52_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4268 (all A (-v3_struct_0(A) & l1_orders_2(A) & v1_yellow_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,k10_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)),k7_waybel_1(A,k11_lattice3(A,B,C)))))))))) # label(t88_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4269 (all A all B (l1_orders_2(B) & l1_orders_2(A) -> r5_waybel_1(A,A))) # label(reflexivity_r5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4270 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) & r1_yellow_2(u1_struct_0(A),A,B,k7_grcat_1(A)) <-> v8_waybel_1(B,A)))))) # label(d15_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4271 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) <-> v5_orders_3(C,A,B) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_orders_2(A,k7_yellow_2(u1_struct_0(B),A,D,E),F) <-> r3_orders_2(B,E,k7_yellow_2(u1_struct_0(A),B,C,F))))))) & v5_orders_3(D,B,A)))))))))) # label(t9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4272 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_waybel_1(A,k4_yellow_0(A),B) = B))))) # label(t77_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4273 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_1_waybel_1(A,B) = C -> (v18_waybel_0(B,A,A) -> v8_yellow_0(k5_yellow_0(A,C),A) & v8_yellow_0(k2_yellow_2(A,A,B),A)) & (v22_waybel_0(B,A,A) -> v4_waybel_0(k5_yellow_0(A,C),A) & v4_waybel_0(k2_yellow_2(A,A,B),A)))))))))) # label(t55_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4274 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,D,E) -> r1_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E))))))) <-> v5_orders_3(C,A,B)))))))) # label(d2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4275 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (r5_waybel_1(A,B) -> r5_waybel_1(B,A)))))) # label(t7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4276 (all A (-v3_struct_0(A) & l1_orders_2(A) -> v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) & v5_orders_3(k7_grcat_1(A),A,A) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(k7_grcat_1(A)))) # label(fc3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4277 (exists A (-v3_struct_0(A) & v1_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & l1_orders_2(A))) # label(rc4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4278 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v11_waybel_1(A) <-> v2_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v10_waybel_1(A) & v2_waybel_1(A) & v3_yellow_0(A) & v4_orders_2(A) & v3_orders_2(A)))) # label(d25_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4279 (all A all B all C all D (v2_orders_2(B) & v3_orders_2(B) & v1_lattice3(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & l1_orders_2(B) & v2_lattice3(B) & v4_orders_2(B) -> (r2_hidden(A,a_3_5_waybel_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k12_lattice3(B,D,E) = A & r2_hidden(E,C)))))) # label(fraenkel_a_3_5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4280 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_lattice3(A) -> (v17_waybel_0(C,A,B) <-> v4_waybel_1(C,A,B) & v5_orders_3(C,A,B))))))))) # label(t17_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4281 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> B = k7_funct_2(u1_struct_0(A),u1_struct_0(k2_yellow_2(A,A,B)),u1_struct_0(A),k2_waybel_1(A,A,B),k3_waybel_1(A,A,B)))))) # label(t35_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4282 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (r2_yellow_0(A,B) & r2_hidden(k2_yellow_0(A,B),B) <-> r1_waybel_1(A,B))))) # label(d4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4283 (all A (v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v4_orders_2(A) & v3_orders_2(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)) -> (r2_yellow_5(A,B,k12_lattice3(A,C,D)) -> r2_yellow_5(A,B,C)))))))))) # label(t29_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4284 (all A (v11_waybel_1(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_yellow_5(A,B,C) = k1_yellow_5(A,B,k12_lattice3(A,B,C)))))))) # label(t52_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4285 (all A (v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(A,C,B) -> k12_lattice3(A,B,C) = C))))))) # label(t10_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4286 (all A (v4_orders_2(A) & v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_yellow_0(A) = k12_lattice3(A,B,k3_yellow_0(A)))))) # label(t28_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4287 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r3_orders_2(A,k7_waybel_1(A,B),k7_waybel_1(A,k12_lattice3(A,B,C))) & r3_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,k12_lattice3(A,B,C))))))))) # label(t44_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4288 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(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)) -> (r3_orders_2(A,B,C) -> r3_orders_2(A,k1_yellow_5(A,D,C),k1_yellow_5(A,D,B))))))))))) # label(t41_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4289 (all A (v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (v2_waybel_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)) -> k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D)) = k13_lattice3(A,B,k12_lattice3(A,C,D))))))))))) # label(t20_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4290 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,B,C) = k1_yellow_5(A,B,k1_yellow_5(A,B,C)))))))) # label(t57_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4291 (all A (v4_orders_2(A) & v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(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)) -> (k12_lattice3(A,C,D) = k3_yellow_0(A) & r3_orders_2(A,B,D) & r3_orders_2(A,B,C) -> B = k3_yellow_0(A)))))))))) # label(t23_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4292 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_yellow_5(A,B,C) = k1_yellow_5(A,k13_lattice3(A,B,C),C))))))) # label(t58_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4293 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_yellow_5(A,B,C),u1_struct_0(A)))) # label(dt_k1_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4294 (all A (l1_orders_2(A) & v11_waybel_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)) -> k13_lattice3(A,B,k1_yellow_5(A,C,B)) = k13_lattice3(A,B,C))))))) # label(t54_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4295 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(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)) -> (r3_orders_2(A,B,D) & r3_orders_2(A,C,D) -> r3_orders_2(A,k13_lattice3(A,B,C),D)))))))))) # label(t9_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4296 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k13_lattice3(A,B,B) = B)))) # label(t1_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4297 (all A (v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r1_yellow_5(A,B,k3_yellow_0(A)))))) # label(t31_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4298 (all A (v11_waybel_1(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_yellow_0(A) = k13_lattice3(A,B,k7_waybel_1(A,B)) & k3_yellow_0(A) = k12_lattice3(A,B,k7_waybel_1(A,B)))))) # label(t37_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4299 (all A all B all C (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v2_lattice3(A) -> k3_yellow_5(A,C,B) = k3_yellow_5(A,B,C))) # label(commutativity_k3_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4300 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_yellow_5(A,B,k1_yellow_5(A,C,D)) = k13_lattice3(A,k1_yellow_5(A,B,C),k12_lattice3(A,B,D)))))))))) # label(t56_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4301 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_yellow_5(A,k3_yellow_0(A),B) = k3_yellow_0(A))))) # label(t26_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4302 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) & k12_lattice3(A,C,D) = k3_yellow_0(A) -> k3_yellow_0(A) = k12_lattice3(A,B,D)))))))))) # label(t25_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4303 (all A all B all C (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v2_lattice3(A) -> k2_yellow_5(A,B,C) = k3_yellow_5(A,B,C))) # label(redefinition_k3_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4304 (all A (v4_orders_2(A) & v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r1_yellow_5(A,B,C) & r1_orders_2(A,C,D) & -r1_yellow_5(A,B,D)))))))))) # label(t32_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4305 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v1_yellow_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_orders_2(A,B,k3_yellow_0(A)) -> B = k3_yellow_0(A)))))) # label(t22_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4306 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_yellow_5(A,B,C) -> B = k1_yellow_5(A,k13_lattice3(A,B,C),C)))))))) # label(t72_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4307 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v3_orders_2(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)) -> k12_lattice3(A,B,k1_yellow_5(A,C,D)) = k1_yellow_5(A,k12_lattice3(A,B,C),D))))))))) # label(t18_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4308 (all A (l1_orders_2(A) & v11_waybel_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)) -> (k3_yellow_0(A) = k12_lattice3(A,B,D) & r3_orders_2(A,B,k13_lattice3(A,C,D)) -> r3_orders_2(A,B,C)))))))))) # label(t49_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4309 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(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)) -> k12_lattice3(A,k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,C,D)),k13_lattice3(A,D,B)) = k13_lattice3(A,k13_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,C,D)),k12_lattice3(A,D,B)))))))))) # label(t36_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4310 (all A (v11_waybel_1(A) & l1_orders_2(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)) -> k13_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,C,B)) = k1_yellow_5(A,k13_lattice3(A,B,C),k12_lattice3(A,B,C)))))))) # label(t63_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4311 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k13_lattice3(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)))))))) # label(t55_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4312 (all A (v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,k1_yellow_5(A,B,C),B))))))) # label(t14_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4313 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_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)) -> k13_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,B,D)) = k1_yellow_5(A,B,k12_lattice3(A,C,D)))))))))) # label(t61_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4314 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) = k7_waybel_1(A,k13_lattice3(A,B,C)) & k13_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) = k7_waybel_1(A,k12_lattice3(A,B,C)))))))) # label(t39_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4315 (all A (v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_yellow_0(A) = k13_lattice3(A,B,C) -> k3_yellow_0(A) = B & C = k3_yellow_0(A)))))))) # label(t24_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4316 (all A (v11_waybel_1(A) & l1_orders_2(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)) -> (r3_orders_2(A,B,C) -> r3_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B))))))))) # label(t40_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4317 (all A (v2_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (v2_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_yellow_5(A,k13_lattice3(A,B,C),D) = k13_lattice3(A,k1_yellow_5(A,B,D),k1_yellow_5(A,C,D))))))))))) # label(t21_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4318 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,B,k7_waybel_1(A,C)) = k1_yellow_5(A,B,C))))))) # label(d1_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4319 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_yellow_5(A,B,B) = k3_yellow_0(A))))) # label(t67_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4320 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D))))))))))) # label(t7_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4321 (all A (v11_waybel_1(A) & l1_orders_2(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)) -> k7_waybel_1(A,k1_yellow_5(A,B,C)) = k13_lattice3(A,k7_waybel_1(A,B),C))))))) # label(t69_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4322 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k12_lattice3(A,B,B))))) # label(t2_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4323 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_yellow_0(A) != k11_lattice3(A,B,C) <-> r1_yellow_5(A,B,C)))))))) # label(d3_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4324 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_yellow_0(A) = k1_yellow_5(A,B,C) <-> r3_orders_2(A,B,C)))))))) # label(t48_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4325 (all A (v11_waybel_1(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_yellow_5(A,k1_yellow_5(A,B,C),D) = k1_yellow_5(A,B,k13_lattice3(A,C,D)))))))))) # label(t64_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4326 (all A all B all C (v2_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v4_orders_2(A) -> (r2_yellow_5(A,B,C) -> r2_yellow_5(A,C,B)))) # label(symmetry_r2_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4327 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_yellow_0(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r1_yellow_5(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D)) & -r1_yellow_5(A,B,C)))))))))) # label(t35_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4328 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r3_orders_2(A,k7_waybel_1(A,k13_lattice3(A,B,C)),k7_waybel_1(A,B)) & r3_orders_2(A,k7_waybel_1(A,k13_lattice3(A,B,C)),k7_waybel_1(A,C)))))))) # label(t45_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4329 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_yellow_5(A,B,k3_yellow_0(A)) = B)))) # label(t68_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4330 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_yellow_0(A) = k1_yellow_5(A,B,k13_lattice3(A,B,C)))))))) # label(t51_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4331 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,k12_lattice3(A,B,C)) -> r1_orders_2(A,D,B)))))))))) # label(t4_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4332 (all A (l1_orders_2(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)) -> k10_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,C,B)) = k2_yellow_5(A,B,C))))))) # label(d2_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4333 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_yellow_5(A,B,C) <-> k3_yellow_0(A) = k12_lattice3(A,B,C)))))))) # label(t59_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4334 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(A,B,C) -> k13_lattice3(A,B,k1_yellow_5(A,C,B)) = C))))))) # label(t47_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4335 (all A (l1_orders_2(A) & v11_waybel_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)) -> k12_lattice3(A,k1_yellow_5(A,B,C),C) = k3_yellow_0(A))))))) # label(t53_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4336 (all A (l1_orders_2(A) & v11_waybel_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)) -> k13_lattice3(A,k1_yellow_5(A,B,C),C) = k13_lattice3(A,B,C))))))) # label(t50_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4337 (all A (v4_orders_2(A) & v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(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)) -> (r2_yellow_5(A,B,C) & r1_orders_2(A,C,D) -> r2_yellow_5(A,B,D)))))))))) # label(t27_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4338 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D))))))))))) # label(t6_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4339 (all A (v2_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(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)) -> (r3_orders_2(A,B,C) & r3_orders_2(A,B,D) -> k3_yellow_0(A) = B | r1_yellow_5(A,C,D)))))))))) # label(t34_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4340 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k1_yellow_5(A,B,D),k1_yellow_5(A,C,D))))))))))) # label(t13_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4341 (all A all B all C (v4_orders_2(A) & v1_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v2_lattice3(A) -> m1_subset_1(k3_yellow_5(A,B,C),u1_struct_0(A)))) # label(dt_k3_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4342 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r1_yellow_5(A,B,k12_lattice3(A,C,D)) & -(r1_yellow_5(A,B,C) & r1_yellow_5(A,B,D))))))))))) # label(t33_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4343 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r1_yellow_5(A,k1_yellow_5(A,B,C),C))))))) # label(t71_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4344 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) -> k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A))) # label(t65_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4345 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_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)) -> (r3_orders_2(A,k1_yellow_5(A,B,C),D) -> r3_orders_2(A,B,k13_lattice3(A,C,D))))))))))) # label(t38_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4346 (all A (v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r2_yellow_5(A,B,B) <-> k3_yellow_0(A) != B))))) # label(t17_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4347 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (v2_waybel_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)) -> (k10_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)) = B -> r1_orders_2(A,B,k10_lattice3(A,C,D)))))))))))) # label(t19_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4348 (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_orders_2(A) -> m1_subset_1(k2_yellow_5(A,B,C),u1_struct_0(A)))) # label(dt_k2_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4349 (all A (v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v2_orders_2(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)) -> (r3_orders_2(A,k1_yellow_5(A,C,B),D) & r3_orders_2(A,k1_yellow_5(A,B,C),D) -> r3_orders_2(A,k3_yellow_5(A,B,C),D)))))))))) # label(t16_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4350 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_yellow_5(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)) = k12_lattice3(A,B,k1_yellow_5(A,C,D)))))))))) # label(t62_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4351 (all A (v11_waybel_1(A) & l1_orders_2(A) & -v3_struct_0(A) -> k3_yellow_0(A) = k7_waybel_1(A,k4_yellow_0(A)))) # label(t66_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4352 (all A (v11_waybel_1(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r1_yellow_5(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)))))))) # label(t70_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4353 (all A (v3_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(A,B,C) -> C = k13_lattice3(A,B,C)))))))) # label(t8_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4354 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(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)) -> k12_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,B,D)) = k1_yellow_5(A,B,k13_lattice3(A,C,D)))))))))) # label(t60_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4355 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_orders_2(A,k12_lattice3(A,B,C),k13_lattice3(A,B,D)))))))))) # label(t5_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4356 (all A (l1_orders_2(A) & v11_waybel_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)) -> (r3_orders_2(A,B,k1_yellow_5(A,C,B)) -> k3_yellow_0(A) = B))))))) # label(t46_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4357 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,D) -> r1_orders_2(A,k1_yellow_5(A,B,C),D)))))))))) # label(t12_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4358 (all A (v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,k13_lattice3(A,B,C),D) -> r1_orders_2(A,B,D)))))))))) # label(t3_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4359 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,k1_yellow_5(A,B,C),k3_yellow_5(A,B,C)))))))) # label(t15_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.18/5.21 4360 (all A (-v3_struct_0(A) & l1_orders_2(A) & v11_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_orders_2(A,D,E) & r3_orders_2(A,B,C) -> r3_orders_2(A,k1_yellow_5(A,B,E),k1_yellow_5(A,C,D))))))))))))) # label(t42_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.94/5.96 4361 (all A all B all C (v2_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v4_orders_2(A) -> (r1_yellow_5(A,B,C) <-> r2_yellow_5(A,B,C)))) # label(redefinition_r2_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.94/5.96 4362 (all A (v2_orders_2(A) & v4_orders_2(A) & v11_waybel_1(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r6_waybel_1(A,B,C) <-> k7_waybel_1(A,B) = C))))))) # label(t11_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.94/5.96 4363 (all A (l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v1_yellow_0(A) & v4_orders_2(A) & v3_orders_2(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)) -> (r2_yellow_5(A,B,k1_yellow_5(A,C,D)) -> r2_yellow_5(A,B,C)))))))))) # label(t30_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.94/5.96 4364 (all A (-v3_struct_0(A) & v11_waybel_1(A) & l1_orders_2(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)) -> (r3_orders_2(A,B,k13_lattice3(A,C,D)) -> r3_orders_2(A,k1_yellow_5(A,B,D),C) & r3_orders_2(A,k1_yellow_5(A,B,C),D)))))))))) # label(t43_yellow_5) # label(axiom) # label(non_clause). [assumption]. 5.94/5.96 4365 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> v1_orders_2(k1_latsum_1(A,B)) & l1_orders_2(k1_latsum_1(A,B)))) # label(dt_k1_latsum_1) # label(axiom) # label(non_clause). [assumption]. 5.94/5.96 4366 -(all A all B all C all D -(r2_hidden(B,k2_xboole_0(C,D)) & -(r2_hidden(B,D) & r2_hidden(A,k4_xboole_0(C,D))) & -(r2_hidden(B,k4_xboole_0(C,D)) & r2_hidden(A,D)) & -(r2_hidden(A,D) & r2_hidden(B,D)) & -(r2_hidden(A,k4_xboole_0(C,D)) & r2_hidden(B,k4_xboole_0(C,D))) & r2_hidden(A,k2_xboole_0(C,D)))) # label(t1_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption]. 5.94/5.96 5.94/5.96 ============================== end of process non-clausal formulas === 5.94/5.96 5.94/5.96 ============================== PROCESS INITIAL CLAUSES =============== 5.94/5.96 5.94/5.96 ============================== PREDICATE ELIMINATION ================= 5.94/5.96 4367 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 4368 -r2_tarski(A,B) | -r2_hidden(C,B) | r2_hidden(f7(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 4369 -r2_tarski(A,B) | -r2_hidden(C,B) | r2_hidden(k4_tarski(f7(A,B,C),C),f6(A,B)) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 4370 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f6(A,B)) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | E != C | F = D # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 4371 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f6(A,B)) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | E = C | F != D # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 4372 -r2_tarski(A,B) | -r2_hidden(C,A) | r2_hidden(f8(A,B,C),B) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 4373 -r2_tarski(A,B) | -r2_hidden(C,A) | r2_hidden(k4_tarski(C,f8(A,B,C)),f6(A,B)) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/5.96 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(f7(A,B,D),A). [resolve(4367,a,4368,a)]. 5.94/5.96 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f7(A,B,D),D),f6(A,B)). [resolve(4367,a,4369,a)]. 5.94/5.96 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F != D | V6 = E. [resolve(4367,a,4370,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F = D | V6 != E. [resolve(4367,a,4371,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(f8(A,B,D),B). [resolve(4367,a,4372,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(k4_tarski(D,f8(A,B,D)),f6(A,B)). [resolve(4367,a,4373,a)]. 5.94/6.00 4374 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(f7(A,B,E),A). [resolve(4374,a,4368,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(k4_tarski(f7(A,B,E),E),f6(A,B)). [resolve(4374,a,4369,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 != E | V7 = F. [resolve(4374,a,4370,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 = E | V7 != F. [resolve(4374,a,4371,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(f8(A,B,E),B). [resolve(4374,a,4372,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(k4_tarski(E,f8(A,B,E)),f6(A,B)). [resolve(4374,a,4373,a)]. 5.94/6.00 4375 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(f7(A,B,D),A). [resolve(4375,a,4368,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f7(A,B,D),D),f6(A,B)). [resolve(4375,a,4369,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F != D | V6 = E. [resolve(4375,a,4370,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F = D | V6 != E. [resolve(4375,a,4371,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(f8(A,B,D),B). [resolve(4375,a,4372,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(k4_tarski(D,f8(A,B,D)),f6(A,B)). [resolve(4375,a,4373,a)]. 5.94/6.00 4376 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(15)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(f7(A,B,E),A). [resolve(4376,a,4368,a)]. 5.94/6.00 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(k4_tarski(f7(A,B,E),E),f6(A,B)). [resolve(4376,a,4369,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 != E | V7 = F. [resolve(4376,a,4370,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 = E | V7 != F. [resolve(4376,a,4371,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(f8(A,B,E),B). [resolve(4376,a,4372,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(k4_tarski(E,f8(A,B,E)),f6(A,B)). [resolve(4376,a,4373,a)]. 6.03/6.04 4377 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(f7(A,B,D),A). [resolve(4377,a,4368,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f7(A,B,D),D),f6(A,B)). [resolve(4377,a,4369,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F != D | V6 = E. [resolve(4377,a,4370,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F = D | V6 != E. [resolve(4377,a,4371,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(f8(A,B,D),B). [resolve(4377,a,4372,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(k4_tarski(D,f8(A,B,D)),f6(A,B)). [resolve(4377,a,4373,a)]. 6.03/6.04 4378 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(f7(A,B,E),A). [resolve(4378,a,4368,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(k4_tarski(f7(A,B,E),E),f6(A,B)). [resolve(4378,a,4369,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 != E | V7 = F. [resolve(4378,a,4370,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 = E | V7 != F. [resolve(4378,a,4371,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(f8(A,B,E),B). [resolve(4378,a,4372,a)]. 6.03/6.04 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(k4_tarski(E,f8(A,B,E)),f6(A,B)). [resolve(4378,a,4373,a)]. 6.03/6.08 4379 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(f7(A,B,D),A). [resolve(4379,a,4368,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,B) | r2_hidden(k4_tarski(f7(A,B,D),D),f6(A,B)). [resolve(4379,a,4369,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F != D | V6 = E. [resolve(4379,a,4370,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f6(A,B)) | -r2_hidden(k4_tarski(F,V6),f6(A,B)) | F = D | V6 != E. [resolve(4379,a,4371,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(f8(A,B,D),B). [resolve(4379,a,4372,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A) | -r2_hidden(D,A) | r2_hidden(k4_tarski(D,f8(A,B,D)),f6(A,B)). [resolve(4379,a,4373,a)]. 6.03/6.08 4380 r2_tarski(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(f7(A,B,E),A). [resolve(4380,a,4368,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,B) | r2_hidden(k4_tarski(f7(A,B,E),E),f6(A,B)). [resolve(4380,a,4369,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 != E | V7 = F. [resolve(4380,a,4370,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | -r2_hidden(k4_tarski(V6,V7),f6(A,B)) | V6 = E | V7 != F. [resolve(4380,a,4371,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(f8(A,B,E),B). [resolve(4380,a,4372,a)]. 6.03/6.08 Derived: r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C) | -r2_hidden(E,A) | r2_hidden(k4_tarski(E,f8(A,B,E)),f6(A,B)). [resolve(4380,a,4373,a)]. 6.03/6.08 4381 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f10(A,B,D),f11(A,B,D)),D) | r2_hidden(f14(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.03/6.08 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(f7(B,C,E),B). [resolve(4381,a,4368,a)]. 6.03/6.08 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f7(B,C,E),E),f6(B,C)). [resolve(4381,a,4369,a)]. 6.03/6.08 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 != E | V7 = F. [resolve(4381,a,4370,a)]. 6.03/6.08 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 = E | V7 != F. [resolve(4381,a,4371,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(f8(B,C,E),C). [resolve(4381,a,4372,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(k4_tarski(E,f8(B,C,E)),f6(B,C)). [resolve(4381,a,4373,a)]. 6.11/6.11 4382 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f10(A,B,D),f11(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(f7(B,C,F),B). [resolve(4382,a,4368,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(k4_tarski(f7(B,C,F),F),f6(B,C)). [resolve(4382,a,4369,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 != F | V8 = V6. [resolve(4382,a,4370,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 = F | V8 != V6. [resolve(4382,a,4371,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(f8(B,C,F),C). [resolve(4382,a,4372,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f10(B,C,D),f11(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(k4_tarski(F,f8(B,C,F)),f6(B,C)). [resolve(4382,a,4373,a)]. 6.11/6.11 4383 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f12(A,B,D),f13(A,B,D)),D) | r2_hidden(f14(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(f7(B,C,E),B). [resolve(4383,a,4368,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f7(B,C,E),E),f6(B,C)). [resolve(4383,a,4369,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 != E | V7 = F. [resolve(4383,a,4370,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 = E | V7 != F. [resolve(4383,a,4371,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(f8(B,C,E),C). [resolve(4383,a,4372,a)]. 6.11/6.11 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(k4_tarski(E,f8(B,C,E)),f6(B,C)). [resolve(4383,a,4373,a)]. 6.11/6.11 4384 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f12(A,B,D),f13(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(f7(B,C,F),B). [resolve(4384,a,4368,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(k4_tarski(f7(B,C,F),F),f6(B,C)). [resolve(4384,a,4369,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 != F | V8 = V6. [resolve(4384,a,4370,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 = F | V8 != V6. [resolve(4384,a,4371,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(f8(B,C,F),C). [resolve(4384,a,4372,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | r2_hidden(k4_tarski(f12(B,C,D),f13(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(k4_tarski(F,f8(B,C,F)),f6(B,C)). [resolve(4384,a,4373,a)]. 6.11/6.14 4385 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) = f10(A,B,D) | f13(A,B,D) = f11(A,B,D) | r2_hidden(f14(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(f7(B,C,E),B). [resolve(4385,a,4368,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f7(B,C,E),E),f6(B,C)). [resolve(4385,a,4369,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 != E | V7 = F. [resolve(4385,a,4370,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 = E | V7 != F. [resolve(4385,a,4371,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(f8(B,C,E),C). [resolve(4385,a,4372,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(k4_tarski(E,f8(B,C,E)),f6(B,C)). [resolve(4385,a,4373,a)]. 6.11/6.14 4386 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) = f10(A,B,D) | f13(A,B,D) = f11(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(f7(B,C,F),B). [resolve(4386,a,4368,a)]. 6.11/6.14 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(k4_tarski(f7(B,C,F),F),f6(B,C)). [resolve(4386,a,4369,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 != F | V8 = V6. [resolve(4386,a,4370,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 = F | V8 != V6. [resolve(4386,a,4371,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(f8(B,C,F),C). [resolve(4386,a,4372,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) = f10(B,C,D) | f13(B,C,D) = f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(k4_tarski(F,f8(B,C,F)),f6(B,C)). [resolve(4386,a,4373,a)]. 6.11/6.17 4387 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) != f10(A,B,D) | f13(A,B,D) != f11(A,B,D) | r2_hidden(f14(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(f7(B,C,E),B). [resolve(4387,a,4368,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,C) | r2_hidden(k4_tarski(f7(B,C,E),E),f6(B,C)). [resolve(4387,a,4369,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 != E | V7 = F. [resolve(4387,a,4370,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f6(B,C)) | -r2_hidden(k4_tarski(V6,V7),f6(B,C)) | V6 = E | V7 != F. [resolve(4387,a,4371,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(f8(B,C,E),C). [resolve(4387,a,4372,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | r2_hidden(f14(B,C,D),B) | -r2_hidden(E,B) | r2_hidden(k4_tarski(E,f8(B,C,E)),f6(B,C)). [resolve(4387,a,4373,a)]. 6.11/6.17 4388 r2_tarski(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) != f10(A,B,D) | f13(A,B,D) != f11(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(15)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(f7(B,C,F),B). [resolve(4388,a,4368,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,C) | r2_hidden(k4_tarski(f7(B,C,F),F),f6(B,C)). [resolve(4388,a,4369,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 != F | V8 = V6. [resolve(4388,a,4370,a)]. 6.11/6.17 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f6(B,C)) | -r2_hidden(k4_tarski(V7,V8),f6(B,C)) | V7 = F | V8 != V6. [resolve(4388,a,4371,a)]. 6.41/6.42 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(f8(B,C,F),C). [resolve(4388,a,4372,a)]. 6.41/6.42 Derived: -r2_hidden(A,B) | -r2_hidden(k4_tarski(A,f9(B,C,D)),D) | f12(B,C,D) != f10(B,C,D) | f13(B,C,D) != f11(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f14(B,C,D),E),D) | -r2_hidden(F,B) | r2_hidden(k4_tarski(F,f8(B,C,F)),f6(B,C)). [resolve(4388,a,4373,a)]. 6.41/6.42 4389 -r1_tarski(A,f18(B)) | r2_tarski(A,f18(B)) | r2_hidden(A,f18(B)) # label(t9_tarski) # label(axiom). [clausify(21)]. 6.41/6.42 Derived: -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)) | -r2_hidden(C,f18(B)) | r2_hidden(f7(A,f18(B),C),A). [resolve(4389,b,4368,a)]. 6.41/6.42 Derived: -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)) | -r2_hidden(C,f18(B)) | r2_hidden(k4_tarski(f7(A,f18(B),C),C),f6(A,f18(B))). [resolve(4389,b,4369,a)]. 6.41/6.42 Derived: -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)) | -r2_hidden(k4_tarski(C,D),f6(A,f18(B))) | -r2_hidden(k4_tarski(E,F),f6(A,f18(B))) | E != C | F = D. [resolve(4389,b,4370,a)]. 6.41/6.42 Derived: -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)) | -r2_hidden(k4_tarski(C,D),f6(A,f18(B))) | -r2_hidden(k4_tarski(E,F),f6(A,f18(B))) | E = C | F != D. [resolve(4389,b,4371,a)]. 6.41/6.42 Derived: -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)) | -r2_hidden(C,A) | r2_hidden(f8(A,f18(B),C),f18(B)). [resolve(4389,b,4372,a)]. 6.41/6.42 Derived: -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)) | -r2_hidden(C,A) | r2_hidden(k4_tarski(C,f8(A,f18(B),C)),f6(A,f18(B))). [resolve(4389,b,4373,a)]. 6.41/6.42 4390 -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | r2_tarski(A,f36(B)) # label(t136_zfmisc_1) # label(axiom). [clausify(211)]. 6.41/6.42 Derived: -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | -r2_hidden(C,f36(B)) | r2_hidden(f7(A,f36(B),C),A). [resolve(4390,c,4368,a)]. 6.41/6.42 Derived: -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | -r2_hidden(C,f36(B)) | r2_hidden(k4_tarski(f7(A,f36(B),C),C),f6(A,f36(B))). [resolve(4390,c,4369,a)]. 6.41/6.42 Derived: -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | -r2_hidden(k4_tarski(C,D),f6(A,f36(B))) | -r2_hidden(k4_tarski(E,F),f6(A,f36(B))) | E != C | F = D. [resolve(4390,c,4370,a)]. 6.41/6.42 Derived: -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | -r2_hidden(k4_tarski(C,D),f6(A,f36(B))) | -r2_hidden(k4_tarski(E,F),f6(A,f36(B))) | E = C | F != D. [resolve(4390,c,4371,a)]. 6.41/6.42 Derived: -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | -r2_hidden(C,A) | r2_hidden(f8(A,f36(B),C),f36(B)). [resolve(4390,c,4372,a)]. 6.41/6.42 Derived: -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)) | -r2_hidden(C,A) | r2_hidden(k4_tarski(C,f8(A,f36(B),C)),f6(A,f36(B))). [resolve(4390,c,4373,a)]. 6.41/6.42 4391 -r2_tarski(A,B) | r2_wellord2(A,B) # label(redefinition_r2_wellord2) # label(axiom). [clausify(1326)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | r2_hidden(f14(A,B,C),A). [resolve(4391,a,4367,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f10(A,B,C),f11(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C). [resolve(4391,a,4374,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | r2_hidden(f14(A,B,C),A). [resolve(4391,a,4375,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | r2_hidden(k4_tarski(f12(A,B,C),f13(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C). [resolve(4391,a,4376,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | r2_hidden(f14(A,B,C),A). [resolve(4391,a,4377,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) = f10(A,B,C) | f13(A,B,C) = f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C). [resolve(4391,a,4378,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | r2_hidden(f14(A,B,C),A). [resolve(4391,a,4379,a)]. 6.41/6.42 Derived: r2_wellord2(A,B) | r2_hidden(f9(A,B,C),B) | f12(A,B,C) != f10(A,B,C) | f13(A,B,C) != f11(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f14(A,B,C),D),C). [resolve(4391,a,4380,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f10(A,B,D),f11(A,B,D)),D) | r2_hidden(f14(A,B,D),A). [resolve(4391,a,4381,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f10(A,B,D),f11(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D). [resolve(4391,a,4382,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f12(A,B,D),f13(A,B,D)),D) | r2_hidden(f14(A,B,D),A). [resolve(4391,a,4383,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | r2_hidden(k4_tarski(f12(A,B,D),f13(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D). [resolve(4391,a,4384,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) = f10(A,B,D) | f13(A,B,D) = f11(A,B,D) | r2_hidden(f14(A,B,D),A). [resolve(4391,a,4385,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) = f10(A,B,D) | f13(A,B,D) = f11(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D). [resolve(4391,a,4386,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) != f10(A,B,D) | f13(A,B,D) != f11(A,B,D) | r2_hidden(f14(A,B,D),A). [resolve(4391,a,4387,a)]. 124.76/124.79 Derived: r2_wellord2(A,B) | -r2_hidden(C,A) | -r2_hidden(k4_tarski(C,f9(A,B,D)),D) | f12(A,B,D) != f10(A,B,D) | f13(A,B,D) != f11(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f14(A,B,D),E),D). [resolve(4391,a,4388,a)]. 124.76/124.79 Derived: r2_wellord2(A,f18(B)) | -r1_tarski(A,f18(B)) | r2_hidden(A,f18(B)). [resolve(4391,a,4389,b)]. 124.76/124.79 Derived: r2_wellord2(A,f36(B)) | -r1_tarski(A,f36(B)) | r2_hidden(A,f36(B)). [resolve(4391,a,4390,c)]. 124.76/124.79 4392 r2_tarski(A,B) | -r2_wellord2(A,B) # label(redefinition_r2_wellord2) # label(axiom). [clausify(1326)]. 124.76/124.79 Derived: -r2_wellord2(A,B) | -r2_hidden(C,B) | r2_hidden(f7(A,B,C),A). [resolve(4392,a,4368,a)]. 124.76/124.79 Derived: -r2_wellord2(A,B) | -r2_hidden(C,B) | r2_hidden(k4_tarski(f7(A,B,C),C),f6(A,B)). [resolve(4392,a,4369,a)]. 124.76/124.79 Derived: -r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,D),f6(A,B)) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | E != C | F = D. [resolve(4392,a,4370,a)]. 124.76/124.79 Derived: -r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,D),f6(A,B)) | -r2_hidden(k4_tarski(E,F),f6(A,B)) | E = C | F != D. [resolve(4392,a,4371,a)]. 124.76/124.79 Derived: -r2_wellord2(A,B) | -r2_hidden(C,A) | r2_hidden(f8(A,B,C),B). [resolve(4392,a,4372,a)]. 124.76/124.79 Derived: -r2_wellord2(A,B) | -r2_hidden(C,A) | r2_hidden(k4_tarski(C,f8(A,B,C)),f6(A,B)). [resolve(4392,a,4373,a)]. 124.76/124.79 4393 r2_hidden(A,c8) | -r2_hidden(A,f1_s1_xboole_0) | -p1_s1_xboole_0(A) # label(s1_xboole_0) # label(axiom). [clausify(52)]. 124.76/124.79 4394 -r2_hidden(A,c8) | p1_s1_xboole_0(A) # label(s1_xboole_0) # label(axiom). [clausify(52)]. 124.76/124.79 4395 r2_hidden(A,c12) | -r2_hidden(A,f1_s1_subset_1) | -p1_s1_subset_1(A) # label(s1_subset_1) # label(axiom). [clausify(365)]. 124.76/124.79 4396 -r2_hidden(A,c12) | p1_s1_subset_1(A) # label(s1_subset_1) # label(axiom). [clausify(365)]. 124.76/124.79 4397 -m1_subset_1(A,f1_s3_subset_1) | r2_hidden(A,c13) | -p1_s3_subset_1(A) # label(s3_subset_1) # label(axiom). [clausify(406)]. 124.76/124.79 4398 -m1_subset_1(A,f1_s3_subset_1) | -r2_hidden(A,c13) | p1_s3_subset_1(A) # label(s3_subset_1) # label(axiom). [clausify(406)]. 124.76/124.79 4399 p1_s1_relat_1(A,B) | -r2_hidden(k4_tarski(A,B),c17) # label(s1_relat_1) # label(axiom). [clausify(521)]. 124.76/124.79 4400 -r2_hidden(A,f1_s1_relat_1) | -r2_hidden(B,f2_s1_relat_1) | -p1_s1_relat_1(A,B) | r2_hidden(k4_tarski(A,B),c17) # label(s1_relat_1) # label(axiom). [clausify(521)]. 124.76/124.79 4401 -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) = k2_xboole_0(A,k4_relat_1(A)) | -v7_relat_2(A) # label(t47_relat_2) # label(axiom). [clausify(875)]. 124.76/124.79 4402 -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)) | v7_relat_2(A) # label(t47_relat_2) # label(axiom). [clausify(875)]. 124.76/124.79 4403 -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | v7_relat_2(A) # label(d15_relat_2) # label(axiom). [clausify(877)]. 146.17/146.20 Derived: -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) = k2_xboole_0(A,k4_relat_1(A)). [resolve(4403,c,4401,c)]. 146.17/146.20 4404 -v1_relat_1(A) | r7_relat_2(A,k3_relat_1(A)) | -v7_relat_2(A) # label(d15_relat_2) # label(axiom). [clausify(877)]. 146.17/146.20 Derived: -v1_relat_1(A) | r7_relat_2(A,k3_relat_1(A)) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)). [resolve(4404,c,4402,c)]. 146.17/146.20 4405 -v1_relat_1(A) | -v7_relat_2(A) | v6_relat_2(A) # label(t46_relat_2) # label(axiom). [clausify(918)]. 146.17/146.20 Derived: -v1_relat_1(A) | v6_relat_2(A) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)). [resolve(4405,b,4402,c)]. 146.17/146.20 Derived: -v1_relat_1(A) | v6_relat_2(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)). [resolve(4405,b,4403,c)]. 146.17/146.20 4406 -v1_relat_1(A) | -v7_relat_2(A) | v1_relat_2(A) # label(t46_relat_2) # label(axiom). [clausify(918)]. 146.17/146.20 Derived: -v1_relat_1(A) | v1_relat_2(A) | -v1_relat_1(A) | k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)) != k2_xboole_0(A,k4_relat_1(A)). [resolve(4406,b,4402,c)]. 146.17/146.20 Derived: -v1_relat_1(A) | v1_relat_2(A) | -v1_relat_1(A) | -r7_relat_2(A,k3_relat_1(A)). [resolve(4406,b,4403,c)]. 146.17/146.20 4407 -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | -v2_ordinal1(B) # label(d3_ordinal1) # label(axiom). [clausify(950)]. 146.17/146.20 4408 v2_ordinal1(c35) # label(rc1_ordinal1) # label(axiom). [clausify(940)]. 146.17/146.20 4409 v2_ordinal1(c36) # label(rc2_ordinal1) # label(axiom). [clausify(943)]. 146.17/146.20 4410 -v1_funct_1(A) | -v5_ordinal1(A) | -v1_relat_1(A) | v2_ordinal1(k1_relat_1(A)) # label(fc5_ordinal1) # label(axiom). [clausify(947)]. 146.17/146.20 4411 -v3_ordinal1(A) | v2_ordinal1(k1_ordinal1(A)) # label(fc3_ordinal1) # label(axiom). [clausify(948)]. 146.17/146.20 4412 r2_hidden(f188(A),A) | v2_ordinal1(A) # label(d3_ordinal1) # label(axiom). [clausify(950)]. 146.17/146.20 4413 r2_hidden(f189(A),A) | v2_ordinal1(A) # label(d3_ordinal1) # label(axiom). [clausify(950)]. 146.17/146.20 4414 -r2_hidden(f188(A),f189(A)) | v2_ordinal1(A) # label(d3_ordinal1) # label(axiom). [clausify(950)]. 146.17/146.20 4415 -r2_hidden(f189(A),f188(A)) | v2_ordinal1(A) # label(d3_ordinal1) # label(axiom). [clausify(950)]. 146.17/146.20 4416 f189(A) != f188(A) | v2_ordinal1(A) # label(d3_ordinal1) # label(axiom). [clausify(950)]. 146.17/146.20 Derived: -r2_hidden(A,c35) | -r2_hidden(B,c35) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4407,f,4408,a)]. 146.17/146.20 Derived: -r2_hidden(A,c36) | -r2_hidden(B,c36) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4407,f,4409,a)]. 146.17/146.20 Derived: -r2_hidden(A,k1_relat_1(B)) | -r2_hidden(C,k1_relat_1(B)) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | -v1_funct_1(B) | -v5_ordinal1(B) | -v1_relat_1(B). [resolve(4407,f,4410,d)]. 146.17/146.20 Derived: -r2_hidden(A,k1_ordinal1(B)) | -r2_hidden(C,k1_ordinal1(B)) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | -v3_ordinal1(B). [resolve(4407,f,4411,b)]. 146.17/146.20 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | r2_hidden(f188(B),B). [resolve(4407,f,4412,b)]. 146.17/146.20 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | r2_hidden(f189(B),B). [resolve(4407,f,4413,b)]. 146.17/146.20 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | -r2_hidden(f188(B),f189(B)). [resolve(4407,f,4414,b)]. 146.17/146.20 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | -r2_hidden(f189(B),f188(B)). [resolve(4407,f,4415,b)]. 146.17/146.20 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | r2_hidden(C,A) | C = A | f189(B) != f188(B). [resolve(4407,f,4416,b)]. 146.17/146.20 4417 v2_ordinal1(c37) # label(rc3_ordinal1) # label(axiom). [clausify(951)]. 146.17/146.20 Derived: -r2_hidden(A,c37) | -r2_hidden(B,c37) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4417,a,4407,f)]. 146.17/146.20 4418 -v1_ordinal1(A) | -v2_ordinal1(A) | v3_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(953)]. 146.17/146.20 Derived: -v1_ordinal1(c35) | v3_ordinal1(c35). [resolve(4418,b,4408,a)]. 146.17/146.20 Derived: -v1_ordinal1(c36) | v3_ordinal1(c36). [resolve(4418,b,4409,a)]. 150.67/150.69 Derived: -v1_ordinal1(A) | v3_ordinal1(A) | r2_hidden(f188(A),A). [resolve(4418,b,4412,b)]. 150.67/150.69 Derived: -v1_ordinal1(A) | v3_ordinal1(A) | r2_hidden(f189(A),A). [resolve(4418,b,4413,b)]. 150.67/150.69 Derived: -v1_ordinal1(A) | v3_ordinal1(A) | -r2_hidden(f188(A),f189(A)). [resolve(4418,b,4414,b)]. 150.67/150.69 Derived: -v1_ordinal1(A) | v3_ordinal1(A) | -r2_hidden(f189(A),f188(A)). [resolve(4418,b,4415,b)]. 150.67/150.69 Derived: -v1_ordinal1(A) | v3_ordinal1(A) | f189(A) != f188(A). [resolve(4418,b,4416,b)]. 150.67/150.69 Derived: -v1_ordinal1(c37) | v3_ordinal1(c37). [resolve(4418,b,4417,a)]. 150.67/150.69 4419 v2_ordinal1(A) | -v3_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(953)]. 150.67/150.69 Derived: -v3_ordinal1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4419,a,4407,f)]. 150.67/150.69 4420 -v1_ordinal1(A) | -v2_ordinal1(A) | v3_ordinal1(A) # label(cc2_ordinal1) # label(axiom). [clausify(958)]. 150.67/150.69 4421 -v3_ordinal1(A) | v2_ordinal1(A) # label(cc1_ordinal1) # label(axiom). [clausify(961)]. 150.67/150.69 4422 v2_ordinal1(k1_xboole_0) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 150.67/150.69 Derived: -r2_hidden(A,k1_xboole_0) | -r2_hidden(B,k1_xboole_0) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4422,a,4407,f)]. 150.67/150.69 4423 -v3_ordinal1(A) | v2_ordinal1(k3_tarski(A)) # label(fc4_ordinal1) # label(axiom). [clausify(977)]. 150.67/150.69 Derived: -v3_ordinal1(A) | -r2_hidden(B,k3_tarski(A)) | -r2_hidden(C,k3_tarski(A)) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4423,b,4407,f)]. 150.67/150.69 4424 -v1_xboole_0(A) | v2_ordinal1(A) # label(cc3_ordinal1) # label(axiom). [clausify(1008)]. 150.67/150.69 Derived: -v1_xboole_0(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4424,b,4407,f)]. 150.67/150.69 4425 -v1_ordinal2(A) | -v3_ordinal1(B) | -v5_ordinal1(A) | -v1_funct_1(A) | -v1_relat_1(A) | v2_ordinal1(k1_funct_1(A,B)) # label(fc3_ordinal2) # label(axiom). [clausify(1792)]. 150.67/150.69 Derived: -v1_ordinal2(A) | -v3_ordinal1(B) | -v5_ordinal1(A) | -v1_funct_1(A) | -v1_relat_1(A) | -r2_hidden(C,k1_funct_1(A,B)) | -r2_hidden(D,k1_funct_1(A,B)) | r2_hidden(C,D) | r2_hidden(D,C) | D = C. [resolve(4425,f,4407,f)]. 150.67/150.69 4426 v2_ordinal1(c121) # label(rc1_ordinal2) # label(axiom). [clausify(1829)]. 150.67/150.69 Derived: -r2_hidden(A,c121) | -r2_hidden(B,c121) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4426,a,4407,f)]. 150.67/150.69 Derived: -v1_ordinal1(c121) | v3_ordinal1(c121). [resolve(4426,a,4418,b)]. 150.67/150.69 4427 v2_ordinal1(k5_ordinal2) # label(fc1_ordinal2_AndLHS) # label(axiom). [assumption]. 150.67/150.69 Derived: -r2_hidden(A,k5_ordinal2) | -r2_hidden(B,k5_ordinal2) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4427,a,4407,f)]. 150.67/150.69 4428 v2_ordinal1(f393(A)) # label(rc2_finset_1) # label(axiom). [clausify(1920)]. 150.67/150.69 Derived: -r2_hidden(A,f393(B)) | -r2_hidden(C,f393(B)) | r2_hidden(A,C) | r2_hidden(C,A) | C = A. [resolve(4428,a,4407,f)]. 150.67/150.69 4429 -m1_subset_1(A,k5_numbers) | v2_ordinal1(A) # label(cc2_card_1) # label(axiom). [clausify(1974)]. 150.67/150.69 Derived: -m1_subset_1(A,k5_numbers) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4429,b,4407,f)]. 150.67/150.69 4430 -v1_card_1(A) | v2_ordinal1(A) # label(cc1_card_1) # label(axiom). [clausify(1997)]. 150.67/150.69 Derived: -v1_card_1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4430,b,4407,f)]. 150.67/150.69 Derived: -v1_card_1(A) | -v1_ordinal1(A) | v3_ordinal1(A). [resolve(4430,b,4418,b)]. 150.67/150.69 4431 -m1_subset_1(A,k5_numbers) | v2_ordinal1(A) # label(cc3_card_1) # label(axiom). [clausify(2004)]. 150.67/150.69 4432 -v3_ordinal1(A) | v2_ordinal1(k3_card_1(A)) # label(fc1_card_1) # label(axiom). [clausify(2005)]. 150.67/150.69 Derived: -v3_ordinal1(A) | -r2_hidden(B,k3_card_1(A)) | -r2_hidden(C,k3_card_1(A)) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4432,b,4407,f)]. 150.67/150.69 4433 v2_ordinal1(c157) # label(rc2_card_1) # label(axiom). [clausify(2007)]. 150.67/150.69 Derived: -r2_hidden(A,c157) | -r2_hidden(B,c157) | r2_hidden(A,B) | r2_hidden(B,A) | B = A. [resolve(4433,a,4407,f)]. 150.67/150.69 Derived: -v1_ordinal1(c157) | v3_ordinal1(c157). [resolve(4433,a,4418,b)]. 150.67/150.69 4434 -v1_finset_1(A) | v2_ordinal1(k1_card_1(A)) # label(fc2_card_1) # label(axiom). [clausify(2034)]. 167.48/167.53 Derived: -v1_finset_1(A) | -r2_hidden(B,k1_card_1(A)) | -r2_hidden(C,k1_card_1(A)) | r2_hidden(B,C) | r2_hidden(C,B) | C = B. [resolve(4434,b,4407,f)]. 167.48/167.53 Derived: -v1_finset_1(A) | -v1_ordinal1(k1_card_1(A)) | v3_ordinal1(k1_card_1(A)). [resolve(4434,b,4418,b)]. 167.48/167.53 4435 r2_hidden(f196(A),A) | v6_ordinal1(A) # label(d9_ordinal1) # label(axiom). [clausify(987)]. 167.48/167.53 4436 r2_hidden(f187(A),A) | -v6_ordinal1(A) | v1_relat_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(946)]. 167.48/167.53 4437 r2_hidden(f187(A),A) | -v6_ordinal1(A) | v1_funct_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(946)]. 167.48/167.53 4438 r2_hidden(f187(A),A) | -v6_ordinal1(A) | v5_ordinal1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(946)]. 167.48/167.53 4439 -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | -v6_ordinal1(A) | v1_relat_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(946)]. 167.48/167.53 4440 -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | -v6_ordinal1(A) | v1_funct_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(946)]. 167.48/167.53 4441 -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | -v6_ordinal1(A) | v5_ordinal1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(946)]. 167.48/167.53 Derived: r2_hidden(f196(A),A) | r2_hidden(f187(A),A) | v1_relat_1(k3_tarski(A)). [resolve(4435,b,4436,b)]. 167.48/167.53 Derived: r2_hidden(f196(A),A) | r2_hidden(f187(A),A) | v1_funct_1(k3_tarski(A)). [resolve(4435,b,4437,b)]. 167.48/167.53 Derived: r2_hidden(f196(A),A) | r2_hidden(f187(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(4435,b,4438,b)]. 167.48/167.53 Derived: r2_hidden(f196(A),A) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v1_relat_1(k3_tarski(A)). [resolve(4435,b,4439,d)]. 167.48/167.53 Derived: r2_hidden(f196(A),A) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v1_funct_1(k3_tarski(A)). [resolve(4435,b,4440,d)]. 167.48/167.53 Derived: r2_hidden(f196(A),A) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v5_ordinal1(k3_tarski(A)). [resolve(4435,b,4441,d)]. 167.48/167.53 4442 r2_hidden(f197(A),A) | v6_ordinal1(A) # label(d9_ordinal1) # label(axiom). [clausify(987)]. 167.48/167.53 Derived: r2_hidden(f197(A),A) | r2_hidden(f187(A),A) | v1_relat_1(k3_tarski(A)). [resolve(4442,b,4436,b)]. 167.48/167.53 Derived: r2_hidden(f197(A),A) | r2_hidden(f187(A),A) | v1_funct_1(k3_tarski(A)). [resolve(4442,b,4437,b)]. 167.48/167.53 Derived: r2_hidden(f197(A),A) | r2_hidden(f187(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(4442,b,4438,b)]. 167.48/167.53 Derived: r2_hidden(f197(A),A) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v1_relat_1(k3_tarski(A)). [resolve(4442,b,4439,d)]. 167.48/167.53 Derived: r2_hidden(f197(A),A) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v1_funct_1(k3_tarski(A)). [resolve(4442,b,4440,d)]. 167.48/167.53 Derived: r2_hidden(f197(A),A) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v5_ordinal1(k3_tarski(A)). [resolve(4442,b,4441,d)]. 167.48/167.53 4443 -r3_xboole_0(f196(A),f197(A)) | v6_ordinal1(A) # label(d9_ordinal1) # label(axiom). [clausify(987)]. 167.48/167.53 Derived: -r3_xboole_0(f196(A),f197(A)) | r2_hidden(f187(A),A) | v1_relat_1(k3_tarski(A)). [resolve(4443,b,4436,b)]. 167.48/167.53 Derived: -r3_xboole_0(f196(A),f197(A)) | r2_hidden(f187(A),A) | v1_funct_1(k3_tarski(A)). [resolve(4443,b,4437,b)]. 167.48/167.53 Derived: -r3_xboole_0(f196(A),f197(A)) | r2_hidden(f187(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(4443,b,4438,b)]. 167.48/167.53 Derived: -r3_xboole_0(f196(A),f197(A)) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v1_relat_1(k3_tarski(A)). [resolve(4443,b,4439,d)]. 167.48/167.53 Derived: -r3_xboole_0(f196(A),f197(A)) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v1_funct_1(k3_tarski(A)). [resolve(4443,b,4440,d)]. 167.48/167.53 Derived: -r3_xboole_0(f196(A),f197(A)) | -v1_funct_1(f187(A)) | -v5_ordinal1(f187(A)) | -v1_relat_1(f187(A)) | v5_ordinal1(k3_tarski(A)). [resolve(4443,b,4441,d)]. 167.48/167.53 4444 -r2_hidden(A,B) | -r2_hidden(C,B) | r3_xboole_0(A,C) | -v6_ordinal1(B) # label(d9_ordinal1) # label(axiom). [clausify(987)]. 167.48/167.53 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r3_xboole_0(A,C) | r2_hidden(f196(B),B). [resolve(4444,d,4435,b)]. 172.03/172.06 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r3_xboole_0(A,C) | r2_hidden(f197(B),B). [resolve(4444,d,4442,b)]. 172.03/172.06 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r3_xboole_0(A,C) | -r3_xboole_0(f196(B),f197(B)). [resolve(4444,d,4443,b)]. 172.03/172.06 4445 -r2_hidden(A,B) | r1_tarski(f394(B),A) | -v6_ordinal1(B) | k1_xboole_0 = B | -v1_finset_1(B) # label(t30_finset_1) # label(axiom). [clausify(1923)]. 172.03/172.06 Derived: -r2_hidden(A,B) | r1_tarski(f394(B),A) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f196(B),B). [resolve(4445,c,4435,b)]. 172.03/172.06 Derived: -r2_hidden(A,B) | r1_tarski(f394(B),A) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f197(B),B). [resolve(4445,c,4442,b)]. 172.03/172.06 Derived: -r2_hidden(A,B) | r1_tarski(f394(B),A) | k1_xboole_0 = B | -v1_finset_1(B) | -r3_xboole_0(f196(B),f197(B)). [resolve(4445,c,4443,b)]. 172.03/172.06 4446 r2_hidden(f394(A),A) | -v6_ordinal1(A) | k1_xboole_0 = A | -v1_finset_1(A) # label(t30_finset_1) # label(axiom). [clausify(1923)]. 172.03/172.06 Derived: r2_hidden(f394(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f196(A),A). [resolve(4446,b,4435,b)]. 172.03/172.06 Derived: r2_hidden(f394(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f197(A),A). [resolve(4446,b,4442,b)]. 172.03/172.06 Derived: r2_hidden(f394(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | -r3_xboole_0(f196(A),f197(A)). [resolve(4446,b,4443,b)]. 172.03/172.06 4447 r2_hidden(f396(A),A) | -v6_ordinal1(A) | k1_xboole_0 = A | -v1_finset_1(A) # label(t31_finset_1) # label(axiom). [clausify(1941)]. 172.03/172.06 Derived: r2_hidden(f396(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f196(A),A). [resolve(4447,b,4435,b)]. 172.03/172.06 Derived: r2_hidden(f396(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | r2_hidden(f197(A),A). [resolve(4447,b,4442,b)]. 172.03/172.06 Derived: r2_hidden(f396(A),A) | k1_xboole_0 = A | -v1_finset_1(A) | -r3_xboole_0(f196(A),f197(A)). [resolve(4447,b,4443,b)]. 172.03/172.06 4448 -r2_hidden(A,B) | r1_tarski(A,f396(B)) | -v6_ordinal1(B) | k1_xboole_0 = B | -v1_finset_1(B) # label(t31_finset_1) # label(axiom). [clausify(1941)]. 172.03/172.06 Derived: -r2_hidden(A,B) | r1_tarski(A,f396(B)) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f196(B),B). [resolve(4448,c,4435,b)]. 172.03/172.06 Derived: -r2_hidden(A,B) | r1_tarski(A,f396(B)) | k1_xboole_0 = B | -v1_finset_1(B) | r2_hidden(f197(B),B). [resolve(4448,c,4442,b)]. 172.03/172.06 Derived: -r2_hidden(A,B) | r1_tarski(A,f396(B)) | k1_xboole_0 = B | -v1_finset_1(B) | -r3_xboole_0(f196(B),f197(B)). [resolve(4448,c,4443,b)]. 172.03/172.06 4449 -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | v6_ordinal1(f452(B)) | k1_xboole_0 = B # label(t176_orders_1) # label(axiom). [clausify(2250)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | r2_hidden(f187(f452(B)),f452(B)) | v1_relat_1(k3_tarski(f452(B))). [resolve(4449,d,4436,b)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | r2_hidden(f187(f452(B)),f452(B)) | v1_funct_1(k3_tarski(f452(B))). [resolve(4449,d,4437,b)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | r2_hidden(f187(f452(B)),f452(B)) | v5_ordinal1(k3_tarski(f452(B))). [resolve(4449,d,4438,b)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | -v1_funct_1(f187(f452(B))) | -v5_ordinal1(f187(f452(B))) | -v1_relat_1(f187(f452(B))) | v1_relat_1(k3_tarski(f452(B))). [resolve(4449,d,4439,d)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | -v1_funct_1(f187(f452(B))) | -v5_ordinal1(f187(f452(B))) | -v1_relat_1(f187(f452(B))) | v1_funct_1(k3_tarski(f452(B))). [resolve(4449,d,4440,d)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | -v1_funct_1(f187(f452(B))) | -v5_ordinal1(f187(f452(B))) | -v1_relat_1(f187(f452(B))) | v5_ordinal1(k3_tarski(f452(B))). [resolve(4449,d,4441,d)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | -r2_hidden(C,f452(B)) | -r2_hidden(D,f452(B)) | r3_xboole_0(C,D). [resolve(4449,d,4444,d)]. 172.03/172.06 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | -r2_hidden(C,f452(B)) | r1_tarski(f394(f452(B)),C) | k1_xboole_0 = f452(B) | -v1_finset_1(f452(B)). [resolve(4449,d,4445,c)]. 172.12/172.11 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | r2_hidden(f394(f452(B)),f452(B)) | k1_xboole_0 = f452(B) | -v1_finset_1(f452(B)). [resolve(4449,d,4446,b)]. 172.12/172.11 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | r2_hidden(f396(f452(B)),f452(B)) | k1_xboole_0 = f452(B) | -v1_finset_1(f452(B)). [resolve(4449,d,4447,b)]. 172.12/172.11 Derived: -r1_tarski(A,f451(B)) | A = f451(B) | -r2_hidden(A,B) | k1_xboole_0 = B | -r2_hidden(C,f452(B)) | r1_tarski(C,f396(f452(B))) | k1_xboole_0 = f452(B) | -v1_finset_1(f452(B)). [resolve(4449,d,4448,c)]. 172.12/172.11 4450 r2_hidden(f451(A),A) | v6_ordinal1(f452(A)) | k1_xboole_0 = A # label(t176_orders_1) # label(axiom). [clausify(2250)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | r2_hidden(f187(f452(A)),f452(A)) | v1_relat_1(k3_tarski(f452(A))). [resolve(4450,b,4436,b)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | r2_hidden(f187(f452(A)),f452(A)) | v1_funct_1(k3_tarski(f452(A))). [resolve(4450,b,4437,b)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | r2_hidden(f187(f452(A)),f452(A)) | v5_ordinal1(k3_tarski(f452(A))). [resolve(4450,b,4438,b)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | -v1_funct_1(f187(f452(A))) | -v5_ordinal1(f187(f452(A))) | -v1_relat_1(f187(f452(A))) | v1_relat_1(k3_tarski(f452(A))). [resolve(4450,b,4439,d)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | -v1_funct_1(f187(f452(A))) | -v5_ordinal1(f187(f452(A))) | -v1_relat_1(f187(f452(A))) | v1_funct_1(k3_tarski(f452(A))). [resolve(4450,b,4440,d)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | -v1_funct_1(f187(f452(A))) | -v5_ordinal1(f187(f452(A))) | -v1_relat_1(f187(f452(A))) | v5_ordinal1(k3_tarski(f452(A))). [resolve(4450,b,4441,d)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | -r2_hidden(B,f452(A)) | -r2_hidden(C,f452(A)) | r3_xboole_0(B,C). [resolve(4450,b,4444,d)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | -r2_hidden(B,f452(A)) | r1_tarski(f394(f452(A)),B) | k1_xboole_0 = f452(A) | -v1_finset_1(f452(A)). [resolve(4450,b,4445,c)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | r2_hidden(f394(f452(A)),f452(A)) | k1_xboole_0 = f452(A) | -v1_finset_1(f452(A)). [resolve(4450,b,4446,b)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | r2_hidden(f396(f452(A)),f452(A)) | k1_xboole_0 = f452(A) | -v1_finset_1(f452(A)). [resolve(4450,b,4447,b)]. 172.12/172.11 Derived: r2_hidden(f451(A),A) | k1_xboole_0 = A | -r2_hidden(B,f452(A)) | r1_tarski(B,f396(f452(A))) | k1_xboole_0 = f452(A) | -v1_finset_1(f452(A)). [resolve(4450,b,4448,c)]. 172.12/172.11 4451 k1_xboole_0 = A | r2_hidden(f456(A),A) | v6_ordinal1(f457(A)) # label(t177_orders_1) # label(axiom). [clausify(2268)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | r2_hidden(f187(f457(A)),f457(A)) | v1_relat_1(k3_tarski(f457(A))). [resolve(4451,c,4436,b)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | r2_hidden(f187(f457(A)),f457(A)) | v1_funct_1(k3_tarski(f457(A))). [resolve(4451,c,4437,b)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | r2_hidden(f187(f457(A)),f457(A)) | v5_ordinal1(k3_tarski(f457(A))). [resolve(4451,c,4438,b)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | -v1_funct_1(f187(f457(A))) | -v5_ordinal1(f187(f457(A))) | -v1_relat_1(f187(f457(A))) | v1_relat_1(k3_tarski(f457(A))). [resolve(4451,c,4439,d)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | -v1_funct_1(f187(f457(A))) | -v5_ordinal1(f187(f457(A))) | -v1_relat_1(f187(f457(A))) | v1_funct_1(k3_tarski(f457(A))). [resolve(4451,c,4440,d)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | -v1_funct_1(f187(f457(A))) | -v5_ordinal1(f187(f457(A))) | -v1_relat_1(f187(f457(A))) | v5_ordinal1(k3_tarski(f457(A))). [resolve(4451,c,4441,d)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | -r2_hidden(B,f457(A)) | -r2_hidden(C,f457(A)) | r3_xboole_0(B,C). [resolve(4451,c,4444,d)]. 172.12/172.11 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | -r2_hidden(B,f457(A)) | r1_tarski(f394(f457(A)),B) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4451,c,4445,c)]. 172.26/172.23 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | r2_hidden(f394(f457(A)),f457(A)) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4451,c,4446,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | r2_hidden(f396(f457(A)),f457(A)) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4451,c,4447,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | r2_hidden(f456(A),A) | -r2_hidden(B,f457(A)) | r1_tarski(B,f396(f457(A))) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4451,c,4448,c)]. 172.26/172.23 4452 k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | v6_ordinal1(f457(A)) # label(t177_orders_1) # label(axiom). [clausify(2268)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | r2_hidden(f187(f457(A)),f457(A)) | v1_relat_1(k3_tarski(f457(A))). [resolve(4452,e,4436,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | r2_hidden(f187(f457(A)),f457(A)) | v1_funct_1(k3_tarski(f457(A))). [resolve(4452,e,4437,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | r2_hidden(f187(f457(A)),f457(A)) | v5_ordinal1(k3_tarski(f457(A))). [resolve(4452,e,4438,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | -v1_funct_1(f187(f457(A))) | -v5_ordinal1(f187(f457(A))) | -v1_relat_1(f187(f457(A))) | v1_relat_1(k3_tarski(f457(A))). [resolve(4452,e,4439,d)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | -v1_funct_1(f187(f457(A))) | -v5_ordinal1(f187(f457(A))) | -v1_relat_1(f187(f457(A))) | v1_funct_1(k3_tarski(f457(A))). [resolve(4452,e,4440,d)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | -v1_funct_1(f187(f457(A))) | -v5_ordinal1(f187(f457(A))) | -v1_relat_1(f187(f457(A))) | v5_ordinal1(k3_tarski(f457(A))). [resolve(4452,e,4441,d)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | -r2_hidden(C,f457(A)) | -r2_hidden(D,f457(A)) | r3_xboole_0(C,D). [resolve(4452,e,4444,d)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | -r2_hidden(C,f457(A)) | r1_tarski(f394(f457(A)),C) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4452,e,4445,c)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | r2_hidden(f394(f457(A)),f457(A)) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4452,e,4446,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | r2_hidden(f396(f457(A)),f457(A)) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4452,e,4447,b)]. 172.26/172.23 Derived: k1_xboole_0 = A | -r2_hidden(B,A) | -r1_tarski(f456(A),B) | B = f456(A) | -r2_hidden(C,f457(A)) | r1_tarski(C,f396(f457(A))) | k1_xboole_0 = f457(A) | -v1_finset_1(f457(A)). [resolve(4452,e,4448,c)]. 172.26/172.23 4453 r2_hidden(f466(A),A) | v6_ordinal1(f467(A)) | k1_xboole_0 = A # label(t175_orders_1) # label(axiom). [clausify(2387)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | r2_hidden(f187(f467(A)),f467(A)) | v1_relat_1(k3_tarski(f467(A))). [resolve(4453,b,4436,b)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | r2_hidden(f187(f467(A)),f467(A)) | v1_funct_1(k3_tarski(f467(A))). [resolve(4453,b,4437,b)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | r2_hidden(f187(f467(A)),f467(A)) | v5_ordinal1(k3_tarski(f467(A))). [resolve(4453,b,4438,b)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | -v1_funct_1(f187(f467(A))) | -v5_ordinal1(f187(f467(A))) | -v1_relat_1(f187(f467(A))) | v1_relat_1(k3_tarski(f467(A))). [resolve(4453,b,4439,d)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | -v1_funct_1(f187(f467(A))) | -v5_ordinal1(f187(f467(A))) | -v1_relat_1(f187(f467(A))) | v1_funct_1(k3_tarski(f467(A))). [resolve(4453,b,4440,d)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | -v1_funct_1(f187(f467(A))) | -v5_ordinal1(f187(f467(A))) | -v1_relat_1(f187(f467(A))) | v5_ordinal1(k3_tarski(f467(A))). [resolve(4453,b,4441,d)]. 172.26/172.23 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | -r2_hidden(B,f467(A)) | -r2_hidden(C,f467(A)) | r3_xboole_0(B,C). [resolve(4453,b,4444,d)]. 172.26/172.27 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | -r2_hidden(B,f467(A)) | r1_tarski(f394(f467(A)),B) | k1_xboole_0 = f467(A) | -v1_finset_1(f467(A)). [resolve(4453,b,4445,c)]. 172.26/172.27 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | r2_hidden(f394(f467(A)),f467(A)) | k1_xboole_0 = f467(A) | -v1_finset_1(f467(A)). [resolve(4453,b,4446,b)]. 172.26/172.27 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | r2_hidden(f396(f467(A)),f467(A)) | k1_xboole_0 = f467(A) | -v1_finset_1(f467(A)). [resolve(4453,b,4447,b)]. 172.26/172.27 Derived: r2_hidden(f466(A),A) | k1_xboole_0 = A | -r2_hidden(B,f467(A)) | r1_tarski(B,f396(f467(A))) | k1_xboole_0 = f467(A) | -v1_finset_1(f467(A)). [resolve(4453,b,4448,c)]. 172.26/172.27 4454 -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | v6_ordinal1(f467(B)) | k1_xboole_0 = B # label(t175_orders_1) # label(axiom). [clausify(2387)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | r2_hidden(f187(f467(B)),f467(B)) | v1_relat_1(k3_tarski(f467(B))). [resolve(4454,d,4436,b)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | r2_hidden(f187(f467(B)),f467(B)) | v1_funct_1(k3_tarski(f467(B))). [resolve(4454,d,4437,b)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | r2_hidden(f187(f467(B)),f467(B)) | v5_ordinal1(k3_tarski(f467(B))). [resolve(4454,d,4438,b)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | -v1_funct_1(f187(f467(B))) | -v5_ordinal1(f187(f467(B))) | -v1_relat_1(f187(f467(B))) | v1_relat_1(k3_tarski(f467(B))). [resolve(4454,d,4439,d)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | -v1_funct_1(f187(f467(B))) | -v5_ordinal1(f187(f467(B))) | -v1_relat_1(f187(f467(B))) | v1_funct_1(k3_tarski(f467(B))). [resolve(4454,d,4440,d)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | -v1_funct_1(f187(f467(B))) | -v5_ordinal1(f187(f467(B))) | -v1_relat_1(f187(f467(B))) | v5_ordinal1(k3_tarski(f467(B))). [resolve(4454,d,4441,d)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | -r2_hidden(C,f467(B)) | -r2_hidden(D,f467(B)) | r3_xboole_0(C,D). [resolve(4454,d,4444,d)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | -r2_hidden(C,f467(B)) | r1_tarski(f394(f467(B)),C) | k1_xboole_0 = f467(B) | -v1_finset_1(f467(B)). [resolve(4454,d,4445,c)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | r2_hidden(f394(f467(B)),f467(B)) | k1_xboole_0 = f467(B) | -v1_finset_1(f467(B)). [resolve(4454,d,4446,b)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | r2_hidden(f396(f467(B)),f467(B)) | k1_xboole_0 = f467(B) | -v1_finset_1(f467(B)). [resolve(4454,d,4447,b)]. 172.26/172.27 Derived: -r2_hidden(A,B) | -r1_tarski(f466(B),A) | A = f466(B) | k1_xboole_0 = B | -r2_hidden(C,f467(B)) | r1_tarski(C,f396(f467(B))) | k1_xboole_0 = f467(B) | -v1_finset_1(f467(B)). [resolve(4454,d,4448,c)]. 172.26/172.27 4455 k1_xboole_0 = A | r2_hidden(f472(A),A) | v6_ordinal1(f473(A)) # label(t178_orders_1) # label(axiom). [clausify(2389)]. 172.26/172.27 Derived: k1_xboole_0 = A | r2_hidden(f472(A),A) | r2_hidden(f187(f473(A)),f473(A)) | v1_relat_1(k3_tarski(f473(A))). [resolve(4455,c,4436,b)]. 172.26/172.27 Derived: k1_xboole_0 = A | r2_hidden(f472(A),A) | r2_hidden(f187(f473(A)),f473(A)) | v1_funct_1(k3_tarski(f473(A))). [resolve(4455,c,4437,b)]. 172.26/172.27 Derived: k1_xboole_0 = A | r2_hidden(f472(A),A) | r2_hidden(f187(f473(A)),f473(A)) | v5_ordinal1(k3_tarski(f473(A))). [resolve(4455,c,4438,b)]. 172.26/172.27 Derived: k1_xboole_0 = A | r2_hidden(f472(A),A) | -v1_funct_1(f187(f473(A))) | -v5_ordinal1(f187(f473(A))) | -v1_relat_1(f187(f473(A))) | v1_relat_1(k3_tarski(f473(A))). [resolve(4455,c,4439,d)]. 172.26/172.27 Derived: k1_xboole_0 = A | r2_hidden(f472(A),A) | -v1_funct_1(f187(f473(A))) | -v5_ordinal1(f187(f473(A))) | -v1_relat_1(f187(f473(A))) | v1_funct_1(k3_tarski(f473(A))). [resolve(4455,c,4Alarm clock 180.09/180.05 Prover9 interrupted 180.09/180.05 EOF